2024 · november · Mathematics · Grade 10

Grade 10 Mathematics — KZN November style

Notes

Answer all questions. Show working. Calculators allowed unless stated. g = 9.8 m·s⁻².

90 min · 116 Marks · 30 questions

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Sit it timed Formula sheet

Question breakdown

1.1 · 6 Marks
Simplify 3(x − 2) − (x + 4).
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: Simplify 3(x − 2) − (x + 4).
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 · 2 · 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: Simplify 3(x − 2) − (x + 4). Circle that word — that is the missing variable.
Find
We are required to find: Simplify 3(x − 2) − (x + 4). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3x − 6 − x − 4 = 2x − 10. Then substitute the given, one line at a time, to get Simplify 3(x − 2) − (x + 4).
In other words — as if you have never seen this before
If you have never seen this before: 3x − 6 − x − 4 = 2x − 10. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 · 2 · 4. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3x−6−x−4=2x−10.
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: 3 · 2 · 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: Simplify 3(x − 2) − (x + 4). Circle that word — that is the missing variable. Find: We are required to find: Simplify 3(x − 2) − (x + 4). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 3x − 6 − x − 4 = 2x − 10. Then substitute the given, one line at a time, to get Simplify 3(x − 2) − (x + 4).
  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: 3 · 2 · 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
  3x−6−x−4=2x−10.
  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
  3x−6−x−4=2x−10.
  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
  2x − 10
  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
2x − 10
Copy onto your answer sheet — in this order
Answer: 2x − 10
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…”
1.2 · 8 Marks
2⁵2²=
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: 2⁵2² =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 2². 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: 2⁵2²=. Circle that word — that is the missing variable.
Find
We are required to find: 2⁵2²=. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 2³ = 8. Then substitute the given, one line at a time, to get 2⁵2²=.
In other words — as if you have never seen this before
If you have never seen this before: 2³ = 8. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 2². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
2³=8.
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 · 2². 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: 2⁵2²=. Circle that word — that is the missing variable. Find: We are required to find: 2⁵2²=. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 2³ = 8. Then substitute the given, one line at a time, to get 2⁵2²=.
  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 · 2². 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=8.
  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
  2³=8.
  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
  8
  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
8
Copy onto your answer sheet — in this order
Answer: 8
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…”
2.1 · 10 Marks
Tₙ=3n+1. T₁₂=
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: Tₙ = 3n + 1. T₁₂ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3n · 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: T₁₂ =. Circle that word — that is the missing variable.
Find
We are required to find: T₁₂ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3(12)+1=37. Then substitute the given, one line at a time, to get T₁₂ =.
In other words — as if you have never seen this before
If you have never seen this before: 3(12)+1=37. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3n · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3(12)+1=37.
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: 3n · 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: T₁₂ =. Circle that word — that is the missing variable. Find: We are required to find: T₁₂ =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 3(12)+1=37. Then substitute the given, one line at a time, to get T₁₂ =.
  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: 3n · 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
  3(12)+1=37.
  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
  3(12)+1=37.
  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
  37
  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
37
Copy onto your answer sheet — in this order
Answer: 37
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…”
2.2 · 12 Marks · Probability
P(even) on a fair die
Formulas
P(A)=n(A)n(S)
Classical probability
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(even) on a fair die
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: P(even) on a fair die. Circle that word — that is the missing variable.
Find
We are required to find: P(even) on a fair die. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 2,4,6 out of 6. Then substitute the given, one line at a time, to get P(even) on a fair die.
In other words — as if you have never seen this before
If you have never seen this before: 2,4,6 out of 6. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
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?
2,4,6 out of 6.
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: P(even) on a fair die. Circle that word — that is the missing variable. Find: We are required to find: P(even) on a fair die. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 2,4,6 out of 6. Then substitute the given, one line at a time, to get P(even) on a fair die.
  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
  2,4,6 out of 6.
  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
  2,4,6 out of 6.
  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
  12
  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
12
Copy onto your answer sheet — in this order
Answer: 12
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…”
3.1 · 12 Marks · Analytical geometry
Distance (1; 1) to (4; 5)
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
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: Distance (1; 1) to (4; 5)
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 1 · 4 · 5. 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: Distance (1; 1) to (4; 5). Circle that word — that is the missing variable.
