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.
1.2 · 10 Marks
Solve 5x−3=17
Notes: 5x − 3 on the left, 17 on the right.
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 5x − 3 = 17
Before any working — hunt first
Given
Numbers and units already in the sentence: 5x · 3 · 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 5x − 3 = 17. Circle that word — that is the missing variable.
Find
We are required to find: Solve 5x − 3 = 17. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 5x = 20 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Solve 5x − 3 = 17.
In other words — as if you have never seen this before
Undo −3 first (add 3), then undo ×5 (divide by 5). Reverse BODMAS.
2. What do we already know?
5x − 3 on the left, 17 on the right.
3. Which method — and why this one?
Undo −3 first (add 3), then undo ×5 (divide by 5). Reverse BODMAS.
4. Step-by-step working
01 / 05
Add 3
5x=20.
5x=20
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 5
x=4.
x=4
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
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: 5x=20
Answer: x=4
6. Check it like a marker
5(4)−3=20−3=17. Both sides match.
7. A trap first-timers fall into
Dividing by 5 first splits the −3 and makes 1 − 35. Do not.
2.1 · 10 Marks · Surface area & volume
Area of a rectangle 8 m by 3 m
Formulas
Vcyl=πr²h
Cylinder volume
Notes: l=8 m. b=3 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 8 m by 3 m
Before any working — hunt first
Given
Numbers and units already in the sentence: 8 m · 3 m. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Area of a rectangle 8 m by 3 m. Circle that word — that is the missing variable.
Find
We are required to find: Area of a rectangle 8 m by 3 m. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write A = 24 m² 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 8 m by 3 m.
In other words — as if you have never seen this before
A=l×b. Units squared.
2. What do we already know?
l=8 m. b=3 m. Unknown: area.
3. Which method — and why this one?
A=l×b. 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: 8 m · 3 m. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Area of a rectangle 8 m by 3 m. Circle that word — that is the missing variable.
Find: We are required to find: Area of a rectangle 8 m by 3 m. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write A = 24 m² 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 8 m by 3 m.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
l=8 m. b=3 m. Unknown: area.
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=l×b. 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
Multiply
A=8×3=24 m².
A=24 m²
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
24 m²
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
24 m²
Copy onto your answer sheet — in this order
Formula: A=24 m²
Answer: 24 m²
6. Check it like a marker
Perimeter would be 22 m. The paper asked area, not perimeter.
7. A trap first-timers fall into
22 m is the perimeter. Read the asking-word: area.
2.2 · 12 Marks · Probability
3²×3⁴=
Formulas
P(A)=n(A)n(S)
Classical probability
Notes: Same base 3. Indices 2 and 4. Product.
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 3⁶ 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
Same base, multiply: add the indices.
2. What do we already know?
Same base 3. Indices 2 and 4. Product.
3. Which method — and why this one?
Same base, multiply: add the indices.
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 · 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 3⁶ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 3² × 3⁴ =.
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
Same base 3. Indices 2 and 4. Product.
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
Same base, multiply: add the indices.
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
Add indices
2+4=6, so 3⁶.
3⁶
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
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
Copy onto your answer sheet — in this order
Formula: 3⁶
Answer: 3⁶
6. Check it like a marker
9×81=729=3⁶.
7. A trap first-timers fall into
3⁸ multiplies the indices. 9⁶ multiplies the bases. Both wrong.
5 · 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…”
6 · 2 Marks · Trigonometry
sin θ = 513 in a right triangle. 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: sin θ = 513 in a right triangle. cos θ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 5/ · 13 in. 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: cos θ =. Circle that word — that is the missing variable.
Find
We are required to find: 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: 1213. Then substitute the given, one line at a time, to get cos θ =.
In other words — as if you have never seen this before
1213
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5/ · 13 in. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
1213
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: 5/ · 13 in. 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: cos θ =. Circle that word — that is the missing variable.
Find: We are required to find: 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: 1213. Then substitute the given, one line at a time, to get 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: 5/ · 13 in. 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
1213
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
3-4-5 scaled: 5-12-13. Adjacent = 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.
