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
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.
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.
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.
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.
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.
Do not write (x−9)². That expands to x² − 18x + 81.
1.2 · 10 Marks
A grain truck from Bloemfontein covers 240 km at 80 kmh. Time?
Notes: Distance Δx = 240 km. Speed v = 80 kmh. Unknown: time t.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A grain truck from Bloemfontein covers 240 km at 80 kmh. Time?
Before any working — hunt first
Given
Numbers and units already in the sentence: 240 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
Write t = Δxv with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Time.
In other words — as if you have never seen this before
t = distancespeed. Units: km(km/h) leaves hours.
2. What do we already know?
Distance Δx = 240 km. Speed v = 80 kmh. Unknown: time t.
3. Which method — and why this one?
t = distancespeed. Units: km(km/h) leaves hours.
4. Step-by-step working
01 / 05
Write the formula
t=Δxv.
t=Δxv
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Substitute
t=24080=3 hours.
t=3 h
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
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.
04 / 05
Step F — Box the answer with its unit
3 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.
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
3 h
Copy onto your answer sheet — in this order
Formula: t=Δxv
Answer: 3 h
6. Check it like a marker
80 kmh × 3 h = 240 km. Matches the given distance.
7. A trap first-timers fall into
Do not multiply 240 × 80. Speed is not added to distance.
2.1 · 10 Marks
Solve 4x+5=21.
Notes: 4x + 5 on the left. 21 on the right. Unknown x.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Solve 4x + 5 = 21.
Before any working — hunt first
Given
Numbers and units already in the sentence: 4x · 5 · 21. 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 4x + 5 = 21. Circle that word — that is the missing variable.
Find
We are required to find: Solve 4x + 5 = 21. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 4x = 16 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Solve 4x + 5 = 21.
In other words — as if you have never seen this before
Undo +5 first (subtract 5), then undo ×4 (divide by 4). Same to both sides.
2. What do we already know?
4x + 5 on the left. 21 on the right. Unknown x.
3. Which method — and why this one?
Undo +5 first (subtract 5), then undo ×4 (divide by 4). Same to both sides.
4. Step-by-step working
01 / 05
Subtract 5
4x+5−5=21−5→4x=16.
4x=16
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Divide by 4
x=164=4.
x=4
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
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.
04 / 05
Step F — Box the answer with its unit
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.
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=4
Copy onto your answer sheet — in this order
Formula: 4x=16
Answer: x=4
6. Check it like a marker
4(4)+5=16+5=21. Both sides match.
7. A trap first-timers fall into
Do not divide by 4 first — that splits the +5 and makes a mess. Reverse BODMAS.
2.2 · 12 Marks · Analytical geometry
Gradient of the line through (1; 2) and (5; 10)
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
Notes: Point A(1; 2) and B(5; 10). Unknown: m.
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: Gradient of the line through (1; 2) and (5; 10)
In other words — as if you have never seen this before
m = (y₂ − y₁)/(x₂ − x₁). Rise over run, same order on top and bottom.
2. What do we already know?
Point A(1; 2) and B(5; 10). Unknown: m.
3. Which method — and why this one?
m = (y₂ − y₁)/(x₂ − x₁). Rise over run, same order on top and bottom.
4. Step-by-step working
01 / 05
Write the formula
m=(y₂ − y₁)(x₂ − x₁).
m=(y₂−y₁)(x₂−x₁)
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Substitute
m=(10 − 2)(5 − 1)=84=2.
m=2
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
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.
04 / 05
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.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
2
Copy onto your answer sheet — in this order
Formula: m=(y₂−y₁)(x₂−x₁)
Answer: 2
6. Check it like a marker
From x = 1 to 5 we add 4. From y = 2 to 10 we add 8. 84=2.
7. A trap first-timers fall into
Do not swap to (x₂−x₁)/(y₂−y₁). That is run over rise, the reciprocal.