Find
We are required to find: Distance (1; 1) to (4; 5). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: √(9+16)=5. Then substitute the given, one line at a time, to get Distance (1; 1) to (4; 5).
In other words — as if you have never seen this before
If you have never seen this before: √(9+16)=5. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 1 · 4 · 5. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
9+16=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 · 1 · 4 · 5. 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: Distance (1; 1) to (4; 5). Circle that word — that is the missing variable. Find: We are required to find: Distance (1; 1) to (4; 5). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: √(9+16)=5. Then substitute the given, one line at a time, to get Distance (1; 1) to (4; 5).
  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 · 1 · 4 · 5. 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
  9+16=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
  Reason
  9+16=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
  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
5
Copy onto your answer sheet — in this order
Answer: 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…”
3.2 · 12 Marks · Surface area & volume
Volume of a cube of side 4 cm
Formulas
V_cyl=πr²h
Cylinder volume
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: Volume of a cube of side 4 cm
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 cm. 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: Volume of a cube of side 4 cm. Circle that word — that is the missing variable.
Find
We are required to find: Volume of a cube of side 4 cm. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: s³ = 64. Then substitute the given, one line at a time, to get Volume of a cube of side 4 cm.
In other words — as if you have never seen this before
If you have never seen this before: s³ = 64. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4 cm. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
s³=64.
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: 4 cm. 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: Volume of a cube of side 4 cm. Circle that word — that is the missing variable. Find: We are required to find: Volume of a cube of side 4 cm. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: s³ = 64. Then substitute the given, one line at a time, to get Volume of a cube of side 4 cm.
  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: 4 cm. 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
  s³=64.
  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
  s³=64.
  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
  64 cm³
  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
64 cm³
Copy onto your answer sheet — in this order
Answer: 64 cm³
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 · 2 Marks · Probability
A die is fair. P(rolling a 6)?
Formulas
P(A)=n(A)n(S)
Classical probability
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 die is fair. P(rolling a 6)?
Before any working — hunt first
Given
Numbers and units already in the sentence: 6. 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(rolling a 6). Circle that word — that is the missing variable.
Find
We are required to find: P(rolling a 6). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: One favourable outcome out of six faces. Then substitute the given, one line at a time, to get P(rolling a 6).
In other words — as if you have never seen this before
One favourable outcome out of six faces.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 6. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
One favourable outcome out of six faces.
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. 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(rolling a 6). Circle that word — that is the missing variable. Find: We are required to find: P(rolling a 6). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: One favourable outcome out of six faces. Then substitute the given, one line at a time, to get P(rolling a 6).
  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. 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
  One favourable outcome out of six faces.
  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
  One favourable outcome out of six faces.
  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
  16
  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
16
Copy onto your answer sheet — in this order
Answer: 16
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 · 2 Marks · Factorisation
Factorise fully: x² − 9.
Formulas
a²−b²=(a − b)(a + b)
Difference of squares
x²+(p+q)x+pq=(x+p)(x+q)
Trinomial
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: Factorise fully: x² − 9.
Before any working — hunt first
Given
Numbers and units already in the sentence: 9. 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: Factorise fully: x² − 9. Circle that word — that is the missing variable.
Find
We are required to find: Factorise fully: x² − 9. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: (x−3)(x+3). Then substitute the given, one line at a time, to get Factorise fully: x² − 9.
In other words — as if you have never seen this before
(x−3)(x+3)
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 9. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
(x−3)(x+3)
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: 9. 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: Factorise fully: x² − 9. Circle that word — that is the missing variable. Find: We are required to find: Factorise fully: x² − 9. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: (x−3)(x+3). Then substitute the given, one line at a time, to get Factorise fully: x² − 9.
  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: 9. 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
  (x−3)(x+3)
  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
  Difference of squares.
  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
  (x−3)(x+3)
  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
(x−3)(x+3)
Copy onto your answer sheet — in this order
Answer: (x−3)(x+3)
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…”
9 · 2 Marks · Factorisation
Factorise x² − 16.