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
1213
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
1213
Copy onto your answer sheet — in this order
Answer: 1213
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
7 · 2 Marks · 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…”
8 · 2 Marks · Number patterns
Solve x + 4 > 10.
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: Solve x + 4 > 10.
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 10. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solve x + 4 > 10. Circle that word — that is the missing variable.
Find
We are required to find: Solve x + 4 > 10. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Subtract 4: x > 6. Then substitute the given, one line at a time, to get Solve x + 4 > 10.
In other words — as if you have never seen this before
Subtract 4: x > 6. Open circle on the number line.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4 · 10. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Subtract 4: x > 6. Open circle on the number line.
4. Step-by-step working
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 · 10. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solve x + 4 > 10. Circle that word — that is the missing variable.
Find: We are required to find: Solve x + 4 > 10. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Subtract 4: x > 6. Then substitute the given, one line at a time, to get Solve x + 4 > 10.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 4 · 10. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Subtract 4: x > 6. Open circle on the number line.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Subtract 4: x > 6. Open circle on the number line.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
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…”
9 · 2 Marks · Factorisation
Factorise x² − 16.
Formulas
a²−b²=(a − b)(a + b)
Difference of squares
x²+(p+q)x+pq=(x+p)(x+q)
Trinomial
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Factorise x² − 16.
Before any working — hunt first
Given
Numbers and units already in the sentence: 16. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Factorise x² − 16. Circle that word — that is the missing variable.
Find
We are required to find: Factorise x² − 16. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Difference of squares: a² − b² = (a−b)(a+b). Then substitute the given, one line at a time, to get Factorise x² − 16.
In other words — as if you have never seen this before
Difference of squares: a² − b² = (a−b)(a+b).
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 16. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Difference of squares: a² − b² = (a−b)(a+b).
4. Step-by-step working
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…”
10 · 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…”
11 · 3 Marks · Analytical geometry
Distance (1; 1) to (4; 5)
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 (1; 1) to (4; 5)
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 1 · 4 · 5. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance (1; 1) to (4; 5). Circle that word — that is the missing variable.
Find
We are required to find: Distance (1; 1) to (4; 5). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 5. Then substitute the given, one line at a time, to get Distance (1; 1) to (4; 5).
In other words — as if you have never seen this before
5
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 1 · 4 · 5. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
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: 1 · 1 · 4 · 5. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance (1; 1) to (4; 5). Circle that word — that is the missing variable.
Find: We are required to find: Distance (1; 1) to (4; 5). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 5. Then substitute the given, one line at a time, to get Distance (1; 1) to (4; 5).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1 · 1 · 4 · 5. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
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
Reason
√9+16=5.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
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
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
5
Copy onto your answer sheet — in this order
Answer: 5
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
12 · 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…”
13 · 2 Marks · Probability
A die is fair. P(rolling a 6)?
Formulas
P(A)=n(A)n(S)
Classical probability
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A die is fair. P(rolling a 6)?
Before any working — hunt first
Given
Numbers and units already in the sentence: 6. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(rolling a 6). Circle that word — that is the missing variable.
Find
We are required to find: P(rolling a 6). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: One favourable outcome out of six faces. Then substitute the given, one line at a time, to get P(rolling a 6).
In other words — as if you have never seen this before
One favourable outcome out of six faces.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 6. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
One favourable outcome out of six faces.
4. Step-by-step working
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. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(rolling a 6). Circle that word — that is the missing variable.
Find: We are required to find: P(rolling a 6). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: One favourable outcome out of six faces. Then substitute the given, one line at a time, to get P(rolling a 6).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 6. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
One favourable outcome out of six faces.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
One favourable outcome out of six faces.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
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
16
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
16
Copy onto your answer sheet — in this order
Answer: 16
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
14 · 2 Marks · Statistics
Mean of 4, 6, 8, 10
Statistics
Formulas
x̄=Σxn
Mean
Notes: Four numbers: 4, 6, 8, 10. Unknown: arithmetic 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 4, 6, 8, 10
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 6 · 8 · 10. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Mean of 4, 6, 8, 10. Circle that word — that is the missing variable.