5 · 2 Marks · Trigonometry
sin of a right triangle opposite 3, hypotenuse 5
Trigonometry
Formulas
sin θ=opphyp
Sine
tan θ=oppadj
Tangent
Notes: opp=3. hyp=5. A 3-4-5 triangle.
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: sin of a right triangle opposite 3, hypotenuse 5
In other words — as if you have never seen this before
sin = oppositehypotenuse.
2. What do we already know?
opp=3. hyp=5. A 3-4-5 triangle.
3. Which method — and why this one?
sin = oppositehypotenuse.
4. Step-by-step working
01 / 07
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 07
Step B — Write the given in a column
opp=3. hyp=5. A 3-4-5 triangle.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
03 / 07
Step C — Name the method in words
sin = oppositehypotenuse.
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.
04 / 07
SOH
sin=35.
35
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
05 / 07
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
06 / 07
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.
07 / 07
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
35
Copy onto your answer sheet — in this order
Formula: 35
Answer: 35
6. Check it like a marker
cos would be 45. tan would be 34. Match the ratio to the name.
7. A trap first-timers fall into
34 is tan. 45 is cos. Write SOH CAH TOA in the margin.
6 · 3 Marks · Analytical geometry
Distance between (0; 0) and (6; 8) is
Analytical geometry
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
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.
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).
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.
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.
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.
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.
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.
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…”
7 · 3 Marks · Functions
A die is fair. P(rolling an even number)?
Functions
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
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.
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.
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.
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.
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.
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
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.
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).
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.
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.
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.
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.
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.
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
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
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.
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).
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.
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.
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.
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.
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.
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…”
10 · 3 Marks · Probability
P(red) from 3 red and 7 blue marbles?
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(red) from 3 red and 7 blue marbles?
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 red · 7 blue. 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(red) from 3 red and 7 blue marbles. Circle that word — that is the missing variable.
Find
We are required to find: P(red) from 3 red and 7 blue marbles. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 310. Then substitute the given, one line at a time, to get P(red) from 3 red and 7 blue marbles.
In other words — as if you have never seen this before
310
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 red · 7 blue. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
310
4. Step-by-step working
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.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3 red · 7 blue. 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(red) from 3 red and 7 blue marbles. Circle that word — that is the missing variable.
Find: We are required to find: P(red) from 3 red and 7 blue marbles. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 310. Then substitute the given, one line at a time, to get P(red) from 3 red and 7 blue marbles.
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).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3 red · 7 blue. 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.
04 / 08
Step C — Name the method in words
310
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.
05 / 08
Reason
3 favourable out of 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.
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.
07 / 08
Step F — Box the answer with its unit
310
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.
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
310
Copy onto your answer sheet — in this order
Answer: 310
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 · Statistics
Mean of 2, 4, 6 is
Statistics
Formulas
x̄=Σxn
Mean
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: Mean of 2, 4, 6 is
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 4 · 6 is. 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: Mean of 2, 4, 6 is. Circle that word — that is the missing variable.
Find
We are required to find: Mean of 2, 4, 6 is. 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)3=4. Then substitute the given, one line at a time, to get Mean of 2, 4, 6 is.
In other words — as if you have never seen this before
(2+4+6)3=4.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 4 · 6 is. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
(2+4+6)3=4.
4. Step-by-step working
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.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2 · 4 · 6 is. 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: Mean of 2, 4, 6 is. Circle that word — that is the missing variable.
Find: We are required to find: Mean of 2, 4, 6 is. 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)3=4. Then substitute the given, one line at a time, to get Mean of 2, 4, 6 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).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 2 · 4 · 6 is. 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.
04 / 08
Step C — Name the method in words
(2+4+6)3=4.
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.
05 / 08
Working
(2+4+6)3=4.
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.
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.
07 / 08
Step F — Box the answer with its unit
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.
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
4
Copy onto your answer sheet — in this order
Answer: 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…”
12 · 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
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.
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.
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.
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.
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).
13 · 4 Marks
(3²)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: (3²)³ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3². 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)³ =. Circle that word — that is the missing variable.
