2025 · practice · Mathematical Literacy · Grade 11

Grade 11 Mathematical Literacy — Western Cape practice

Notes

Answer every question. Show the formula, the substitution, and the answer with units. Calculators allowed. These are original practice papers in the style of the province, not a copy of a department PDF.

90 min · 92 Marks · 30 questions

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

Sit it timed Formula sheet

Question breakdown

1.1 · 6 Marks
An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT amount?
Notes: An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT 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: An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT amount?
Before any working — hunt first
Given
Numbers and units already in the sentence: R1400 excluding · 15%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable.
Find
We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
In other words — as if you have never seen this before
VAT=0.15×1400=210.
2. What do we already know?
An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT amount?
3. Which method — and why this one?
VAT=0.15×1400=210.
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: R1400 excluding · 15%. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable. Find: We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
  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
  An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT amount?
  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
  VAT=0.15×1400=210.
  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
  VAT=0.15×1400=210.
  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
  R210.00
  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
R210.00
Copy onto your answer sheet — in this order
Answer: R210.00
6. Check it like a marker
VAT=0.15×1400=210.
7. A trap first-timers fall into
R1610.00
1.2 · 6 Marks
Total including that VAT
Notes: Total including that VAT
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: Total including that VAT
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: Total including that VAT. Circle that word — that is the missing variable.
Find
We are required to find: Total including that VAT. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Total = 1400 + 210 = 1610. Then substitute the given, one line at a time, to get Total including that VAT.
In other words — as if you have never seen this before
Total=1400+210=1610.
2. What do we already know?
Total including that VAT
3. Which method — and why this one?
Total=1400+210=1610.
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: Total including that VAT. Circle that word — that is the missing variable. Find: We are required to find: Total including that VAT. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Total = 1400 + 210 = 1610. Then substitute the given, one line at a time, to get Total including that VAT.
  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
  Total including that VAT
  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
  Total=1400+210=1610.
  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
  Total=1400+210=1610.
  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
  R1610.00
  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
R1610.00
Copy onto your answer sheet — in this order
Answer: R1610.00
6. Check it like a marker
Total=1400+210=1610.
7. A trap first-timers fall into
R210.00
2.1 · 8 Marks · Simple and compound interest
R8000 at 8% per year simple interest for 2 years. Interest earned?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs compound interest
Notes: R8000 at 8% per year simple interest for 2 years. Interest earned?
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: R8000 at 8% per year simple interest for 2 years. Interest earned?
Before any working — hunt first
Given
Numbers and units already in the sentence: R8000 at · 8% · 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: 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 = 8000 × 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
I=Pin=8000×0.08×2=1280.
2. What do we already know?
R8000 at 8% per year simple interest for 2 years. Interest earned?
3. Which method — and why this one?
I=Pin=8000×0.08×2=1280.
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: R8000 at · 8% · 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: 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 = 8000 × 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
  R8000 at 8% per year simple interest for 2 years. Interest earned?
  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=8000×0.08×2=1280.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  I=Pin=8000×0.08×2=1280.
  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
  R1280.00
  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
R1280.00
Copy onto your answer sheet — in this order
Answer: R1280.00
6. Check it like a marker
I=Pin=8000×0.08×2=1280.
7. A trap first-timers fall into
R9280.00
2.2 · 6 Marks
Two towns are 9 km apart. Map scale 1:100 000. Map distance?
Notes: Two towns are 9 km apart. Map scale 1:100 000. Map distance?
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 towns are 9 km apart. Map scale 1:100 000. Map distance?
Before any working — hunt first
Given
Numbers and units already in the sentence: 9 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable.
Find
We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 9 km = 900000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
In other words — as if you have never seen this before
9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
2. What do we already know?
Two towns are 9 km apart. Map scale 1:100 000. Map distance?
3. Which method — and why this one?
9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
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 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable. Find: We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 9 km = 900000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
  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
  Two towns are 9 km apart. Map scale 1:100 000. Map distance?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
  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
  9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
  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
  9 cm
  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
9 cm
Copy onto your answer sheet — in this order
Answer: 9 cm
6. Check it like a marker
9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
7. A trap first-timers fall into
90 cm
3.1 · 4 Marks
A till slip that already includes VAT. To find the VAT inside it you
Notes: A till slip that already includes VAT. To find the VAT inside it you
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 till slip that already includes VAT. To find the VAT inside it you
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: the VAT inside it you. Circle that word — that is the missing variable.
Find
We are required to find: the VAT inside it you. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Inclusive price is 115%. Then substitute the given, one line at a time, to get the VAT inside it you.
In other words — as if you have never seen this before
Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
2. What do we already know?
A till slip that already includes VAT. To find the VAT inside it you
3. Which method — and why this one?
Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