Formulas
a²−b²=(a − b)(a + b)
Difference of squares
x²+(p+q)x+pq=(x+p)(x+q)
Trinomial
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: Factorise x² − 16.
Before any working — hunt first
Given
Numbers and units already in the sentence: 16. 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: Factorise x² − 16. Circle that word — that is the missing variable.
Find
We are required to find: Factorise x² − 16. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Difference of squares: a² − b² = (a−b)(a+b). Then substitute the given, one line at a time, to get Factorise x² − 16.
In other words — as if you have never seen this before
Difference of squares: a² − b² = (a−b)(a+b).
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 16. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Difference of squares: a² − b² = (a−b)(a+b).
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: 16. 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: Factorise x² − 16. Circle that word — that is the missing variable. Find: We are required to find: Factorise x² − 16. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Difference of squares: a² − b² = (a−b)(a+b). Then substitute the given, one line at a time, to get Factorise x² − 16.
  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: 16. 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
  Difference of squares: a² − b² = (a−b)(a+b).
  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
  Difference of squares: a² − b² = (a−b)(a+b).
  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
  (x−4)(x+4)
  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
(x−4)(x+4)
Copy onto your answer sheet — in this order
Answer: (x−4)(x+4)
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 · 4 Marks
Tₙ=5n−2. Which term equals 48?
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: Tₙ = 5n − 2. Which term equals 48?
Before any working — hunt first
Given
Numbers and units already in the sentence: 5n · 2 · 48. 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: Which term equals 48. Circle that word — that is the missing variable.
Find
We are required to find: Which term equals 48. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 5n − 2 = 48. Then substitute the given, one line at a time, to get Which term equals 48.
In other words — as if you have never seen this before
5n−2=48→5n=50→n=10.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5n · 2 · 48. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
5n−2=48→5n=50→n=10.
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: 5n · 2 · 48. 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: Which term equals 48. Circle that word — that is the missing variable. Find: We are required to find: Which term equals 48. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 5n − 2 = 48. Then substitute the given, one line at a time, to get Which term equals 48.
  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: 5n · 2 · 48. 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
  5n−2=48→5n=50→n=10.
  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
  5n−2=48→5n=50→n=10.
  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
  10th
  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
10th
Copy onto your answer sheet — in this order
Answer: 10th
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 · 2 Marks · Surface area & volume
Area of a rectangle 8 m by 3 m
Formulas
V_cyl=πr²h
Cylinder volume
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: Area of a rectangle 8 m by 3 m
Before any working — hunt first
Given
Numbers and units already in the sentence: 8 m · 3 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: Area of a rectangle 8 m by 3 m. Circle that word — that is the missing variable.
Find
We are required to find: Area of a rectangle 8 m by 3 m. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: A = ℓ × b = 24. Then substitute the given, one line at a time, to get Area of a rectangle 8 m by 3 m.
In other words — as if you have never seen this before
A=ℓ×b=24.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 8 m · 3 m. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
A=ℓ×b=24.
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: 8 m · 3 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: Area of a rectangle 8 m by 3 m. Circle that word — that is the missing variable. Find: We are required to find: Area of a rectangle 8 m by 3 m. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: A = ℓ × b = 24. Then substitute the given, one line at a time, to get Area of a rectangle 8 m by 3 m.
  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: 8 m · 3 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
  A=ℓ×b=24.
  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=ℓ×b=24.
  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 m²
  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 m²
Copy onto your answer sheet — in this order
Answer: 24 m²
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 · 3 Marks · Simple & compound interest
R1000 at 10% p.a. compound for 2 years. Amount A =
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
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: R1000 at 10% p.a. compound for 2 years. Amount A =
Before any working — hunt first
Given
Numbers and units already in the sentence: R1000 at · 10% · 2 years. 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: Amount A =. Circle that word — that is the missing variable.
Find
We are required to find: Amount A =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: A=P(1+i)ⁿ=1000(1. Then substitute the given, one line at a time, to get Amount A =.
In other words — as if you have never seen this before
A=P(1+i)ⁿ=1000(1.1)²=1210.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R1000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
A=P(1+i)ⁿ=1000(1.1)²=1210.