Find
We are required to find: (3²)³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Power of a power: 3⁶ = 729. Then substitute the given, one line at a time, to get (3²)³ =.
In other words — as if you have never seen this before
Power of a power: 3⁶ = 729.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Power of a power: 3⁶ = 729.
4. Step-by-step working
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.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3². 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)³ =. Circle that word — that is the missing variable.
Find: We are required to find: (3²)³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Power of a power: 3⁶ = 729. Then substitute the given, one line at a time, to get (3²)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).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3². 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.
04 / 08
Step C — Name the method in words
Power of a power: 3⁶ = 729.
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.
05 / 08
Working
Power of a power: 3⁶ = 729.
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.
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.
07 / 08
Step F — Box the answer with its unit
729
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.
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
729
Copy onto your answer sheet — in this order
Answer: 729
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 · 4 Marks · Functions
x-intercept of y = 2x − 8
Functions
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: x-intercept of y = 2x − 8
Before any working — hunt first
Given
Numbers and units already in the sentence: 2x · 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: x-intercept of y = 2x − 8. Circle that word — that is the missing variable.
Find
We are required to find: x-intercept of y = 2x − 8. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 0=2x−8. Then substitute the given, one line at a time, to get x-intercept of y = 2x − 8.
In other words — as if you have never seen this before
0=2x−8→x=4.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2x · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
0=2x−8→x=4.
4. Step-by-step working
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.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2x · 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: x-intercept of y = 2x − 8. Circle that word — that is the missing variable.
Find: We are required to find: x-intercept of y = 2x − 8. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 0=2x−8. Then substitute the given, one line at a time, to get x-intercept of y = 2x − 8.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 2x · 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.
04 / 08
Step C — Name the method in words
0=2x−8→x=4.
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.
05 / 08
Working
0=2x−8→x=4.
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.
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.
07 / 08
Step F — Box the answer with its unit
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.
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
4
Copy onto your answer sheet — in this order
Answer: 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…”
15 · 2 Marks · Analytical geometry
Gradient of the line through (1; 2) and (5; 14).
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
Notes: Point A (1; 2), point B (5; 14). Unknown: gradient m.
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: Gradient of the line through (1; 2) and (5; 14).
In other words — as if you have never seen this before
Gradient is rise over run: change in y divided by change in x, in the same order.
2. What do we already know?
Point A (1; 2), point B (5; 14). Unknown: gradient m.
3. Which method — and why this one?
Gradient is rise over run: change in y divided by change in x, in the same order.
4. Step-by-step working
01 / 06
Write the formula
m = (y₂ − y₁) / (x₂ − x₁). Call (1; 2) point 1 and (5; 14) point 2.
m=(y₂ − y₁)(x₂ − x₁)
Why this step: Order matters. If you subtract the x’s the other way, you must also flip the y’s, or the sign of m flips.
02 / 06
Substitute
m=(14 − 2)(5 − 1)=124.
m=124
Why this step: Rise 12, run 4. A 12-up-for-4-along line is steep, so m around 3 is sensible — not 12, not 1/3.
03 / 06
Simplify
124=3. So m = 3. From x = 1 to x = 5 we add 4; y must add 12, which is 3 × 4.
m=3
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.
04 / 06
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.
05 / 06
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.
06 / 06
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
Formula: m=(y₂ − y₁)(x₂ − x₁)
Answer: 3
6. Check it like a marker
Start at (1; 2), add 4 to x and 12 to y: (5; 14). Lands on the second point.
7. A trap first-timers fall into
Writing 412=13 — that is run over rise. Gradient is never “along over up”.
16 · 3 Marks
Sequence 4; 9; 14; 19; … T₂₅=
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: Sequence 4; 9; 14; 19; … T₂₅ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 9 · 14 · 19. 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: Sequence 4; 9; 14; 19; … T₂₅ =. Circle that word — that is the missing variable.
Find
We are required to find: Sequence 4; 9; 14; 19; … T₂₅ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 124. Then substitute the given, one line at a time, to get Sequence 4; 9; 14; 19; … T₂₅ =.