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: the VAT inside it you. Circle that word — that is the missing variable. Find: We are required to find: the VAT inside it you. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Inclusive price is 115%. Then substitute the given, one line at a time, to get the VAT inside it you.
  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
  A till slip that already includes VAT. To find the VAT inside it you
  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
  Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
  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
  Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
  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
  divide by 1.15, then subtract from the total
  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
divide by 1.15, then subtract from the total
Copy onto your answer sheet — in this order
Answer: divide by 1.15, then subtract from the total
6. Check it like a marker
Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
7. A trap first-timers fall into
take 15% of the inclusive price
3.2 · 6 Marks · Tree diagrams and relative frequency
Probability of a red marble from 3 red and 7 blue
Formulas
P(A then B)=P(A)×P(B given A)
Compound events
Notes: Probability of a red marble from 3 red and 7 blue
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: Probability of a red marble from 3 red and 7 blue
In other words — as if you have never seen this before
3 favourable out of 10 marbles.
2. What do we already know?
Probability of a red marble from 3 red and 7 blue
3. Which method — and why this one?
3 favourable out of 10 marbles.
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
  Probability of a red marble from 3 red and 7 blue
  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
  3 favourable out of 10 marbles.
  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
  3 favourable out of 10 marbles.
  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
  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.
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
310
Copy onto your answer sheet — in this order
Answer: 310
6. Check it like a marker
3 favourable out of 10 marbles.
7. A trap first-timers fall into
37
7 · 2 Marks · Inflation and exchange rates
A price rises with 5% inflation. Multiply the old price by
Formulas
new price=old price×(1 + inflation rate)
One-year inflation
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 price rises with 5% inflation. Multiply the old price by
Before any working — hunt first
Given
Numbers and units already in the sentence: 5%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Multiply the old price by. Circle that word — that is the missing variable.
Find
We are required to find: Multiply the old price by. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Increase of 5% is × 1. Then substitute the given, one line at a time, to get Multiply the old price by.
In other words — as if you have never seen this before
Increase of 5% is × 1.05.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5%. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Increase of 5% is × 1.05.
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%. 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: Multiply the old price by. Circle that word — that is the missing variable. Find: We are required to find: Multiply the old price by. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Increase of 5% is × 1. Then substitute the given, one line at a time, to get Multiply the old price by.
  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%. 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
  Increase of 5% is × 1.05.
  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
  Increase of 5% is × 1.05.
  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
  1.05
  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
1.05
Copy onto your answer sheet — in this order
Answer: 1.05
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
8 · 2 Marks · Cost, income and break-even
Break-even is where
Formulas
break-even: income=cost
Break-even point
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: Break-even is where
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: Break-even is where. Circle that word — that is the missing variable.
Find
We are required to find: Break-even is where. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: The graphs meet: no profit, no loss. Then substitute the given, one line at a time, to get Break-even is where.
In other words — as if you have never seen this before
The graphs meet: no profit, no loss.
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?
The graphs meet: no profit, no loss.
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: Break-even is where. Circle that word — that is the missing variable. Find: We are required to find: Break-even is where. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: The graphs meet: no profit, no loss. Then substitute the given, one line at a time, to get Break-even is where.
  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
  The graphs meet: no profit, no loss.
  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
  The graphs meet: no profit, no loss.
  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
  income equals cost
  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
income equals cost
Copy onto your answer sheet — in this order
Answer: income equals cost
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 · 4 Marks · Simple and compound interest
Which is larger after 2 years on R1 000 at 10%: simple or annual compound?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs 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: Which is larger after 2 years on R1 000 at 10%: simple or annual compound?
In other words — as if you have never seen this before
Simple A=1200. Compound A=1210.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 years · R1 · 000 at · 10%. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Simple A=1200. Compound A=1210.
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: 2 years · R1 · 000 at · 10%. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
3. 03 / 07
  Step C — Name the method in words
  Simple A=1200. Compound A=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.
4. 04 / 07
  Working
  Simple A=1200. Compound A=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.
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
  compound (R1 210 vs 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.
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
compound (R1 210 vs R1 200)
Copy onto your answer sheet — in this order
Answer: compound (R1 210 vs 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…”
10 · 2 Marks · Volume, surface area and packing
A wall 6 m by 3 m. Paint covers 4 m² per tin. Tins (round up)?
Formulas
V_box=L×W×Htins=area to paintcoverage per tin
Packing and covering
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 wall 6 m by 3 m. Paint covers 4 m² per tin. Tins (round up)?
Before any working — hunt first
Given
Numbers and units already in the sentence: 6 m · 3 m · 4 m². 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: Tins (round up). Circle that word — that is the missing variable.
Find
We are required to find: Tins (round up). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Area 18 m². Then substitute the given, one line at a time, to get Tins (round up).
In other words — as if you have never seen this before
Area 18 m². 184=4.5→5 tins.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 6 m · 3 m · 4 m². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Area 18 m². 184=4.5→5 tins.