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: R1000 at · 10% · 2 years. 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: Amount A =. Circle that word — that is the missing variable. Find: We are required to find: Amount A =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: A=P(1+i)ⁿ=1000(1. Then substitute the given, one line at a time, to get Amount 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: R1000 at · 10% · 2 years. 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
  A=P(1+i)ⁿ=1000(1.1)²=1210.
  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=P(1+i)ⁿ=1000(1.1)²=1210.
  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
  R1210
  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
R1210
Copy onto your answer sheet — in this order
Answer: R1210
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 · 3 Marks · Analytical geometry
Distance between (0; 0) and (6; 8) is
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
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: Distance between (0; 0) and (6; 8) is
Before any working — hunt first
Given
Numbers and units already in the sentence: 0 · 0 · 6 · 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: Distance between (0; 0) and (6; 8) is. Circle that word — that is the missing variable.
Find
We are required to find: Distance between (0; 0) and (6; 8) is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: √(36+64)=10. Then substitute the given, one line at a time, to get Distance between (0; 0) and (6; 8) is.
In other words — as if you have never seen this before
36+64=10. A 6-8-10 triangle.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0 · 0 · 6 · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
36+64=10. A 6-8-10 triangle.
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 · 0 · 6 · 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: Distance between (0; 0) and (6; 8) is. Circle that word — that is the missing variable. Find: We are required to find: Distance between (0; 0) and (6; 8) is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: √(36+64)=10. Then substitute the given, one line at a time, to get Distance between (0; 0) and (6; 8) 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: 0 · 0 · 6 · 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
  36+64=10. A 6-8-10 triangle.
  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
  36+64=10. A 6-8-10 triangle.
  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
  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
Copy onto your answer sheet — in this order
Answer: 10
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…”
14 · 2 Marks
3²×3⁴=
Notes: Same base 3. Exponents 2 and 4. Multiply.
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: 3² × 3⁴ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3² · 3. 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: 3² × 3⁴ =. Circle that word — that is the missing variable.
Find
We are required to find: 3² × 3⁴ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write aᵐ × aⁿ = aᵐ⁺ⁿ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 3² × 3⁴ =.
In other words — as if you have never seen this before
aᵐ×aⁿ=aᵐ⁺ⁿ. Add 2+4=6.
2. What do we already know?
Same base 3. Exponents 2 and 4. Multiply.
3. Which method — and why this one?
aᵐ×aⁿ=aᵐ⁺ⁿ. Add 2+4=6.
4. Step-by-step working
1. 01 / 05
  Write the law
  Keep the base, add the indices.
  aᵐ×aⁿ=aᵐ⁺ⁿ
  Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
2. 02 / 05
  Add
  2+4=6, so 3⁶.
  3⁶
  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
  3⁶
  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
3⁶
Copy onto your answer sheet — in this order
Formula: aᵐ×aⁿ=aᵐ⁺ⁿ
Answer: 3⁶
6. Check it like a marker
9 × 81 = 729. And 3⁶ = 729. Matches.
7. A trap first-timers fall into
Do not write 9⁶ (multiplied bases) or 3⁸ (multiplied exponents — that is a power of a power).
15 · 2 Marks
Expand (x + 5)(x − 2).
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: Expand (x + 5)(x − 2).
Before any working — hunt first
Given
Numbers and units already in the sentence: 5 · 2. 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: Expand (x + 5)(x − 2). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 2).
In other words — as if you have never seen this before
x² + 3x − 10
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
x² + 3x − 10
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 · 2. 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: Expand (x + 5)(x − 2). Circle that word — that is the missing variable. Find: We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 2).
  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 · 2. 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
  x² + 3x − 10
  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
  FOIL: x² − 2x + 5x − 10 = x² + 3x − 10. The middle terms add, they do not cancel.
  x²+3x−10
  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
  x² + 3x − 10
  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
x² + 3x − 10
Copy onto your answer sheet — in this order
Formula: x² + 3x − 10
Answer: x² + 3x − 10
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 · 2 Marks · Simple & compound interest
Simple interest formula is
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
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: Simple interest formula 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: Simple interest formula is. Circle that word — that is the missing variable.