Find
We are required to find: Mean of 4, 6, 8, 10. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write sum = 28 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Mean of 4, 6, 8, 10.
In other words — as if you have never seen this before
Mean=sumcount.
2. What do we already know?
Four numbers: 4, 6, 8, 10. Unknown: arithmetic mean.
3. Which method — and why this one?
Mean=sumcount.
4. Step-by-step working
01 / 05
Add
4+6+8+10=28.
sum=28
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Divide
284=7.
mean=7
Why this step: Write the formula before numbers. The memo awards a method mark for the law 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
7
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
7
Copy onto your answer sheet — in this order
Formula: sum=28
Answer: 7
6. Check it like a marker
The numbers sit equally around 7. 4 and 10, 6 and 8.
7. A trap first-timers fall into
28 is the sum, not the mean. Do not forget to divide.
15 · 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…”
16 · 2 Marks · Analytical geometry
Gradient of the line through (2; 3) and (6; 11)
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: Gradient of the line through (2; 3) and (6; 11)
In other words — as if you have never seen this before
2
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 3 · 6 · 11. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
2
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
Copy these onto the left of your page, one per line, with units: 2 · 3 · 6 · 11. 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.
03 / 07
Step C — Name the method in words
2
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
04 / 07
Working
m = (11 − 3)/(6 − 2) = 84=2. Rise over run, top minus bottom in the same order.
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.
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
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.
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
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…”
17 · 2 Marks · Simple & compound interest
R5 000 at 8% p.a. simple interest for 3 years. Interest earned?
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: R5 000 at 8% p.a. simple interest for 3 years. Interest earned?
Before any working — hunt first
Given
Numbers and units already in the sentence: R5 · 000 at · 8% · 3 years. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Interest earned. Circle that word — that is the missing variable.
Find
We are required to find: Interest earned. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: R1 200. Then substitute the given, one line at a time, to get Interest earned.
In other words — as if you have never seen this before
R1 200
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R5 · 000 at · 8% · 3 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R1 200
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: R5 · 000 at · 8% · 3 years. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Interest earned. Circle that word — that is the missing variable.
Find: We are required to find: Interest earned. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: R1 200. Then substitute the given, one line at a time, to get Interest earned.
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: R5 · 000 at · 8% · 3 years. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
R1 200
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
I=Pin=5000×0.08×3=1200.
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
R1 200
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
R1 200
Copy onto your answer sheet — in this order
Answer: R1 200
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 · 3 Marks
When you divide −2x ≥ 8 by −2, the inequality
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: When you divide −2x ≥ 8 by −2, the inequality
In other words — as if you have never seen this before
Dividing by a negative reverses ≥ to ≤. 8/−2=−4.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2x · 8 by · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Dividing by a negative reverses ≥ to ≤. 8/−2=−4.
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
Copy these onto the left of your page, one per line, with units: 2x · 8 by · 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.
03 / 07
Step C — Name the method in words
Dividing by a negative reverses ≥ to ≤. 8/−2=−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.
04 / 07
Working
Dividing by a negative reverses ≥ to ≤. 8/−2=−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.
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
flips: 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.
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
flips: x ≤ −4
Copy onto your answer sheet — in this order
Answer: flips: 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…”
19 · 2 Marks · Simple & compound interest
Simple interest on R2000 at 10% for 2 years is
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Simple interest on R2000 at 10% for 2 years is
In other words — as if you have never seen this before
I=Pin=2000×0.1×2=400.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R2000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
I=Pin=2000×0.1×2=400.
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
Copy these onto the left of your page, one per line, with units: R2000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
03 / 07
Step C — Name the method in words
I=Pin=2000×0.1×2=400.
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
Working
I=Pin=2000×0.1×2=400.
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.
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
R400
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
R400
Copy onto your answer sheet — in this order
Answer: R400
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
A taxi from Gqeberha to Mthatha is 480 km at 80 kmh. Time?
