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2025 · practice · Physical Sciences — Physics · Grade 11

Grade 11 Physics — North West momentum & circuits

Notes

Answer all questions. Show a formula, substitution and a boxed answer with units. g = 9.8 m·s⁻². Calculators allowed.

90 min · 106 Marks · 30 questions

Learn the paper in the app: notes, a marks breakdown, the formula you need, and the board working. You do not need to download it.

Question breakdown

  1. 1.1 · 8 Marks

    m=0.2 kg, v=10 ms. p?

    Notes: m=0.2 kg. v=10 ms.

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: m=0.2 kg, v=10 ms. p?

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 0.2 kg · 10 ms. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: p. Circle that word — that is the missing variable.

    Find

    We are required to find: p. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    Write p = 2 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives p.

    In other words — as if you have never seen this before

    p=mv.

    2. What do we already know?

    m=0.2 kg. v=10 ms.

    3. Which method — and why this one?

    p=mv.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 0.2 kg · 10 ms. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: p. Circle that word — that is the missing variable. Find: We are required to find: p. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: Write p = 2 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives p.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      m=0.2 kg. v=10 ms.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      p=mv.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Multiply

      p=0.2×10=2 kg·ms.

      p=2

      Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      2 kg·ms

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    2 kg·ms

    Copy onto your answer sheet — in this order

    Formula: p=2

    Answer: 2 kg·ms

    6. Check it like a marker

    A cricket ball order of magnitude. Sensible.

    7. A trap first-timers fall into

    mv is not momentum.

  2. 1.2 · 10 Marks

    Series current through 2 Ω then 3 Ω on 10 V

    Notes: Series 2 Ω + 3 Ω. V = 10 V. Same current through both.

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Series current through 2 Ω then 3 Ω on 10 V

    In other words — as if you have never seen this before

    R=5 Ω. I=VR=2 A.

    2. What do we already know?

    Series 2 Ω + 3 Ω. V = 10 V. Same current through both.

    3. Which method — and why this one?

    R=5 Ω. I=VR=2 A.

    4. Step-by-step working

    1. 01 / 05

      Add series

      R=5 Ω.

      R=5 Ω

      Why this step: One job per line so you can find a slip, and so a marker can follow the marks.

    2. 02 / 05

      Ohm

      I=105=2 A.

      I=2 A

      Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.

    3. 03 / 05

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    4. 04 / 05

      Step F — Box the answer with its unit

      2 A

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    5. 05 / 05

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    2 A

    Copy onto your answer sheet — in this order

    Formula: R=5 Ω

    Answer: 2 A

    6. Check it like a marker

    2 V on 2 Ω plus 6 V on 3 Ω = 8 V… wait 2×2=4 V and 2×3=6 V = 10 V. Yes.

    7. A trap first-timers fall into

    Using one resistor only (10/2=5 A) ignores the other.

  3. 2.1 · 10 Marks

    Free fall from rest, t=2 s, g=10. v?

    Notes: u=0. a=g=10 down. t=2 s.

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Free fall from rest, t=2 s, g=10. v?

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 2 s · 10. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: v. Circle that word — that is the missing variable.

    Find

    We are required to find: v. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    Write 20 ms with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives v.

    In other words — as if you have never seen this before

    v=u+at=10×2=20 ms down.

    2. What do we already know?

    u=0. a=g=10 down. t=2 s.

    3. Which method — and why this one?

    v=u+at=10×2=20 ms down.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 2 s · 10. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: v. Circle that word — that is the missing variable. Find: We are required to find: v. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: Write 20 ms with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives v.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      u=0. a=g=10 down. t=2 s.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      v=u+at=10×2=20 ms down.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      v = u + at

      v=0+10×2=20 ms.

      20 ms

      Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      20 ms

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    20 ms

    Copy onto your answer sheet — in this order

    Formula: 20 ms

    Answer: 20 ms

    6. Check it like a marker

    Δx = ½gt² = 20 m. A 2-second drop from rest is about two storeys. Sensible.

    7. A trap first-timers fall into

    v = gt is not a formula on the sheet.

  4. 2.2 · 12 Marks

    Efficiency = usefulinput. Useful 80 J, input 100 J

    Notes: Useful energy 80 J. Input 100 J.

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Efficiency = usefulinput. Useful 80 J, input 100 J

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 80 J · 100 J. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Useful 80 J, input 100 J. Circle that word — that is the missing variable.

    Find

    We are required to find: Useful 80 J, input 100 J. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    Write 80% with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Useful 80 J, input 100 J.

