2025 · practice · Mathematics · Grade 10

Grade 10 Mathematics — Gauteng style practice

Notes

Answer all questions. Show working. Calculators allowed.

90 min · 111 Marks · 30 questions

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Sit it timed Formula sheet

Question breakdown

1.1 · 4 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: Difference of squares. 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
If you have never seen this before: Difference of squares. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 9. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Difference of squares.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 9. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Factorise fully: x² − 9. Circle that word — that is the missing variable. Find: We are required to find: Factorise fully: x² − 9. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Difference of squares. Then substitute the given, one line at a time, to get Factorise fully: x² − 9.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 9. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  Difference of squares.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Reason
  Difference of squares.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  (x−3)(x+3)
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
(x−3)(x+3)
Copy onto your answer sheet — in this order
Answer: (x−3)(x+3)
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
1.2 · 6 Marks · Analytical geometry
The line through (0; 1) and (2; 7). Gradient?
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: The line through (0; 1) and (2; 7). Gradient?
Before any working — hunt first
Given
Numbers and units already in the sentence: 0 · 1 · 2 · 7. 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: Gradient. Circle that word — that is the missing variable.
Find
We are required to find: Gradient. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: m = (7−1)(2−0)=3. Then substitute the given, one line at a time, to get Gradient.
In other words — as if you have never seen this before
If you have never seen this before: m = (7−1)(2−0)=3. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0 · 1 · 2 · 7. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
m=(7−1)(2−0)=3.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 0 · 1 · 2 · 7. 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: Gradient. Circle that word — that is the missing variable. Find: We are required to find: Gradient. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: m = (7−1)(2−0)=3. Then substitute the given, one line at a time, to get Gradient.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 0 · 1 · 2 · 7. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  m=(7−1)(2−0)=3.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Reason
  m=(7−1)(2−0)=3.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  3
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3
Copy onto your answer sheet — in this order
Answer: 3
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
2.1 · 8 Marks · Simple & compound interest
R5 000 at 8% p.a. simple interest for 3 years. Interest earned?
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: I = Pin = 5000×0. Then substitute the given, one line at a time, to get Interest earned.
In other words — as if you have never seen this before
If you have never seen this before: I = Pin = 5000×0.08×3 = 1200. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 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?
I=Pin=5000×0.08×3=1200.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 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: I = Pin = 5000×0. 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).
3. 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.
4. 04 / 08
  Step C — Name the method in words
  I=Pin=5000×0.08×3=1200.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Reason
  I=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.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  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.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
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…”
2.2 · 8 Marks · Trigonometry
sin θ = 513 in a right triangle. cos θ =
Formulas
sin θ=opphyp
Sine
tan θ=oppadj
Tangent
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 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: 3-4-5 scaled: 5-12-13. Then substitute the given, one line at a time, to get cos θ =.
In other words — as if you have never seen this before
If you have never seen this before: 3-4-5 scaled: 5-12-13. Adjacent = 12. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5/ · 13 in. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3-4-5 scaled: 5-12-13. Adjacent = 12.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 5/ · 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: 3-4-5 scaled: 5-12-13. 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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 5/ · 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.
4. 04 / 08
  Step C — Name the method in words
  3-4-5 scaled: 5-12-13. Adjacent = 12.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 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.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  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.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
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…”
3.1 · 12 Marks
Sequence 4; 9; 14; 19; … T₂₅=
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Sequence 4; 9; 14; 19; … T₂₅ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 9 · 14 · 19. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Sequence 4; 9; 14; 19; … T₂₅ =. Circle that word — that is the missing variable.
Find
We are required to find: Sequence 4; 9; 14; 19; … T₂₅ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: a=4, d=5. Then substitute the given, one line at a time, to get Sequence 4; 9; 14; 19; … T₂₅ =.