In other words — as if you have never seen this before
124
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4 · 9 · 14 · 19. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
124
4. Step-by-step working
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.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 4 · 9 · 14 · 19. 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: Sequence 4; 9; 14; 19; … T₂₅ =. Circle that word — that is the missing variable.
Find: We are required to find: Sequence 4; 9; 14; 19; … T₂₅ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 124. Then substitute the given, one line at a time, to get Sequence 4; 9; 14; 19; … T₂₅ =.
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).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 4 · 9 · 14 · 19. 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.
04 / 08
Step C — Name the method in words
124
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.
05 / 08
Reason
a=4, d=5. T₂₅=4+24×5=124.
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.
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.
07 / 08
Step F — Box the answer with its unit
124
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.
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
124
Copy onto your answer sheet — in this order
Answer: 124
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 · Functions
x + y = 10 and x − y = 2. x =
Functions
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: x + y = 10 and x − y = 2. x =
Before any working — hunt first
Given
Numbers and units already in the sentence: 10 and · 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: x =. Circle that word — that is the missing variable.
Find
We are required to find: x =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Add: 2x = 12, x = 6. Then substitute the given, one line at a time, to get x =.
In other words — as if you have never seen this before
Add: 2x=12, x=6.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 10 and · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Add: 2x=12, x=6.
4. Step-by-step working
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.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 10 and · 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: x =. Circle that word — that is the missing variable.
Find: We are required to find: x =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Add: 2x = 12, x = 6. Then substitute the given, one line at a time, to get x =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 10 and · 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.
04 / 08
Step C — Name the method in words
Add: 2x=12, 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.
05 / 08
Working
Add: 2x=12, x=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.
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.
07 / 08
Step F — Box the answer with its unit
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.
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
Copy onto your answer sheet — in this order
Answer: 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…”
18 · 2 Marks
Sum of interior angles of a triangle is
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Sum of interior angles of a triangle 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: Sum of interior angles of a triangle is. Circle that word — that is the missing variable.
Find
We are required to find: Sum of interior angles of a triangle is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Triangle interior angles sum to 180°. Then substitute the given, one line at a time, to get Sum of interior angles of a triangle is.
In other words — as if you have never seen this before
Triangle interior angles sum to 180°.
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?
Triangle interior angles sum to 180°.
4. Step-by-step working
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.
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: Sum of interior angles of a triangle is. Circle that word — that is the missing variable.
Find: We are required to find: Sum of interior angles of a triangle is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Triangle interior angles sum to 180°. Then substitute the given, one line at a time, to get Sum of interior angles of a triangle 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).
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.
04 / 08
Step C — Name the method in words
Triangle interior angles sum to 180°.
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.
05 / 08
Working
Triangle interior angles sum to 180°.
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.
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.
07 / 08
Step F — Box the answer with its unit
180°
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.
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
180°
Copy onto your answer sheet — in this order
Answer: 180°
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
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: 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
2x − 10
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?
2x − 10
4. Step-by-step working
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.
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: 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).
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.
04 / 08
Step C — Name the method in words
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.
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.
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.
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.
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…”
20 · 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
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.
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.
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.
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.
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.
21 · 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
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.
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).
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.
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.
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.
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.
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.
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%.
22 · 3 Marks · Trigonometry
cos θ = adjacenthypotenuse. If adj=9, hyp=15, cos θ =
Trigonometry
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
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.
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).
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.
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.
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.
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.
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.
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…”
23 · 3 Marks · Surface area & volume
Area of a rectangle 9 m by 4 m
Formulas
Vcyl=πr²h
Cylinder volume
Notes: ℓ=9 m, b=4 m. Unknown: area.
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 9 m by 4 m
Before any working — hunt first
Given
Numbers and units already in the sentence: 9 m · 4 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 9 m by 4 m. Circle that word — that is the missing variable.
Find
We are required to find: Area of a rectangle 9 m by 4 m. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write A = ℓb with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Area of a rectangle 9 m by 4 m.