    In other words — as if you have never seen this before

    Efficiency = (useful / input) × 100%.

    2. What do we already know?

    Useful energy 80 J. Input 100 J.

    3. Which method — and why this one?

    Efficiency = (useful / input) × 100%.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 80 J · 100 J. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Useful 80 J, input 100 J. Circle that word — that is the missing variable. Find: We are required to find: Useful 80 J, input 100 J. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: Write 80% with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Useful 80 J, input 100 J.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Useful energy 80 J. Input 100 J.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      Efficiency = (useful / input) × 100%.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Divide then percent

      80100=0.8=80%.

      80%

      Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      80%

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    80%

    Copy onto your answer sheet — in this order

    Formula: 80%

    Answer: 80%

    6. Check it like a marker

    20 J was wasted. 80+20=100.

    7. A trap first-timers fall into

    Writing 80 without % loses the unit the memo wants.

  5. 5 · 3 Marks

    F=IℓB at 90°, I=4 A, ℓ=0.25 m, B=0.5 T. F=

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: F = IℓB at 90°, I=4 A, ℓ=0.25 m, B=0.5 T. F=

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 90° · 4 A · 0.25 m · 0.5 T. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: F=. Circle that word — that is the missing variable.

    Find

    We are required to find: F=. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: 0. Then substitute the given, one line at a time, to get F=.

    In other words — as if you have never seen this before

    0.5 N

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 90° · 4 A · 0.25 m · 0.5 T. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    0.5 N

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 90° · 4 A · 0.25 m · 0.5 T. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: F=. Circle that word — that is the missing variable. Find: We are required to find: F=. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 0. Then substitute the given, one line at a time, to get F=.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 90° · 4 A · 0.25 m · 0.5 T. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      0.5 N

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Reason

      4×0.25×0.5=0.5 N.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      0.5 N

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    0.5 N

    Copy onto your answer sheet — in this order

    Answer: 0.5 N

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  6. 6 · 4 Marks · Friction

    N = 100 N, μ_s = 0.4. Max static friction is

    NWFf

    Formulas

    fs ≤ μs N

    Static friction (maximum at the point of slipping)

    fk=μk N

    Kinetic friction

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: N = 100 N, μ_s = 0.4. Max static friction is

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 100 N · 0.4. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Max static friction is. Circle that word — that is the missing variable.

    Find

    We are required to find: Max static friction is. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: f_s(max) = μ_s N = 40 N. Then substitute the given, one line at a time, to get Max static friction is.

    In other words — as if you have never seen this before

    fs(max)=μs N=40 N.

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 100 N · 0.4. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    fs(max)=μs N=40 N.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 100 N · 0.4. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Max static friction is. Circle that word — that is the missing variable. Find: We are required to find: Max static friction is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: f_s(max) = μ_s N = 40 N. Then substitute the given, one line at a time, to get Max static friction is.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 100 N · 0.4. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      fs(max)=μs N=40 N.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      fs(max)=μs N=40 N.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      40 N

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    40 N

    Copy onto your answer sheet — in this order

    Answer: 40 N

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  7. 7 · 2 Marks

    n=1.5 into air. sin c=

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: n = 1.5 into air. sin c =

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 1.5 into. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin c =. Circle that word — that is the missing variable.

    Find

    We are required to find: sin c =. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: sin c = n₂/n₁ = 11. Then substitute the given, one line at a time, to get sin c =.

    In other words — as if you have never seen this before

    sin c=n₂n₁=11.5.

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 1.5 into. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    sin c=n₂n₁=11.5.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 1.5 into. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin c =. Circle that word — that is the missing variable. Find: We are required to find: sin c =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: sin c = n₂/n₁ = 11. Then substitute the given, one line at a time, to get sin c =.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 1.5 into. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      sin c=n₂n₁=11.5.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      sin c=n₂n₁=11.5.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      11.5

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    11.5

    Copy onto your answer sheet — in this order

    Answer: 11.5

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  8. 8 · 2 Marks · Friction

    m = 4 kg. Horizontal F = 20 N, friction 4 N. a?

    NWFf

    Formulas

    fs ≤ μs N

    Static friction (maximum at the point of slipping)

    fk=μk N

    Kinetic friction

    Notes: m = 4 kg. Applied 20 N. Friction 4 N opposite. Unknown: a.

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: m = 4 kg. Horizontal F = 20 N, friction 4 N. a?