In other words — as if you have never seen this before
If you have never seen this before: a=4, d=5. T₂₅ = 4+24×5 = 124. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4 · 9 · 14 · 19. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
a=4, d=5. T₂₅=4+24×5=124.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 4 · 9 · 14 · 19. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Sequence 4; 9; 14; 19; … T₂₅ =. Circle that word — that is the missing variable. Find: We are required to find: Sequence 4; 9; 14; 19; … T₂₅ =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: a=4, d=5. Then substitute the given, one line at a time, to get Sequence 4; 9; 14; 19; … T₂₅ =.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 4 · 9 · 14 · 19. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  a=4, d=5. T₂₅=4+24×5=124.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Reason
  a=4, d=5. T₂₅=4+24×5=124.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  124
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
124
Copy onto your answer sheet — in this order
Answer: 124
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
3.2 · 12 Marks · Probability
P(red) from 3 red and 7 blue marbles?
Formulas
P(A)=n(A)n(S)
Classical probability
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: P(red) from 3 red and 7 blue marbles?
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 red · 7 blue. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(red) from 3 red and 7 blue marbles. Circle that word — that is the missing variable.
Find
We are required to find: P(red) from 3 red and 7 blue marbles. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3 favourable out of 10. Then substitute the given, one line at a time, to get P(red) from 3 red and 7 blue marbles.
In other words — as if you have never seen this before
If you have never seen this before: 3 favourable out of 10. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 red · 7 blue. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3 favourable out of 10.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 3 red · 7 blue. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(red) from 3 red and 7 blue marbles. Circle that word — that is the missing variable. Find: We are required to find: P(red) from 3 red and 7 blue marbles. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 3 favourable out of 10. Then substitute the given, one line at a time, to get P(red) from 3 red and 7 blue marbles.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 3 red · 7 blue. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  3 favourable out of 10.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Reason
  3 favourable out of 10.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  310
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
310
Copy onto your answer sheet — in this order
Answer: 310
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
7 · 3 Marks · Functions
A die is fair. P(rolling an even number)?
Formulas
y=mx+c
Straight line
Notes: A fair six-face die. Even faces: 2, 4, 6. That is three faces. Total faces: 6.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A die is fair. P(rolling an even number)?
Before any working — hunt first
Given
Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(rolling an even number). Circle that word — that is the missing variable.
Find
We are required to find: P(rolling an even number). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write P = 12 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives P(rolling an even number).
In other words — as if you have never seen this before
Probability = favourabletotal, when every face is equally likely.
2. What do we already know?
A fair six-face die. Even faces: 2, 4, 6. That is three faces. Total faces: 6.
3. Which method — and why this one?
Probability = favourabletotal, when every face is equally likely.
4. Step-by-step working
1. 01 / 05
  Count favourable
  Even numbers on a die: 2, 4 and 6. Three outcomes. Do not include 0 — dice do not have a 0.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
2. 02 / 05
  Divide
  P = 36. Simplify by 3: 12. Leaving 36 is not wrong, but NSC usually wants the simplest form.
  P=12
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
3. 03 / 05
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
4. 04 / 05
  Step F — Box the answer with its unit
  12
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
5. 05 / 05
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
12
Copy onto your answer sheet — in this order
Formula: P=12
Answer: 12
6. Check it like a marker
Odd would also be 12. Together they add to 1. Good.
7. A trap first-timers fall into
Writing 3, or 13 (thinking 2,4,6 out of the even “ideas”). Always divide by 6, the faces.
8 · 2 Marks · Probability
A die is fair. P(rolling a 6)?
Formulas
P(A)=n(A)n(S)
Classical probability
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A die is fair. P(rolling a 6)?
Before any working — hunt first
Given
Numbers and units already in the sentence: 6. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(rolling a 6). Circle that word — that is the missing variable.
Find
We are required to find: P(rolling a 6). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: One favourable outcome out of six faces. Then substitute the given, one line at a time, to get P(rolling a 6).
In other words — as if you have never seen this before
One favourable outcome out of six faces.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 6. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
One favourable outcome out of six faces.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 6. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(rolling a 6). Circle that word — that is the missing variable. Find: We are required to find: P(rolling a 6). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: One favourable outcome out of six faces. Then substitute the given, one line at a time, to get P(rolling a 6).