In other words — as if you have never seen this before
A=ℓ×b. Units squared.
2. What do we already know?
ℓ=9 m, b=4 m. Unknown: area.
3. Which method — and why this one?
A=ℓ×b. Units squared.
4. Step-by-step working
01 / 05
Write A = ℓb
Length times breadth.
A=ℓb
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Multiply
9×4=36 m².
A=36 m²
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
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.
04 / 05
Step F — Box the answer with its unit
36 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.
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 m²
Copy onto your answer sheet — in this order
Formula: A=ℓb
Answer: 36 m²
6. Check it like a marker
Perimeter would be 26 m. Area is 36 m². Different quantity, different units.
7. A trap first-timers fall into
13 m is a half-perimeter mix-up. 26 m is the perimeter. The paper asked for area.
24 · 2 Marks · Factorisation
Factorise x² − 25.
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 − 25.
Before any working — hunt first
Given
Numbers and units already in the sentence: 25. 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 − 25. Circle that word — that is the missing variable.
Find
We are required to find: Factorise x² − 25. 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 with a = x, b = 5. Then substitute the given, one line at a time, to get Factorise x² − 25.
In other words — as if you have never seen this before
Difference of squares with a = x, b = 5.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 25. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Difference of squares with a = x, b = 5.
4. Step-by-step working
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.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 25. 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 − 25. Circle that word — that is the missing variable.
Find: We are required to find: Factorise x² − 25. 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 with a = x, b = 5. Then substitute the given, one line at a time, to get Factorise x² − 25.
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).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 25. 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.
04 / 08
Step C — Name the method in words
Difference of squares with a = x, b = 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.
05 / 08
Working
Difference of squares with a = x, b = 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.
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.
07 / 08
Step F — Box the answer with its unit
(x−5)(x+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.
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−5)(x+5)
Copy onto your answer sheet — in this order
Answer: (x−5)(x+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…”
25 · 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
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.
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).
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.
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.
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.
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.
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.
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…”
26 · 3 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: 12. 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
12
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?
12
4. Step-by-step working
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.
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: 12. 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).
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.
04 / 08
Step C — Name the method in words
12
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.
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.
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.
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.
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…”
27 · 3 Marks · Surface area & volume
A square of side 6 cm. Area?
Formulas
Vcyl=πr²h
Cylinder volume
Notes: s=6 cm. Square.
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 square of side 6 cm. Area?
Before any working — hunt first
Given
Numbers and units already in the sentence: 6 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: Area. Circle that word — that is the missing variable.
Find
We are required to find: Area. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 36 cm² with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Area.
In other words — as if you have never seen this before
A=s². Units squared.
2. What do we already know?
s=6 cm. Square.
3. Which method — and why this one?
A=s². Units squared.
4. Step-by-step working
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.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 6 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: Area. Circle that word — that is the missing variable.
Find: We are required to find: Area. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write 36 cm² with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Area.
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).
03 / 08
Step B — Write the given in a column
s=6 cm. Square.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
A=s². Units squared.
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.
05 / 08
Square the side
6×6=36 cm².
36 cm²
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
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.
07 / 08
Step F — Box the answer with its unit
36 cm²
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.
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
36 cm²
Copy onto your answer sheet — in this order
Formula: 36 cm²
Answer: 36 cm²
6. Check it like a marker
Perimeter is 24 cm. Different asking-word.
7. A trap first-timers fall into
24 cm is perimeter. Area is squared.
28 · 2 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: 37. Then substitute the given, one line at a time, to get T₁₂ =.
In other words — as if you have never seen this before
37
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?
37
4. Step-by-step working
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.
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: 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).
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.
04 / 08
Step C — Name the method in words
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.
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.
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.
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.
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…”
29 · 2 Marks · Number patterns
Which number is irrational?
Number patterns
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
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.
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).
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.
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.
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.
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.
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.
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…”
30 · 2 Marks · Functions
2x+y=11, x−y=1. y=
Functions
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
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.
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).
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.
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.
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.
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.
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.
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…”