Find
We are required to find: Simple interest formula is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: I = principal × rate × time. Then substitute the given, one line at a time, to get Simple interest formula is.
In other words — as if you have never seen this before
I=principal×rate×time.
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?
I=principal×rate×time.
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: Simple interest formula is. Circle that word — that is the missing variable. Find: We are required to find: Simple interest formula is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: I = principal × rate × time. Then substitute the given, one line at a time, to get Simple interest formula 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
  I=principal×rate×time.
  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
  I=principal×rate×time.
  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
  I=Pin
  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
I=Pin
Copy onto your answer sheet — in this order
Answer: I=Pin
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 · 2 Marks
10% of R250
Notes: 10% of 250. Percent means hundredths.
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: 10% of R250
Before any working — hunt first
Given
Numbers and units already in the sentence: 10% · R250. 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: 10% of R250. Circle that word — that is the missing variable.
Find
We are required to find: 10% of R250. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write R25 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 10% of R250.
In other words — as if you have never seen this before
10% = 0.1. Multiply. Or 25010.
2. What do we already know?
10% of 250. Percent means hundredths.
3. Which method — and why this one?
10% = 0.1. Multiply. Or 25010.
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% · R250. 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: 10% of R250. Circle that word — that is the missing variable. Find: We are required to find: 10% of R250. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: Write R25 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 10% of R250.
  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
  10% of 250. Percent means hundredths.
  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
  10% = 0.1. Multiply. Or 25010.
  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
  Convert then multiply
  0.1×250=25.
  R25
  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
  R25
  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
R25
Copy onto your answer sheet — in this order
Formula: R25
Answer: R25
6. Check it like a marker
10 × R25 = R250. Recovers the whole.
7. A trap first-timers fall into
R2.50 is 1%. R2500 is 1000%.
18 · 2 Marks · Number patterns
Which number is irrational?
Formulas
Tₙ=a+(n − 1)d
nth term
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: Which number is irrational?
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: Which number is irrational. Circle that word — that is the missing variable.
Find
We are required to find: Which number is irrational. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: √2 cannot be ab. Then substitute the given, one line at a time, to get Which number is irrational.
In other words — as if you have never seen this before
√2 cannot be ab. √9=3 is rational.
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?
√2 cannot be ab. √9=3 is rational.
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: Which number is irrational. Circle that word — that is the missing variable. Find: We are required to find: Which number is irrational. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: √2 cannot be ab. Then substitute the given, one line at a time, to get Which number is irrational.
  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
  √2 cannot be ab. √9=3 is rational.
  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
  √2 cannot be ab. √9=3 is rational.
  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
  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
Copy onto your answer sheet — in this order
Answer: √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…”
19 · 2 Marks
Solve 2x+5=17.
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: Solve 2x + 5 = 17.
Before any working — hunt first
Given
Numbers and units already in the sentence: 2x · 5 · 17. 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: Solve 2x + 5 = 17. Circle that word — that is the missing variable.
Find
We are required to find: Solve 2x + 5 = 17. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: x = 6. Then substitute the given, one line at a time, to get Solve 2x + 5 = 17.
In other words — as if you have never seen this before
x=6
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2x · 5 · 17. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
x=6
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: 2x · 5 · 17. 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: Solve 2x + 5 = 17. Circle that word — that is the missing variable. Find: We are required to find: Solve 2x + 5 = 17. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: x = 6. Then substitute the given, one line at a time, to get Solve 2x + 5 = 17.
  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: 2x · 5 · 17. 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
  x=6
  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
  Subtract 5: 2x = 12. Divide by 2: x = 6. Check: 2(6)+5 = 17.
  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
  x=6
  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
x=6
Copy onto your answer sheet — in this order
Answer: x=6
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 · 2 Marks
2⁻²=
Notes: Negative exponent on 2.
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: 2⁻² =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2⁻². 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: 2⁻² =. Circle that word — that is the missing variable.
Find
We are required to find: 2⁻² =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write a⁻ⁿ = 1aⁿ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 2⁻² =.