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 6. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  One favourable outcome out of six faces.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  One favourable outcome out of six faces.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  16
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
16
Copy onto your answer sheet — in this order
Answer: 16
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
9 · 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
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 2/ · 3 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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 2/ · 3 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.
4. 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.
5. 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.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  x=12
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
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…”
10 · 2 Marks
Expand (x + 5)(x − 2).
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Expand (x + 5)(x − 2).
Before any working — hunt first
Given
Numbers and units already in the sentence: 5 · 2. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x + 5)(x − 2). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 2).
In other words — as if you have never seen this before
x² + 3x − 10
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
x² + 3x − 10
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 5 · 2. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x + 5)(x − 2). Circle that word — that is the missing variable. Find: We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 2).
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 5 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  x² + 3x − 10
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  FOIL: x² − 2x + 5x − 10 = x² + 3x − 10. The middle terms add, they do not cancel.
  x²+3x−10
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  x² + 3x − 10
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
x² + 3x − 10
Copy onto your answer sheet — in this order
Formula: x² + 3x − 10
Answer: x² + 3x − 10
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
11 · 2 Marks · Exponents
2³×2²=
Formulas
aᵐ·aⁿ=aᵐ⁺ⁿ
Same base, add
a⁻ⁿ=1aⁿ
Negative exponent
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: 2³ × 2² =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2³ · 2². Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2³ × 2² =. Circle that word — that is the missing variable.
Find
We are required to find: 2³ × 2² =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Same base: add exponents. Then substitute the given, one line at a time, to get 2³ × 2² =.
In other words — as if you have never seen this before
Same base: add exponents. 3+2=5.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2³ · 2². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Same base: add exponents. 3+2=5.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 2³ · 2². Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2³ × 2² =. Circle that word — that is the missing variable. Find: We are required to find: 2³ × 2² =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Same base: add exponents. Then substitute the given, one line at a time, to get 2³ × 2² =.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 2³ · 2². Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  Same base: add exponents. 3+2=5.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  Same base: add exponents. 3+2=5.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  2⁵
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
2⁵
Copy onto your answer sheet — in this order
Answer: 2⁵
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
12 · 2 Marks · Functions
x + y = 10 and x − y = 2. x =
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
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 10 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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 10 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.
4. 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.
5. 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.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  6
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
6
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…”
13 · 2 Marks
Expand (x+3)(x+4)
Notes: Two binomials. Unknown: expanded trinomial.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Expand (x+3)(x+4)
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 · 4. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x+3)(x+4). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x+3)(x+4). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x²+4x+3x+12 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x+3)(x+4).
In other words — as if you have never seen this before
FOIL: First, Outer, Inner, Last. Then collect like terms.
2. What do we already know?
Two binomials. Unknown: expanded trinomial.
3. Which method — and why this one?
FOIL: First, Outer, Inner, Last. Then collect like terms.
4. Step-by-step working
1. 01 / 05
  FOIL
  x² + 4x + 3x + 12.
  x²+4x+3x+12
  Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
2. 02 / 05
  Collect
  x² + 7x + 12.
  x²+7x+12
  Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
3. 03 / 05
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
4. 04 / 05
  Step F — Box the answer with its unit
  x²+7x+12
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
5. 05 / 05
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
x²+7x+12
Copy onto your answer sheet — in this order
Formula: x²+4x+3x+12
Answer: x²+7x+12
6. Check it like a marker
At x=1: (4)(5)=20 and 1+7+12=20. Matches.
7. A trap first-timers fall into
x²+12 forgets the middle terms. They do not cancel — both plus.
14 · 3 Marks
Solve x²−5x+6=0
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 x² − 5x + 6 = 0
Before any working — hunt first
Given
Numbers and units already in the sentence: 5x · 6 · 0. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solve x² − 5x + 6 = 0. Circle that word — that is the missing variable.
Find
We are required to find: Solve x² − 5x + 6 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: (x−2)(x−3)=0. Then substitute the given, one line at a time, to get Solve x² − 5x + 6 = 0.