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 4 kg · 20 N · 4 N. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: a. Circle that word — that is the missing variable.

    Find

    We are required to find: a. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    Write F_net = 16 N with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives a.

    In other words — as if you have never seen this before

    F_net = applied − friction, then a = Fnetm. Draw arrows first.

    2. What do we already know?

    m = 4 kg. Applied 20 N. Friction 4 N opposite. Unknown: a.

    3. Which method — and why this one?

    F_net = applied − friction, then a = Fnetm. Draw arrows first.

    4. Step-by-step working

    1. 01 / 05

      Net force

      Fnet=20−4=16 N forwards.

      Fnet=16 N

      Why this step: One job per line so you can find a slip, and so a marker can follow the marks.

    2. 02 / 05

      Newton 2

      a=Fnetm=164=4 m·s⁻².

      a=4 ms²

      Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.

    3. 03 / 05

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    4. 04 / 05

      Step F — Box the answer with its unit

      4 ms²

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    5. 05 / 05

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    4 ms²

    Copy onto your answer sheet — in this order

    Formula: Fnet=16 N

    Answer: 4 ms²

    6. Check it like a marker

    16 N on 4 kg really is 4 m·s⁻². Units: Nkg=m·s⁻².

    7. A trap first-timers fall into

    Using 204=5 ignores friction. The paper gave 4 N for a reason.

  9. 9 · 2 Marks · Longitudinal waves & sound

    Sound is fastest in

    λA

    Formulas

    v=f λ

    Sound is a wave

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Sound is fastest in

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Sound is fastest in. Circle that word — that is the missing variable.

    Find

    We are required to find: Sound is fastest in. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: steel. Then substitute the given, one line at a time, to get Sound is fastest in.

    In other words — as if you have never seen this before

    steel

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    steel

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Sound is fastest in. Circle that word — that is the missing variable. Find: We are required to find: Sound is fastest in. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: steel. Then substitute the given, one line at a time, to get Sound is fastest in.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      steel

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      Particles that are tightly packed pass a longitudinal wave faster. Steel beats air; vacuum cannot carry sound.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      steel

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    steel

    Copy onto your answer sheet — in this order

    Answer: steel

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  10. 10 · 4 Marks · Friction

    A 5 kg box on a frictionless 30° slope. Component down the slope? (g=9.8)

    NWFf

    Formulas

    fs ≤ μs N

    Static friction (maximum at the point of slipping)

    fk=μk N

    Kinetic friction

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A 5 kg box on a frictionless 30° slope. Component down the slope? (g=9.8)

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 5 kg · 30° · 9.8. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: 8). Circle that word — that is the missing variable.

    Find

    We are required to find: 8). Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: mg sin30 = 49 × 0. Then substitute the given, one line at a time, to get 8).

    In other words — as if you have never seen this before

    mg sin30=49×0.5=24.5 N.

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 5 kg · 30° · 9.8. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    mg sin30=49×0.5=24.5 N.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 5 kg · 30° · 9.8. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 8). Circle that word — that is the missing variable. Find: We are required to find: 8). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: mg sin30 = 49 × 0. Then substitute the given, one line at a time, to get 8).

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 5 kg · 30° · 9.8. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      mg sin30=49×0.5=24.5 N.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      mg sin30=49×0.5=24.5 N.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      24.5 N

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    24.5 N

    Copy onto your answer sheet — in this order

    Answer: 24.5 N

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  11. 11 · 3 Marks

    n=1.5, nair=1. sin c=

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: n=1.5, n_air=1. sin c =

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 1.5 · 1. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin c =. Circle that word — that is the missing variable.

    Find

    We are required to find: sin c =. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: 23. Then substitute the given, one line at a time, to get sin c =.

    In other words — as if you have never seen this before

    23

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 1.5 · 1. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    23

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 1.5 · 1. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin c =. Circle that word — that is the missing variable. Find: We are required to find: sin c =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 23. Then substitute the given, one line at a time, to get sin c =.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 1.5 · 1. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      23

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Reason

      sin c=11.5.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      23

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    23

    Copy onto your answer sheet — in this order

    Answer: 23

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  12. 12 · 2 Marks

    G in F=Gm₁m₂/r² is

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: G in F=Gm₁m₂/r² is

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: G in F=Gm₁m₂/r² is. Circle that word — that is the missing variable.

    Find

    We are required to find: G in F=Gm₁m₂/r² is. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: G = 6. Then substitute the given, one line at a time, to get G in F=Gm₁m₂/r² is.