In other words — as if you have never seen this before
a⁻ⁿ=1aⁿ. 2⁻²=12²=14.
2. What do we already know?
Negative exponent on 2.
3. Which method — and why this one?
a⁻ⁿ=1aⁿ. 2⁻²=12²=14.
4. Step-by-step working
1. 01 / 05
  Write the law
  A negative index means reciprocal.
  a⁻ⁿ=1aⁿ
  Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
2. 02 / 05
  Evaluate
  14=14.
  14
  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
  14
  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
14
Copy onto your answer sheet — in this order
Formula: a⁻ⁿ=1aⁿ
Answer: 14
6. Check it like a marker
2²=4, so 2⁻² is the reciprocal 14. Not negative 4.
7. A trap first-timers fall into
The minus is on the exponent, not on the 2. 2⁻² is not −4.
21 · 2 Marks
Expand (x+3)(x+4)
Notes: Two binomials. Unknown: expanded trinomial.
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: Expand (x+3)(x+4)
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 · 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: Expand (x+3)(x+4). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x+3)(x+4). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x²+4x+3x+12 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x+3)(x+4).
In other words — as if you have never seen this before
FOIL: First, Outer, Inner, Last. Then collect like terms.
2. What do we already know?
Two binomials. Unknown: expanded trinomial.
3. Which method — and why this one?
FOIL: First, Outer, Inner, Last. Then collect like terms.
4. Step-by-step working
1. 01 / 05
  FOIL
  x² + 4x + 3x + 12.
  x²+4x+3x+12
  Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
2. 02 / 05
  Collect
  x² + 7x + 12.
  x²+7x+12
  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
  x²+7x+12
  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
x²+7x+12
Copy onto your answer sheet — in this order
Formula: x²+4x+3x+12
Answer: x²+7x+12
6. Check it like a marker
At x=1: (4)(5)=20 and 1+7+12=20. Matches.
7. A trap first-timers fall into
x²+12 forgets the middle terms. They do not cancel — both plus.
22 · 2 Marks
2⁻³=
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: 2⁻³ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2⁻³. 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: 2⁻³ =. Circle that word — that is the missing variable.
Find
We are required to find: 2⁻³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: a⁻ⁿ = 1aⁿ=18. Then substitute the given, one line at a time, to get 2⁻³ =.
In other words — as if you have never seen this before
a⁻ⁿ=1aⁿ=18.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2⁻³. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
a⁻ⁿ=1aⁿ=18.
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: 2⁻³. 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: 2⁻³ =. Circle that word — that is the missing variable. Find: We are required to find: 2⁻³ =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: a⁻ⁿ = 1aⁿ=18. Then substitute the given, one line at a time, to get 2⁻³ =.
  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: 2⁻³. 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
  a⁻ⁿ=1aⁿ=18.
  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⁻ⁿ=1aⁿ=18.
  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
  18
  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
18
Copy onto your answer sheet — in this order
Answer: 18
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…”
23 · 3 Marks · Trigonometry
cos θ = adjacenthypotenuse. If adj=9, hyp=15, cos θ =
Formulas
sin θ=opphyp
Sine
tan θ=oppadj
Tangent
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: cos θ = adjacenthypotenuse. If adj=9, hyp=15, cos θ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 9 · 15. 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: If adj=9, hyp=15, cos θ =. Circle that word — that is the missing variable.
Find
We are required to find: If adj=9, hyp=15, cos θ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 915=35. Then substitute the given, one line at a time, to get If adj=9, hyp=15, cos θ =.
In other words — as if you have never seen this before
915=35.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 9 · 15. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
915=35.
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: 9 · 15. 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: If adj=9, hyp=15, cos θ =. Circle that word — that is the missing variable. Find: We are required to find: If adj=9, hyp=15, cos θ =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 915=35. Then substitute the given, one line at a time, to get If adj=9, hyp=15, cos θ =.
  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: 9 · 15. 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
  915=35.
  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
  915=35.