In other words — as if you have never seen this before
(x−2)(x−3)=0.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5x · 6 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
(x−2)(x−3)=0.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 5x · 6 · 0. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solve x² − 5x + 6 = 0. Circle that word — that is the missing variable. Find: We are required to find: Solve x² − 5x + 6 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: (x−2)(x−3)=0. Then substitute the given, one line at a time, to get Solve x² − 5x + 6 = 0.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 5x · 6 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  (x−2)(x−3)=0.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  (x−2)(x−3)=0.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  x=2 or 3
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
x=2 or 3
Copy onto your answer sheet — in this order
Answer: x=2 or 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…”
15 · 3 Marks · Analytical geometry
Distance between (0; 0) and (6; 8) is
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Distance between (0; 0) and (6; 8) is
Before any working — hunt first
Given
Numbers and units already in the sentence: 0 · 0 · 6 · 8. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance between (0; 0) and (6; 8) is. Circle that word — that is the missing variable.
Find
We are required to find: Distance between (0; 0) and (6; 8) is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: √(36+64)=10. Then substitute the given, one line at a time, to get Distance between (0; 0) and (6; 8) is.
In other words — as if you have never seen this before
36+64=10. A 6-8-10 triangle.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0 · 0 · 6 · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
36+64=10. A 6-8-10 triangle.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 0 · 0 · 6 · 8. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance between (0; 0) and (6; 8) is. Circle that word — that is the missing variable. Find: We are required to find: Distance between (0; 0) and (6; 8) is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: √(36+64)=10. Then substitute the given, one line at a time, to get Distance between (0; 0) and (6; 8) is.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 0 · 0 · 6 · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  36+64=10. A 6-8-10 triangle.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  36+64=10. A 6-8-10 triangle.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  10
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
10
Copy onto your answer sheet — in this order
Answer: 10
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
16 · 3 Marks · Simple & compound interest
Simple interest on R4 000 at 8% p.a. for 3 years.
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
Notes: P = R4 000 (the starting money). i = 8% = 0.08 per year. n = 3 years. Unknown: interest I, not the amount.
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 R4 000 at 8% p.a. for 3 years.
Before any working — hunt first
Given
Numbers and units already in the sentence: R4 · 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: for 3 years. Circle that word — that is the missing variable.
Find
We are required to find: for 3 years. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write i = 0.08 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives for 3 years.
In other words — as if you have never seen this before
Simple interest: I = P × i × n. The interest is a rectangle — principal, rate, time, multiplied.
2. What do we already know?
P = R4 000 (the starting money). i = 8% = 0.08 per year. n = 3 years. Unknown: interest I, not the amount.
3. Which method — and why this one?
Simple interest: I = P × i × n. The interest is a rectangle — principal, rate, time, multiplied.
4. Step-by-step working
1. 01 / 05
  Percent to decimal
  8% means 8 per hundred = 8100=0.08. Never leave the 8 sitting next to 4000.
  i=0.08
  Why this step: If you multiply by 8 you are charging 800% a year. First-timers do this when they are rushing.
2. 02 / 05
  Multiply
  I=4000×0.08×3. First 4000×0.08=320 (one year’s interest). Then 320×3=960.
  I=960
  Why this step: Doing one year first is a gift: you can see whether R320 on R4 000 feels like 8% (it does).
3. 03 / 05
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
4. 04 / 05
  Step F — Box the answer with its unit
  R960
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
5. 05 / 05
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
R960
Copy onto your answer sheet — in this order
Formula: i=0.08
Answer: R960
6. Check it like a marker
Amount A = 4000 + 960 = 4960. That is an option — but the paper asked for interest, not amount.
7. A trap first-timers fall into
Picking R4 960. That is A, the total you have after 3 years. The question said “interest on”.
17 · 3 Marks · Analytical geometry
Gradient of the line through (1; 2) and (5; 10)
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
Notes: Point A(1; 2) and B(5; 10). Unknown: m.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Gradient of the line through (1; 2) and (5; 10)
In other words — as if you have never seen this before
m = (y₂ − y₁)/(x₂ − x₁). Rise over run, same order on top and bottom.