    In other words — as if you have never seen this before

    G=6.67×10⁻¹¹ N·m²·kg⁻².

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    G=6.67×10⁻¹¹ N·m²·kg⁻².

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: G in F=Gm₁m₂/r² is. Circle that word — that is the missing variable. Find: We are required to find: G in F=Gm₁m₂/r² is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: G = 6. Then substitute the given, one line at a time, to get G in F=Gm₁m₂/r² is.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      G=6.67×10⁻¹¹ N·m²·kg⁻².

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      G=6.67×10⁻¹¹ N·m²·kg⁻².

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      universal gravitational constant

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    universal gravitational constant

    Copy onto your answer sheet — in this order

    Answer: universal gravitational constant

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  13. 13 · 2 Marks · Longitudinal waves & sound

    Sound needs

    λA

    Formulas

    v=f λ

    Sound is a wave

    Notes: Sound needs

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Sound needs

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Sound needs. Circle that word — that is the missing variable.

    Find

    We are required to find: Sound needs. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: Sound is a mechanical wave. Then substitute the given, one line at a time, to get Sound needs.

    In other words — as if you have never seen this before

    Sound is a mechanical wave. It cannot travel in a vacuum.

    2. What do we already know?

    Sound needs

    3. Which method — and why this one?

    Sound is a mechanical wave. It cannot travel in a vacuum.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Sound needs. Circle that word — that is the missing variable. Find: We are required to find: Sound needs. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Sound is a mechanical wave. Then substitute the given, one line at a time, to get Sound needs.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Sound needs

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      Sound is a mechanical wave. It cannot travel in a vacuum.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      Sound is a mechanical wave. It cannot travel in a vacuum.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      a medium

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    a medium

    Copy onto your answer sheet — in this order

    Answer: a medium

    6. Check it like a marker

    Sound is a mechanical wave. It cannot travel in a vacuum.

    7. A trap first-timers fall into

    a vacuum

  14. 14 · 2 Marks

    A 1.5 kW heater runs for 4 h. Energy used?

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A 1.5 kW heater runs for 4 h. Energy used?

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 1.5 kW · 4 h. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Energy used. Circle that word — that is the missing variable.

    Find

    We are required to find: Energy used. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: W = Pt = 1. Then substitute the given, one line at a time, to get Energy used.

    In other words — as if you have never seen this before

    W=Pt=1.5 kW×4 h=6 kWh (= 2.16 × 10⁷ J).

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 1.5 kW · 4 h. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    W=Pt=1.5 kW×4 h=6 kWh (= 2.16 × 10⁷ J).

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 1.5 kW · 4 h. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Energy used. Circle that word — that is the missing variable. Find: We are required to find: Energy used. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: W = Pt = 1. Then substitute the given, one line at a time, to get Energy used.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 1.5 kW · 4 h. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      W=Pt=1.5 kW×4 h=6 kWh (= 2.16 × 10⁷ J).

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      W=Pt=1.5 kW×4 h=6 kWh (= 2.16 × 10⁷ J).

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      6 kWh

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    6 kWh

    Copy onto your answer sheet — in this order

    Answer: 6 kWh

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  15. 15 · 2 Marks

    Between parallel plates 200 V apart 0.05 m. E =

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Between parallel plates 200 V apart 0.05 m. E =

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 200 V · 0.05 m. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: E =. Circle that word — that is the missing variable.

    Find

    We are required to find: E =. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: E=Vd=2000. Then substitute the given, one line at a time, to get E =.

    In other words — as if you have never seen this before

    E=Vd=2000.05=4000.

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 200 V · 0.05 m. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    E=Vd=2000.05=4000.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 200 V · 0.05 m. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: E =. Circle that word — that is the missing variable. Find: We are required to find: E =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: E=Vd=2000. Then substitute the given, one line at a time, to get E =.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 200 V · 0.05 m. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      E=Vd=2000.05=4000.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      E=Vd=2000.05=4000.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      4000 N·C⁻¹

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    4000 N·C⁻¹

    Copy onto your answer sheet — in this order

    Answer: 4000 N·C⁻¹

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  16. 16 · 2 Marks

    A 10 N force at 0° to x-axis. F_x =

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A 10 N force at 0° to x-axis. F_x =

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 10 N · 0°. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: F_x =. Circle that word — that is the missing variable.

    Find

    We are required to find: F_x =. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: cos 0° = 1, so F_x = 10 N. Then substitute the given, one line at a time, to get F_x =.