  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
  35
  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
35
Copy onto your answer sheet — in this order
Answer: 35
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…”
24 · 4 Marks · Surface area & volume
A cylinder r = 3 cm, h = 10 cm. Volume in cm³ (use π = 3.14)
Formulas
V_cyl=πr²h
Cylinder volume
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 cylinder r = 3 cm, h = 10 cm. Volume in cm³ (use π = 3.14)
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 cm · 10 cm · 3.14. 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: 14). Circle that word — that is the missing variable.
Find
We are required to find: 14). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: V = πr²h = 3. Then substitute the given, one line at a time, to get 14).
In other words — as if you have never seen this before
V=πr²h=3.14×9×10=282.6 cm³.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 cm · 10 cm · 3.14. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
V=πr²h=3.14×9×10=282.6 cm³.
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: 3 cm · 10 cm · 3.14. 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: 14). Circle that word — that is the missing variable. Find: We are required to find: 14). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: V = πr²h = 3. Then substitute the given, one line at a time, to get 14).
  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: 3 cm · 10 cm · 3.14. 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=πr²h=3.14×9×10=282.6 cm³.
  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=πr²h=3.14×9×10=282.6 cm³.
  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
  282.6
  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
282.6
Copy onto your answer sheet — in this order
Answer: 282.6
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…”
25 · 2 Marks
A taxi from Gqeberha to Mthatha is 480 km at 80 kmh. Time?
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 taxi from Gqeberha to Mthatha is 480 km at 80 kmh. Time?
Before any working — hunt first
Given
Numbers and units already in the sentence: 480 km · 80 kmh. 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: Time. Circle that word — that is the missing variable.
Find
We are required to find: Time. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 6 h. Then substitute the given, one line at a time, to get Time.
In other words — as if you have never seen this before
6 h
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 480 km · 80 kmh. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
6 h
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: 480 km · 80 kmh. 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: Time. Circle that word — that is the missing variable. Find: We are required to find: Time. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 6 h. Then substitute the given, one line at a time, to get Time.
  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: 480 km · 80 kmh. 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
  6 h
  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
  t = distancespeed=480 ÷ 80 = 6 hours. Write units: km(km/h) leaves hours.
  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 h
  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 h
Copy onto your answer sheet — in this order
Answer: 6 h
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 · 3 Marks · Functions
A die is fair. P(rolling an even number)?
Formulas
y=mx+c
Straight line
Notes: A fair six-face die. Even faces: 2, 4, 6. That is three faces. Total faces: 6.
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 die is fair. P(rolling an even number)?
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: P(rolling an even number). Circle that word — that is the missing variable.
Find
We are required to find: P(rolling an even number). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write P = 12 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives P(rolling an even number).
In other words — as if you have never seen this before
Probability = favourabletotal, when every face is equally likely.
2. What do we already know?
A fair six-face die. Even faces: 2, 4, 6. That is three faces. Total faces: 6.
3. Which method — and why this one?
Probability = favourabletotal, when every face is equally likely.
4. Step-by-step working
1. 01 / 05
  Count favourable
  Even numbers on a die: 2, 4 and 6. Three outcomes. Do not include 0 — dice do not have a 0.
  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.
2. 02 / 05
  Divide
  P = 36. Simplify by 3: 12. Leaving 36 is not wrong, but NSC usually wants the simplest form.
  P=12
  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.
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
  12
  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
12
Copy onto your answer sheet — in this order
Formula: P=12
Answer: 12
6. Check it like a marker
Odd would also be 12. Together they add to 1. Good.
7. A trap first-timers fall into
Writing 3, or 13 (thinking 2,4,6 out of the even “ideas”). Always divide by 6, the faces.
27 · 2 Marks
Expand (x+4)(x−1).
Notes: Two brackets: (x+4)(x−1).
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: Expand (x+4)(x−1).
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 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: Expand (x+4)(x−1). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x+4)(x−1). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x² − x + 4x − 4 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x+4)(x−1).
In other words — as if you have never seen this before
FOIL: First, Outer, Inner, Last. Then collect like terms.
2. What do we already know?
Two brackets: (x+4)(x−1).
3. Which method — and why this one?
FOIL: First, Outer, Inner, Last. Then collect like terms.