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A taxi from Gqeberha to Mthatha is 480 km at 80 kmh. Time?
Before any working — hunt first
Given
Numbers and units already in the sentence: 480 km · 80 kmh. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Time. Circle that word — that is the missing variable.
Find
We are required to find: Time. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 6 h. Then substitute the given, one line at a time, to get Time.
In other words — as if you have never seen this before
6 h
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 480 km · 80 kmh. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
6 h
4. Step-by-step working
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: 480 km · 80 kmh. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Time. Circle that word — that is the missing variable.
Find: We are required to find: Time. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 6 h. Then substitute the given, one line at a time, to get Time.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 480 km · 80 kmh. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
6 h
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
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 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.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
6 h
Copy onto your answer sheet — in this order
Answer: 6 h
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
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 · 2 Marks
2⁻²=
Notes: Negative exponent on 2.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 2⁻² =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2⁻². Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2⁻² =. Circle that word — that is the missing variable.
Find
We are required to find: 2⁻² =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write a⁻ⁿ = 1aⁿ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 2⁻² =.
In other words — as if you have never seen this before
a⁻ⁿ=1aⁿ. 2⁻²=12²=14.
2. What do we already know?
Negative exponent on 2.
3. Which method — and why this one?
a⁻ⁿ=1aⁿ. 2⁻²=12²=14.
4. Step-by-step working
01 / 05
Write the law
A negative index means reciprocal.
a⁻ⁿ=1aⁿ
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Evaluate
14=14.
14
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
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
14
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
14
Copy onto your answer sheet — in this order
Formula: a⁻ⁿ=1aⁿ
Answer: 14
6. Check it like a marker
2²=4, so 2⁻² is the reciprocal 14. Not negative 4.
7. A trap first-timers fall into
The minus is on the exponent, not on the 2. 2⁻² is not −4.
23 · 3 Marks · Statistics
Data 1,2,2,3,12. The median 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: Data 1,2,2,3,12. The median is
Before any working — hunt first
Given
Numbers and units already in the sentence: 1,2 · 2,3 · 12. 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: The median is. Circle that word — that is the missing variable.
Find
We are required to find: The median is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Middle of ordered list is 2. Then substitute the given, one line at a time, to get The median is.
In other words — as if you have never seen this before
Middle of ordered list is 2.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1,2 · 2,3 · 12. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Middle of ordered list is 2.
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: 1,2 · 2,3 · 12. 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: The median is. Circle that word — that is the missing variable.
Find: We are required to find: The median is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Middle of ordered list is 2. Then substitute the given, one line at a time, to get The median 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: 1,2 · 2,3 · 12. 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
Middle of ordered list is 2.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Middle of ordered list is 2.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
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…”
24 · 4 Marks · Surface area & volume
A cylinder r = 3 cm, h = 10 cm. Volume in cm³ (use π = 3.14)
Formulas
Vcyl=πr²h
Cylinder volume
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A cylinder r = 3 cm, h = 10 cm. Volume in cm³ (use π = 3.14)
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 cm · 10 cm · 3.14. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 14). Circle that word — that is the missing variable.
Find
We are required to find: 14). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: V = πr²h = 3. Then substitute the given, one line at a time, to get 14).
In other words — as if you have never seen this before
V=πr²h=3.14×9×10=282.6 cm³.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 cm · 10 cm · 3.14. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
V=πr²h=3.14×9×10=282.6 cm³.
4. Step-by-step working
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 cm · 10 cm · 3.14. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 14). Circle that word — that is the missing variable.
Find: We are required to find: 14). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: V = πr²h = 3. Then substitute the given, one line at a time, to get 14).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3 cm · 10 cm · 3.14. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
V=πr²h=3.14×9×10=282.6 cm³.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
V=πr²h=3.14×9×10=282.6 cm³.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
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
282.6
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
282.6
Copy onto your answer sheet — in this order
Answer: 282.6
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
25 · 2 Marks · 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…”
26 · 2 Marks
Expand (x + 5)(x − 2).
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Expand (x + 5)(x − 2).