    In other words — as if you have never seen this before

    cos 0°=1, so Fx=10 N.

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 10 N · 0°. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    cos 0°=1, so Fx=10 N.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 10 N · 0°. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: F_x =. Circle that word — that is the missing variable. Find: We are required to find: F_x =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: cos 0° = 1, so F_x = 10 N. Then substitute the given, one line at a time, to get F_x =.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 10 N · 0°. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      cos 0°=1, so Fx=10 N.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      cos 0°=1, so Fx=10 N.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      10 N

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    10 N

    Copy onto your answer sheet — in this order

    Answer: 10 N

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  17. 17 · 4 Marks · Longitudinal waves & sound

    Particles in a sound wave vibrate

    λA

    Formulas

    v=f λ

    Sound is a wave

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Particles in a sound wave vibrate

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Particles in a sound wave vibrate. Circle that word — that is the missing variable.

    Find

    We are required to find: Particles in a sound wave vibrate. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: Longitudinal. Then substitute the given, one line at a time, to get Particles in a sound wave vibrate.

    In other words — as if you have never seen this before

    Longitudinal.

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    Longitudinal.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Particles in a sound wave vibrate. Circle that word — that is the missing variable. Find: We are required to find: Particles in a sound wave vibrate. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Longitudinal. Then substitute the given, one line at a time, to get Particles in a sound wave vibrate.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      Longitudinal.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      Longitudinal.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      parallel to the direction of travel

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    parallel to the direction of travel

    Copy onto your answer sheet — in this order

    Answer: parallel to the direction of travel

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  18. 18 · 2 Marks

    T=0.02 s. Frequency f?

    Notes: Period T = 0.02 s. Unknown: f.

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: T = 0.02 s. Frequency f?

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 0.02 s. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Frequency f. Circle that word — that is the missing variable.

    Find

    We are required to find: Frequency f. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    Write f = 50 Hz with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Frequency f.

    In other words — as if you have never seen this before

    f = 1T. Frequency is how many cycles in one second.

    2. What do we already know?

    Period T = 0.02 s. Unknown: f.

    3. Which method — and why this one?

    f = 1T. Frequency is how many cycles in one second.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 0.02 s. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Frequency f. Circle that word — that is the missing variable. Find: We are required to find: Frequency f. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: Write f = 50 Hz with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Frequency f.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Period T = 0.02 s. Unknown: f.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      f = 1T. Frequency is how many cycles in one second.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Write f = 1/T

      f=10.02=50 Hz.

      f=50 Hz

      Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      50 Hz

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    50 Hz

    Copy onto your answer sheet — in this order

    Formula: f=50 Hz

    Answer: 50 Hz

    6. Check it like a marker

    50 cycles × 0.02 s = 1 s. Consistent.

    7. A trap first-timers fall into

    Leaving f = 0.02 treats period as frequency.

  19. 19 · 3 Marks

    F=IℓB at 90°, I=5 A, ℓ=0.2 m, B=0.4 T

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: F = IℓB at 90°, I = 5 A, ℓ = 0.2 m, B = 0.4 T

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 90° · 5 A · 0.2 m · 0.4 T. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: 4 T. Circle that word — that is the missing variable.

    Find

    We are required to find: 4 T. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: 0. Then substitute the given, one line at a time, to get 4 T.

    In other words — as if you have never seen this before

    0.4 N

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 90° · 5 A · 0.2 m · 0.4 T. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    0.4 N

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 90° · 5 A · 0.2 m · 0.4 T. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 4 T. Circle that word — that is the missing variable. Find: We are required to find: 4 T. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 0. Then substitute the given, one line at a time, to get 4 T.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 90° · 5 A · 0.2 m · 0.4 T. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      0.4 N

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      5 × 0.2 × 0.4 × sin 90° = 0.4 N. sin 90° = 1, so just multiply the three numbers.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      0.4 N

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    0.4 N

    Copy onto your answer sheet — in this order

    Answer: 0.4 N

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  20. 20 · 3 Marks · Longitudinal waves & sound

    Sound cannot travel through

    λA

    Formulas

    v=f λ

    Sound is a wave

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Sound cannot travel through

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Sound cannot travel through. Circle that word — that is the missing variable.

    Find

    We are required to find: Sound cannot travel through. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: vacuum. Then substitute the given, one line at a time, to get Sound cannot travel through.