2. What do we already know?
Point A(1; 2) and B(5; 10). Unknown: m.
3. Which method — and why this one?
m = (y₂ − y₁)/(x₂ − x₁). Rise over run, same order on top and bottom.
4. Step-by-step working
1. 01 / 05
  Write the formula
  m=(y₂ − y₁)(x₂ − x₁).
  m=(y₂−y₁)(x₂−x₁)
  Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
2. 02 / 05
  Substitute
  m=(10 − 2)(5 − 1)=84=2.
  m=2
  Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
3. 03 / 05
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
4. 04 / 05
  Step F — Box the answer with its unit
  2
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
5. 05 / 05
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
2
Copy onto your answer sheet — in this order
Formula: m=(y₂−y₁)(x₂−x₁)
Answer: 2
6. Check it like a marker
From x = 1 to 5 we add 4. From y = 2 to 10 we add 8. 84=2.
7. A trap first-timers fall into
Do not swap to (x₂−x₁)/(y₂−y₁). That is run over rise, the reciprocal.
18 · 2 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
1. 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.
2. 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.
3. 03 / 05
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
4. 04 / 05
  Step F — Box the answer with its unit
  x=4
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
5. 05 / 05
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
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.
19 · 2 Marks
10% of R250
Notes: 10% of 250. Percent means hundredths.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 10% of R250
Before any working — hunt first
Given
Numbers and units already in the sentence: 10% · R250. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 10% of R250. Circle that word — that is the missing variable.
Find
We are required to find: 10% of R250. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write R25 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 10% of R250.
In other words — as if you have never seen this before
10% = 0.1. Multiply. Or 25010.
2. What do we already know?
10% of 250. Percent means hundredths.
3. Which method — and why this one?
10% = 0.1. Multiply. Or 25010.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 10% · R250. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 10% of R250. Circle that word — that is the missing variable. Find: We are required to find: 10% of R250. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: Write R25 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 10% of R250.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  10% of 250. Percent means hundredths.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  10% = 0.1. Multiply. Or 25010.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Convert then multiply
  0.1×250=25.
  R25
  Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  R25
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
R25
Copy onto your answer sheet — in this order
Formula: R25
Answer: R25
6. Check it like a marker
10 × R25 = R250. Recovers the whole.
7. A trap first-timers fall into
R2.50 is 1%. R2500 is 1000%.
20 · 2 Marks
A grain truck from Bloemfontein covers 240 km at 80 kmh. Time?
Notes: Distance Δx = 240 km. Speed v = 80 kmh. Unknown: time t.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A grain truck from Bloemfontein covers 240 km at 80 kmh. Time?
Before any working — hunt first
Given
Numbers and units already in the sentence: 240 km · 80 kmh. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Time. Circle that word — that is the missing variable.
Find
We are required to find: Time. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write t = Δxv with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Time.
In other words — as if you have never seen this before
t = distancespeed. Units: km(km/h) leaves hours.
2. What do we already know?
Distance Δx = 240 km. Speed v = 80 kmh. Unknown: time t.
3. Which method — and why this one?
t = distancespeed. Units: km(km/h) leaves hours.
4. Step-by-step working
1. 01 / 05
  Write the formula
  t=Δxv.
  t=Δxv
  Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
2. 02 / 05
  Substitute
  t=24080=3 hours.
  t=3 h
  Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
3. 03 / 05
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
4. 04 / 05
  Step F — Box the answer with its unit
  3 h
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
5. 05 / 05
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3 h
Copy onto your answer sheet — in this order
Formula: t=Δxv
Answer: 3 h
6. Check it like a marker
80 kmh × 3 h = 240 km. Matches the given distance.
7. A trap first-timers fall into
Do not multiply 240 × 80. Speed is not added to distance.
21 · 3 Marks · Statistics
Data 1,2,2,3,12. The median is
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
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 1,2 · 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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 1,2 · 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.
4. 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.
5. 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.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  2
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
2
Copy onto your answer sheet — in this order
Answer: 2
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
22 · 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
1. 01 / 07
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 07
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 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.