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 m · 3 m · 4 m². 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: Tins (round up). Circle that word — that is the missing variable. Find: We are required to find: Tins (round up). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Area 18 m². Then substitute the given, one line at a time, to get Tins (round up).
  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 m · 3 m · 4 m². 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
  Area 18 m². 184=4.5→5 tins.
  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
  Area 18 m². 184=4.5→5 tins.
  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…”
11 · 2 Marks
Q₁=20, Q₃=50. IQR?
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: Q₁=20, Q₃=50. IQR?
Before any working — hunt first
Given
Numbers and units already in the sentence: 20 · 50. 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: IQR. Circle that word — that is the missing variable.
Find
We are required to find: IQR. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 50 − 20 = 30. Then substitute the given, one line at a time, to get IQR.
In other words — as if you have never seen this before
50−20=30.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 20 · 50. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
50−20=30.
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: 20 · 50. 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: IQR. Circle that word — that is the missing variable. Find: We are required to find: IQR. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 50 − 20 = 30. Then substitute the given, one line at a time, to get IQR.
  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: 20 · 50. 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
  50−20=30.
  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
  50−20=30.
  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
  30
  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
30
Copy onto your answer sheet — in this order
Answer: 30
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
An invoice in Mbombela shows R800 excluding VAT. VAT is 15%. VAT amount?
Notes: An invoice in Mbombela shows R800 excluding VAT. VAT is 15%. VAT 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: An invoice in Mbombela shows R800 excluding VAT. VAT is 15%. VAT amount?
Before any working — hunt first
Given
Numbers and units already in the sentence: R800 excluding · 15%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable.
Find
We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
In other words — as if you have never seen this before
VAT=0.15×800=120.
2. What do we already know?
An invoice in Mbombela shows R800 excluding VAT. VAT is 15%. VAT amount?
3. Which method — and why this one?
VAT=0.15×800=120.
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: R800 excluding · 15%. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable. Find: We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
  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
  An invoice in Mbombela shows R800 excluding VAT. VAT is 15%. VAT amount?
  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
  VAT=0.15×800=120.
  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
  VAT=0.15×800=120.
  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
  R120.00
  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
R120.00
Copy onto your answer sheet — in this order
Answer: R120.00
6. Check it like a marker
VAT=0.15×800=120.
7. A trap first-timers fall into
R920.00
13 · 2 Marks · Simple and compound interest
Compound R1 000 at 10% p.a. for 2 years. A?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs 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: Compound R1 000 at 10% p.a. for 2 years. A?
Before any working — hunt first
Given
Numbers and units already in the sentence: R1 · 000 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: A. Circle that word — that is the missing variable.
Find
We are required to find: A. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: R1 210. Then substitute the given, one line at a time, to get A.
In other words — as if you have never seen this before
R1 210
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R1 · 000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R1 210
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: R1 · 000 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: A. Circle that word — that is the missing variable. Find: We are required to find: A. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: R1 210. Then substitute the given, one line at a time, to get A.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: R1 · 000 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
  R1 210
  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
  1000×1.1×1.1=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
  R1 210
  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 210
Copy onto your answer sheet — in this order
Answer: R1 210
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
14 · 2 Marks
Hire purchase: extra paid=
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: Hire purchase: extra paid =
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: Hire purchase: extra paid =. Circle that word — that is the missing variable.
Find
We are required to find: Hire purchase: extra paid =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Add all payments, subtract the cash price. Then substitute the given, one line at a time, to get Hire purchase: extra paid =.
In other words — as if you have never seen this before
Add all payments, subtract the cash price.
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?
Add all payments, subtract the cash price.
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: Hire purchase: extra paid =. Circle that word — that is the missing variable. Find: We are required to find: Hire purchase: extra paid =. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Add all payments, subtract the cash price. Then substitute the given, one line at a time, to get Hire purchase: extra paid =.
  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
  Add all payments, subtract the cash price.
  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 all payments, subtract the cash price.
  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
  total instalments − cash price
  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
total instalments − cash price
Copy onto your answer sheet — in this order
Answer: total instalments − cash price
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
15 · 2 Marks
Q₁=12, Q₃=28. IQR?
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: Q₁=12, Q₃=28. IQR?
Before any working — hunt first
Given
Numbers and units already in the sentence: 12 · 28. 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: IQR. Circle that word — that is the missing variable.
Find
We are required to find: IQR. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 16. Then substitute the given, one line at a time, to get IQR.
In other words — as if you have never seen this before
16
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 12 · 28. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
16
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 12 · 28. 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: IQR. Circle that word — that is the missing variable. Find: We are required to find: IQR. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 16. Then substitute the given, one line at a time, to get IQR.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 12 · 28. 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