    In other words — as if you have never seen this before

    vacuum

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    vacuum

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Sound cannot travel through. Circle that word — that is the missing variable. Find: We are required to find: Sound cannot travel through. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: vacuum. Then substitute the given, one line at a time, to get Sound cannot travel through.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      vacuum

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Reason

      Needs a medium.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      vacuum

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    vacuum

    Copy onto your answer sheet — in this order

    Answer: vacuum

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  21. 21 · 2 Marks · Refraction & TIR

    n = cv. If n=1.33, light in the medium is

    ir

    Formulas

    n₁ sinθ₁=n₂ sinθ₂

    Snell’s law

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: n = cv. If n=1.33, light in the medium is

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 1.33. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: 33, light in the medium is. Circle that word — that is the missing variable.

    Find

    We are required to find: 33, light in the medium is. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: v=cn. Then substitute the given, one line at a time, to get 33, light in the medium is.

    In other words — as if you have never seen this before

    v=cn.

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 1.33. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    v=cn.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 1.33. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 33, light in the medium is. Circle that word — that is the missing variable. Find: We are required to find: 33, light in the medium is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: v=cn. Then substitute the given, one line at a time, to get 33, light in the medium is.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 1.33. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      v=cn.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      v=cn.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      slower than in vacuum

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    slower than in vacuum

    Copy onto your answer sheet — in this order

    Answer: slower than in vacuum

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  22. 22 · 2 Marks

    p=8 kg·ms, m=2 kg. Speed v?

    Notes: p=8 kg·ms. m=2 kg. Unknown: v.

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: p = 8 kg·ms, m = 2 kg. Speed v?

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 8 kg·ms · 2 kg. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Speed v. Circle that word — that is the missing variable.

    Find

    We are required to find: Speed v. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    Write v = pm with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Speed v.

    In other words — as if you have never seen this before

    Momentum p=mv so v=pm.

    2. What do we already know?

    p=8 kg·ms. m=2 kg. Unknown: v.

    3. Which method — and why this one?

    Momentum p=mv so v=pm.

    4. Step-by-step working

    1. 01 / 05

      Write the definition

      p=m v→v=pm.

      v=pm

      Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.

    2. 02 / 05

      Substitute

      v=82=4 m·s⁻¹.

      v=4 ms

      Why this step: One job per line so you can find a slip, and so a marker can follow the marks.

    3. 03 / 05

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    4. 04 / 05

      Step F — Box the answer with its unit

      4 ms

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    5. 05 / 05

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    4 ms

    Copy onto your answer sheet — in this order

    Formula: v=pm

    Answer: 4 ms

    6. Check it like a marker

    p = 2 × 4 = 8. Recovers the given momentum.

    7. A trap first-timers fall into

    Do not multiply 8 × 2. That inflates momentum, it does not find speed.

  23. 23 · 2 Marks

    K=½mv². m=2 kg, v=4 ms. K?

    Notes: m = 2 kg. v = 4 ms. Unknown: kinetic energy.

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: K = ½mv². m=2 kg, v=4 ms. K?

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 2 kg · 4 ms. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: K. Circle that word — that is the missing variable.

    Find

    We are required to find: K. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    Write v² = 16 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives K.

    In other words — as if you have never seen this before

    K = ½ m v². Square v first, then multiply.

    2. What do we already know?

    m = 2 kg. v = 4 ms. Unknown: kinetic energy.

    3. Which method — and why this one?

    K = ½ m v². Square v first, then multiply.

    4. Step-by-step working

    1. 01 / 05

      Square v

      v²=16.

      v²=16

      Why this step: One job per line so you can find a slip, and so a marker can follow the marks.

    2. 02 / 05

      Substitute

      K=½×2×16=16 J.

      K=16 J

      Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.

    3. 03 / 05

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    4. 04 / 05

      Step F — Box the answer with its unit

      16 J

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    5. 05 / 05

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    16 J

    Copy onto your answer sheet — in this order

    Formula: v²=16

    Answer: 16 J

    6. Check it like a marker

    ½×2=1, then×16=16. Units kg·m²s²=J.

    7. A trap first-timers fall into

    ½×2×4 = 4 forgets to square v. The ² is not decoration.

  24. 24 · 2 Marks

    F=IℓB at 90°. I=3 A, ℓ=0.5 m, B=0.4 T. F=

    Notes: F=IℓB at 90°. I=3 A, ℓ=0.5 m, B=0.4 T. F=

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: F = IℓB at 90°. I = 3 A, ℓ = 0.5 m, B = 0.4 T. F =

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 90° · 3 A · 0.5 m · 0.4 T. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: F =. Circle that word — that is the missing variable.