3. 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.
4. 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.
5. 05 / 07
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
6. 06 / 07
  Step F — Box the answer with its unit
  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.
7. 07 / 07
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
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…”
23 · 3 Marks · Simple & compound interest
R1000 at 10% p.a. compound for 2 years. Amount A =
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: R1000 at 10% p.a. compound for 2 years. Amount A =
Before any working — hunt first
Given
Numbers and units already in the sentence: R1000 at · 10% · 2 years. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Amount A =. Circle that word — that is the missing variable.
Find
We are required to find: Amount A =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: A=P(1+i)ⁿ=1000(1. Then substitute the given, one line at a time, to get Amount A =.
In other words — as if you have never seen this before
A=P(1+i)ⁿ=1000(1.1)²=1210.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R1000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
A=P(1+i)ⁿ=1000(1.1)²=1210.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R1000 at · 10% · 2 years. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Amount A =. Circle that word — that is the missing variable. Find: We are required to find: Amount A =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: A=P(1+i)ⁿ=1000(1. Then substitute the given, one line at a time, to get Amount A =.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: R1000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  A=P(1+i)ⁿ=1000(1.1)²=1210.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  A=P(1+i)ⁿ=1000(1.1)²=1210.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  R1210
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
R1210
Copy onto your answer sheet — in this order
Answer: R1210
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
24 · 4 Marks · Probability
Two coins. P(two heads)=
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: Two coins. P(two heads) =
Before any working — hunt first
Given
Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(two heads) =. Circle that word — that is the missing variable.
Find
We are required to find: P(two heads) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: HH, HT, TH, TT — one of four. Then substitute the given, one line at a time, to get P(two heads) =.
In other words — as if you have never seen this before
HH, HT, TH, TT — one of four.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
HH, HT, TH, TT — one of four.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(two heads) =. Circle that word — that is the missing variable. Find: We are required to find: P(two heads) =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: HH, HT, TH, TT — one of four. Then substitute the given, one line at a time, to get P(two heads) =.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  HH, HT, TH, TT — one of four.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  HH, HT, TH, TT — one of four.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  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.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
14
Copy onto your answer sheet — in this order
Answer: 14
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
25 · 2 Marks · Factorisation
Factorise x² − 16.
Formulas
a²−b²=(a − b)(a + b)
Difference of squares
x²+(p+q)x+pq=(x+p)(x+q)
Trinomial
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Factorise x² − 16.
Before any working — hunt first
Given
Numbers and units already in the sentence: 16. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Factorise x² − 16. Circle that word — that is the missing variable.
Find
We are required to find: Factorise x² − 16. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Difference of squares: a² − b² = (a−b)(a+b). Then substitute the given, one line at a time, to get Factorise x² − 16.
In other words — as if you have never seen this before
Difference of squares: a² − b² = (a−b)(a+b).
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 16. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Difference of squares: a² − b² = (a−b)(a+b).
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 16. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Factorise x² − 16. Circle that word — that is the missing variable. Find: We are required to find: Factorise x² − 16. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Difference of squares: a² − b² = (a−b)(a+b). Then substitute the given, one line at a time, to get Factorise x² − 16.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 16. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  Difference of squares: a² − b² = (a−b)(a+b).
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  Difference of squares: a² − b² = (a−b)(a+b).
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  (x−4)(x+4)
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
(x−4)(x+4)
Copy onto your answer sheet — in this order
Answer: (x−4)(x+4)
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
26 · 2 Marks
3²×3³=
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 × 3³ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3² · 3³. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 3² × 3³ =. Circle that word — that is the missing variable.
Find
We are required to find: 3² × 3³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3⁵. Then substitute the given, one line at a time, to get 3² × 3³ =.