4. Step-by-step working
1. 01 / 05
  FOIL
  x·x=x². x·(−1)=−x. 4·x=4x. 4·(−1)=−4.
  x²−x+4x−4
  Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
2. 02 / 05
  Collect
  −x+4x=3x. So x²+3x−4.
  x²+3x−4
  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
  x² + 3x − 4
  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
x² + 3x − 4
Copy onto your answer sheet — in this order
Formula: x² − x + 4x − 4
Answer: x² + 3x − 4
6. Check it like a marker
Let x=1: left (5)(0)=0. Right 1+3−4=0. Matches.
7. A trap first-timers fall into
The middle terms add, they do not cancel. Cancelling would need +x and −x.
28 · 2 Marks · Factorisation
Factorise x² − 81.
Formulas
a²−b²=(a − b)(a + b)
Difference of squares
x²+(p+q)x+pq=(x+p)(x+q)
Trinomial
Notes: One expression: x² − 81. 81 is 9².
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: Factorise x² − 81.
Before any working — hunt first
Given
Numbers and units already in the sentence: 81. 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: Factorise x² − 81. Circle that word — that is the missing variable.
Find
We are required to find: Factorise x² − 81. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write a = x, b = 9 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Factorise x² − 81.
In other words — as if you have never seen this before
Difference of squares: a² − b² = (a−b)(a+b). a = x, b = 9.
2. What do we already know?
One expression: x² − 81. 81 is 9².
3. Which method — and why this one?
Difference of squares: a² − b² = (a−b)(a+b). a = x, b = 9.
4. Step-by-step working
1. 01 / 05
  Name the squares
  x² = (x)² and 81 = (9)².
  a=x, b=9
  Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
2. 02 / 05
  Write the brackets
  (x − 9)(x + 9). One minus, one plus.
  (x−9)(x+9)
  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
  (x−9)(x+9)
  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
(x−9)(x+9)
Copy onto your answer sheet — in this order
Formula: a=x, b=9
Answer: (x−9)(x+9)
6. Check it like a marker
FOIL: x² + 9x − 9x − 81 = x² − 81. Middle terms cancel.
7. A trap first-timers fall into
Do not write (x−9)². That expands to x² − 18x + 81.
29 · 2 Marks · Number patterns
Solve x + 4 > 10.
Formulas
Tₙ=a+(n − 1)d
nth term
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: Solve x + 4 > 10.
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 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: Solve x + 4 > 10. Circle that word — that is the missing variable.
Find
We are required to find: Solve x + 4 > 10. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Subtract 4: x > 6. Then substitute the given, one line at a time, to get Solve x + 4 > 10.
In other words — as if you have never seen this before
Subtract 4: x > 6. Open circle on the number line.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4 · 10. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Subtract 4: x > 6. Open circle on the number line.
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: 4 · 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: Solve x + 4 > 10. Circle that word — that is the missing variable. Find: We are required to find: Solve x + 4 > 10. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Subtract 4: x > 6. Then substitute the given, one line at a time, to get Solve x + 4 > 10.
  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: 4 · 10. 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
  Subtract 4: x > 6. Open circle on the number line.
  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
  Subtract 4: x > 6. Open circle on the number line.
  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
  x > 6
  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
x > 6
Copy onto your answer sheet — in this order
Answer: x > 6
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 · 2 Marks · Functions
2x+y=11, x−y=1. y=
Formulas
y=mx+c
Straight line
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: 2x + y = 11, x − y = 1. y =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2x · 11 · 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: y =. Circle that word — that is the missing variable.
Find
We are required to find: y =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: x = 4 from adding, then 4 − y = 1. Then substitute the given, one line at a time, to get y =.
In other words — as if you have never seen this before
x=4 from adding, then 4−y=1.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2x · 11 · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
x=4 from adding, then 4−y=1.
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: 2x · 11 · 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: y =. Circle that word — that is the missing variable. Find: We are required to find: y =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: x = 4 from adding, then 4 − y = 1. Then substitute the given, one line at a time, to get y =.
  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: 2x · 11 · 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
  x=4 from adding, then 4−y=1.
  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
  x=4 from adding, then 4−y=1.
  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
  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
Copy onto your answer sheet — in this order
Answer: 3
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…”