    Find

    We are required to find: F =. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: F = 3 × 0. Then substitute the given, one line at a time, to get F =.

    In other words — as if you have never seen this before

    F=3×0.5×0.4=0.6 N.

    2. What do we already know?

    F=IℓB at 90°. I=3 A, ℓ=0.5 m, B=0.4 T. F=

    3. Which method — and why this one?

    F=3×0.5×0.4=0.6 N.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 90° · 3 A · 0.5 m · 0.4 T. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: F =. Circle that word — that is the missing variable. Find: We are required to find: F =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: F = 3 × 0. Then substitute the given, one line at a time, to get F =.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      F=IℓB at 90°. I=3 A, ℓ=0.5 m, B=0.4 T. F=

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      F=3×0.5×0.4=0.6 N.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      F=3×0.5×0.4=0.6 N.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      0.6 N

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    0.6 N

    Copy onto your answer sheet — in this order

    Answer: 0.6 N

    6. Check it like a marker

    F=3×0.5×0.4=0.6 N.

    7. A trap first-timers fall into

    6 N

  25. 25 · 2 Marks

    A 12 V battery is connected across a 4.0 Ω resistor. I =

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A 12 V battery is connected across a 4.0 Ω resistor. I =

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 12 V · 4.0 Ω. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: I =. Circle that word — that is the missing variable.

    Find

    We are required to find: I =. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: 3. Then substitute the given, one line at a time, to get I =.

    In other words — as if you have never seen this before

    3.0 A

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 12 V · 4.0 Ω. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    3.0 A

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 12 V · 4.0 Ω. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: I =. Circle that word — that is the missing variable. Find: We are required to find: I =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 3. Then substitute the given, one line at a time, to get I =.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 12 V · 4.0 Ω. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      3.0 A

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      Ohm’s law: I = VR=124.0=3.0 A. 48 A multiplies instead of dividing; 0.33 A divides the wrong way.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      3.0 A

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    3.0 A

    Copy onto your answer sheet — in this order

    Answer: 3.0 A

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  26. 26 · 2 Marks

    A wave: f=50 Hz, λ=2 m. Speed v?

    Notes: f=50 Hz. λ=2 m. Unknown: wave speed v.

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A wave: f = 50 Hz, λ = 2 m. Speed v?

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 50 Hz · 2 m. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: Speed v. Circle that word — that is the missing variable.

    Find

    We are required to find: Speed v. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    Write v = fλ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Speed v.

    In other words — as if you have never seen this before

    v = f λ. Frequency times wavelength. Do not divide.

    2. What do we already know?

    f=50 Hz. λ=2 m. Unknown: wave speed v.

    3. Which method — and why this one?

    v = f λ. Frequency times wavelength. Do not divide.

    4. Step-by-step working

    1. 01 / 05

      Write the wave equation

      v=f λ.

      v=fλ

      Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.

    2. 02 / 05

      Substitute

      v=50×2=100 m·s⁻¹.

      v=100 ms

      Why this step: One job per line so you can find a slip, and so a marker can follow the marks.

    3. 03 / 05

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    4. 04 / 05

      Step F — Box the answer with its unit

      100 ms

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    5. 05 / 05

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    100 ms

    Copy onto your answer sheet — in this order

    Formula: v=fλ

    Answer: 100 ms

    6. Check it like a marker

    T = 1f=0.02 s. In 0.02 s the wave travels 100×0.02 = 2 m = λ. Consistent.

    7. A trap first-timers fall into

    v = f/λ = 25 would be wrong. Speed is product, not quotient.

  27. 27 · 4 Marks · Electric fields

    Field lines of an isolated positive charge

    +−F

    Formulas

    E=Fq

    Field definition

    E=Vd

    Uniform field between plates

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Field lines of an isolated positive charge

    In other words — as if you have never seen this before

    Start on + end on −.

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    Start on + end on −.

    4. Step-by-step working

    1. 01 / 07

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 07

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    3. 03 / 07

      Step C — Name the method in words

      Start on + end on −.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    4. 04 / 07

      Working

      Start on + end on −.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    5. 05 / 07

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    6. 06 / 07

      Step F — Box the answer with its unit

      radiate outward

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    7. 07 / 07

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    radiate outward

    Copy onto your answer sheet — in this order

    Answer: radiate outward

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  28. 28 · 3 Marks

    ε=6 V, r=0.5 Ω, R=2.5 Ω. I=

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: ε=6 V, r=0.5 Ω, R=2.5 Ω. I=

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 6 V · 0.5 Ω · 2.5 Ω. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: I=. Circle that word — that is the missing variable.