In other words — as if you have never seen this before
3⁵
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3² · 3³. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3⁵
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 3² · 3³. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 3² × 3³ =. Circle that word — that is the missing variable. Find: We are required to find: 3² × 3³ =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 3⁵. Then substitute the given, one line at a time, to get 3² × 3³ =.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 3² · 3³. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  3⁵
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  Same base: add the indices. 2 + 3 = 5, so 3⁵. Do not multiply the bases.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  3⁵
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3⁵
Copy onto your answer sheet — in this order
Answer: 3⁵
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
27 · 3 Marks · Statistics
Data 2; 5; 5; 8. Mean=
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
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 2 · 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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 2 · 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.
4. 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.
5. 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.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  5
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
5
Copy onto your answer sheet — in this order
Answer: 5
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
28 · 2 Marks
Tₙ=3n+1. T₁₂=
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Tₙ = 3n + 1. T₁₂ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3n · 1. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: T₁₂ =. Circle that word — that is the missing variable.
Find
We are required to find: T₁₂ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 37. Then substitute the given, one line at a time, to get T₁₂ =.
In other words — as if you have never seen this before
37
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3n · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
37
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 3n · 1. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: T₁₂ =. Circle that word — that is the missing variable. Find: We are required to find: T₁₂ =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 37. Then substitute the given, one line at a time, to get T₁₂ =.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 3n · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  37
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Reason
  3(12)+1=37.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  37
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
37
Copy onto your answer sheet — in this order
Answer: 37
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
29 · 2 Marks
A Polokwane taxi covers 210 km at 70 kmh. Time in hours?
Notes: Distance s = 210 km. Speed v = 70 kmh. Unknown: time t in hours.
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 Polokwane taxi covers 210 km at 70 kmh. Time in hours?
Before any working — hunt first
Given
Numbers and units already in the sentence: 210 km · 70 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 in hours. Circle that word — that is the missing variable.
Find
We are required to find: Time in hours. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write t = sv with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Time in hours.
In other words — as if you have never seen this before
Time is distance divided by speed. In words: “how many seventies fit into 210?”
2. What do we already know?
Distance s = 210 km. Speed v = 70 kmh. Unknown: time t in hours.
3. Which method — and why this one?
Time is distance divided by speed. In words: “how many seventies fit into 210?”
4. Step-by-step working
1. 01 / 06
  Write the formula in words
  time = distancespeed. Symbols: t = sv.
  t=sv
  Why this step: We write the formula empty first so the marker can award a method mark even if a number later slips.
2. 02 / 06
  Substitute, do not calculate yet
  t = 21070. Both numbers are in km and kmh, so the km cancel and hours remain.
  t=21070
  Why this step: Matching units is the whole trick. If the paper had given 70 km/h and 210 m you would convert first.
3. 03 / 06
  Calculate one step
  21070=3. So t=3 h. Check: 3×70=210 km. It lands exactly.
  t=3 h
  Why this step: The reverse multiply is the marker’s favourite check. If it does not rebuild 210, you divided the wrong way round.
4. 04 / 06
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
5. 05 / 06
  Step F — Box the answer with its unit
  3 h
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
6. 06 / 06
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3 h
Copy onto your answer sheet — in this order
Formula: t=sv
Answer: 3 h
6. Check it like a marker
3 × 70 = 210. Units are hours, which is what was asked. 14 h would be 21015 — a calculator slip.
7. A trap first-timers fall into
Doing 70210=0.33 h. That is speeddistance, which is the reciprocal of time. Always say the formula in words first.
30 · 4 Marks
(3²)³=
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: (3²)³ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3². Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: (3²)³ =. Circle that word — that is the missing variable.
Find
We are required to find: (3²)³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Power of a power: 3⁶ = 729. Then substitute the given, one line at a time, to get (3²)³ =.
In other words — as if you have never seen this before
Power of a power: 3⁶ = 729.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Power of a power: 3⁶ = 729.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 3². Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: (3²)³ =. Circle that word — that is the missing variable. Find: We are required to find: (3²)³ =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Power of a power: 3⁶ = 729. Then substitute the given, one line at a time, to get (3²)³ =.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 3². Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  Power of a power: 3⁶ = 729.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  Power of a power: 3⁶ = 729.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  729
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
729
Copy onto your answer sheet — in this order
Answer: 729
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”