Before any working — hunt first
Given
Numbers and units already in the sentence: 5 · 2. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x + 5)(x − 2). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 2).
In other words — as if you have never seen this before
x² + 3x − 10
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
x² + 3x − 10
4. Step-by-step working
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: 5 · 2. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x + 5)(x − 2). Circle that word — that is the missing variable.
Find: We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 2).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 5 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
x² + 3x − 10
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
FOIL: x² − 2x + 5x − 10 = x² + 3x − 10. The middle terms add, they do not cancel.
x²+3x−10
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
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
x² + 3x − 10
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
x² + 3x − 10
Copy onto your answer sheet — in this order
Formula: x² + 3x − 10
Answer: x² + 3x − 10
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
27 · 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…”
28 · 2 Marks
Expand (x+4)(x−1).
Notes: Two brackets: (x+4)(x−1).
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Expand (x+4)(x−1).
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 1. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x+4)(x−1). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x+4)(x−1). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x² − x + 4x − 4 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x+4)(x−1).
In other words — as if you have never seen this before
FOIL: First, Outer, Inner, Last. Then collect like terms.
2. What do we already know?
Two brackets: (x+4)(x−1).
3. Which method — and why this one?
FOIL: First, Outer, Inner, Last. Then collect like terms.
4. Step-by-step working
01 / 05
FOIL
x·x=x². x·(−1)=−x. 4·x=4x. 4·(−1)=−4.
x²−x+4x−4
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Collect
−x+4x=3x. So x²+3x−4.
x²+3x−4
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
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 + 3x − 4
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
x² + 3x − 4
Copy onto your answer sheet — in this order
Formula: x² − x + 4x − 4
Answer: x² + 3x − 4
6. Check it like a marker
Let x=1: left (5)(0)=0. Right 1+3−4=0. Matches.
7. A trap first-timers fall into
The middle terms add, they do not cancel. Cancelling would need +x and −x.
29 · 2 Marks
Solve 23 x=8.
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 23 x = 8.
Before any working — hunt first
Given
Numbers and units already in the sentence: 2/ · 3 x · 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: Solve 23 x = 8. Circle that word — that is the missing variable.
Find
We are required to find: Solve 23 x = 8. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Multiply both sides by 32. Then substitute the given, one line at a time, to get Solve 23 x = 8.
In other words — as if you have never seen this before
Multiply both sides by 32. x = 8 × 32=12. The 23 is a stacked fraction times x — not 2 over 3x.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2/ · 3 x · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Multiply both sides by 32. x = 8 × 32=12. The 23 is a stacked fraction times x — not 2 over 3x.
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/ · 3 x · 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: Solve 23 x = 8. Circle that word — that is the missing variable.
Find: We are required to find: Solve 23 x = 8. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Multiply both sides by 32. Then substitute the given, one line at a time, to get Solve 23 x = 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: 2/ · 3 x · 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
Multiply both sides by 32. x = 8 × 32=12. The 23 is a stacked fraction times x — not 2 over 3x.
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
Multiply both sides by 32. x = 8 × 32=12. The 23 is a stacked fraction times x — not 2 over 3x.
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=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
x=12
Copy onto your answer sheet — in this order
Answer: x=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…”
30 · 3 Marks · Statistics
Data 2; 5; 5; 8. Mean=
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: Data 2; 5; 5; 8. Mean =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 5 · 5 · 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: Mean =. Circle that word — that is the missing variable.
Find
We are required to find: Mean =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: (2+5+5+8)4=5. Then substitute the given, one line at a time, to get Mean =.
In other words — as if you have never seen this before
(2+5+5+8)4=5.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 5 · 5 · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
(2+5+5+8)4=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: 2 · 5 · 5 · 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: Mean =. Circle that word — that is the missing variable.
Find: We are required to find: Mean =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: (2+5+5+8)4=5. Then substitute the given, one line at a time, to get Mean =.
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 · 5 · 5 · 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
(2+5+5+8)4=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
(2+5+5+8)4=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
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
5
Copy onto your answer sheet — in this order
Answer: 5
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”