    Find

    We are required to find: I=. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: 2 A. Then substitute the given, one line at a time, to get I=.

    In other words — as if you have never seen this before

    2 A

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 6 V · 0.5 Ω · 2.5 Ω. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    2 A

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 6 V · 0.5 Ω · 2.5 Ω. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: I=. Circle that word — that is the missing variable. Find: We are required to find: I=. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 2 A. Then substitute the given, one line at a time, to get I=.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 6 V · 0.5 Ω · 2.5 Ω. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      2 A

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Reason

      I=63=2.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      2 A

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    2 A

    Copy onto your answer sheet — in this order

    Answer: 2 A

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  29. 29 · 3 Marks · Electric fields

    F on 2 A in 0.5 m at 90° in 0.4 T field?

    +−F

    Formulas

    E=Fq

    Field definition

    E=Vd

    Uniform field between plates

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: F on 2 A in 0.5 m at 90° in 0.4 T field?

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 2 A · 0.5 m · 90° · 0.4 T. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: 4 T field. Circle that word — that is the missing variable.

    Find

    We are required to find: 4 T field. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: F = IℓB sin90 = 2×0. Then substitute the given, one line at a time, to get 4 T field.

    In other words — as if you have never seen this before

    F=IℓB sin90=2×0.5×0.4=0.4 N.

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 2 A · 0.5 m · 90° · 0.4 T. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    F=IℓB sin90=2×0.5×0.4=0.4 N.

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 2 A · 0.5 m · 90° · 0.4 T. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 4 T field. Circle that word — that is the missing variable. Find: We are required to find: 4 T field. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: F = IℓB sin90 = 2×0. Then substitute the given, one line at a time, to get 4 T field.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 2 A · 0.5 m · 90° · 0.4 T. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      F=IℓB sin90=2×0.5×0.4=0.4 N.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      F=IℓB sin90=2×0.5×0.4=0.4 N.

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      0.4 N

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    0.4 N

    Copy onto your answer sheet — in this order

    Answer: 0.4 N

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

  30. 30 · 2 Marks

    Fnet=30 N, m=6 kg. a=

    How we got there

    Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

    Explain in another language · 11

    1. What is the question asking?

    Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: F_net = 30 N, m = 6 kg. a =

    Before any working — hunt first

    Given

    Numbers and units already in the sentence: 30 N · 6 kg. Copy each one into a column. A name without a number is not given.

    Missing

    After you copy the given, the letter that still has no number is missing. The paper is pointing at: a =. Circle that word — that is the missing variable.

    Find

    We are required to find: a =. Write that as a symbol on the left, with a question mark, before you touch a formula.

    Calculate

    What we need to calculate: 5 m·s⁻². Then substitute the given, one line at a time, to get a =.

    In other words — as if you have never seen this before

    5 m·s⁻²

    2. What do we already know?

    Copy these onto the left of your page, one per line, with units: 30 N · 6 kg. Mixing cm with m, or minutes with seconds, loses a method mark.

    3. Which method — and why this one?

    5 m·s⁻²

    4. Step-by-step working

    1. 01 / 08

      Step A — Read the question twice

      Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    2. 02 / 08

      Step A2 — Hunt: Given, Missing, Find, Calculate

      Given: Numbers and units already in the sentence: 30 N · 6 kg. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: a =. Circle that word — that is the missing variable. Find: We are required to find: a =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 5 m·s⁻². Then substitute the given, one line at a time, to get a =.

      Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).

    3. 03 / 08

      Step B — Write the given in a column

      Copy these onto the left of your page, one per line, with units: 30 N · 6 kg. Mixing cm with m, or minutes with seconds, loses a method mark.

      Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.

    4. 04 / 08

      Step C — Name the method in words

      5 m·s⁻²

      Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

    5. 05 / 08

      Working

      a=Fm=306=5 m·s⁻².

      Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

    6. 06 / 08

      Step G — Sense-check the size

      Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

      Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

    7. 07 / 08

      Step F — Box the answer with its unit

      5 m·s⁻²

      Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

    8. 08 / 08

      Step H — What the marker is looking for

      On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

      Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

    5. The answer

    5 m·s⁻²

    Copy onto your answer sheet — in this order

    Answer: 5 m·s⁻²

    6. Check it like a marker

    Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?

    7. A trap first-timers fall into

    First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

Ntsako · fx-991ZA PLUS. Tap to calculate.