  16
  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
  28−12=16.
  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…”
16 · 3 Marks · Cost, income and break-even
C=80+12n, Income=20n. Break-even n?
Formulas
break-even: income=cost
Break-even point
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: C = 80 + 12n, Income = 20n. Break-even n?
Before any working — hunt first
Given
Numbers and units already in the sentence: 80 · 12n · 20n. 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: Break-even n. Circle that word — that is the missing variable.
Find
We are required to find: Break-even n. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 20n = 80+12n. Then substitute the given, one line at a time, to get Break-even n.
In other words — as if you have never seen this before
20n=80+12n→8n=80→n=10.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 80 · 12n · 20n. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
20n=80+12n→8n=80→n=10.
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 80 · 12n · 20n. 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: Break-even n. Circle that word — that is the missing variable. Find: We are required to find: Break-even n. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 20n = 80+12n. Then substitute the given, one line at a time, to get Break-even n.
  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: 80 · 12n · 20n. 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
  20n=80+12n→8n=80→n=10.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  20n=80+12n→8n=80→n=10.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  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…”
17 · 2 Marks
Pula 1 = R1.20. R240 is how many pula?
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: Pula 1 = R1.20. R240 is how many pula?
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · R1.20 · R240 is. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: how many pula. Circle that word — that is the missing variable.
Find
We are required to find: how many pula. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 200. Then substitute the given, one line at a time, to get how many pula.
In other words — as if you have never seen this before
200
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · R1.20 · R240 is. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
200
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 · R1.20 · R240 is. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: how many pula. Circle that word — that is the missing variable. Find: We are required to find: how many pula. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 200. Then substitute the given, one line at a time, to get how many pula.
  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 · R1.20 · R240 is. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  200
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  2401.20=200.
  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
  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
200
Copy onto your answer sheet — in this order
Answer: 200
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
18 · 4 Marks
Boxes 20 cm by 10 cm by 10 cm. How many fit in a 40 cm cube crate?
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: Boxes 20 cm by 10 cm by 10 cm. How many fit in a 40 cm cube crate?
Before any working — hunt first
Given
Numbers and units already in the sentence: 20 cm · 10 cm · 10 cm · 40 cm. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: How many fit in a 40 cm cube crate. Circle that word — that is the missing variable.
Find
We are required to find: How many fit in a 40 cm cube crate. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Crate 40³ = 64 000. Then substitute the given, one line at a time, to get How many fit in a 40 cm cube crate.
In other words — as if you have never seen this before
Crate 40³=64 000. Box 2 000. 64 0002 000=32.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 20 cm · 10 cm · 10 cm · 40 cm. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Crate 40³=64 000. Box 2 000. 64 0002 000=32.
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: 20 cm · 10 cm · 10 cm · 40 cm. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: How many fit in a 40 cm cube crate. Circle that word — that is the missing variable. Find: We are required to find: How many fit in a 40 cm cube crate. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Crate 40³ = 64 000. Then substitute the given, one line at a time, to get How many fit in a 40 cm cube crate.
  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: 20 cm · 10 cm · 10 cm · 40 cm. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  Crate 40³=64 000. Box 2 000. 64 0002 000=32.
  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
  Crate 40³=64 000. Box 2 000. 64 0002 000=32.
  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
  32
  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
32
Copy onto your answer sheet — in this order
Answer: 32
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
19 · 4 Marks
Pula 1 = R1.25. R500 is how many pula?
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: Pula 1 = R1.25. R500 is how many pula?
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · R1.25 · R500 is. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: how many pula. Circle that word — that is the missing variable.
Find
We are required to find: how many pula. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 5001. Then substitute the given, one line at a time, to get how many pula.
In other words — as if you have never seen this before
5001.25=400 pula.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · R1.25 · R500 is. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
5001.25=400 pula.
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 · R1.25 · R500 is. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: how many pula. Circle that word — that is the missing variable. Find: We are required to find: how many pula. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 5001. Then substitute the given, one line at a time, to get how many pula.
  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 · R1.25 · R500 is. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  5001.25=400 pula.
  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
  5001.25=400 pula.
  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
  400
  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
400
Copy onto your answer sheet — in this order
Answer: 400
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
20 · 2 Marks · Tree diagrams and relative frequency
A fair coin twice. P(two tails)?
Formulas
P(A then B)=P(A)×P(B given A)
Compound events
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 fair coin twice. P(two tails)?
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 tails). Circle that word — that is the missing variable.
Find
We are required to find: P(two tails). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 14. Then substitute the given, one line at a time, to get P(two tails).
In other words — as if you have never seen this before
14
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?
14
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 tails). Circle that word — that is the missing variable. Find: We are required to find: P(two tails). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 14. Then substitute the given, one line at a time, to get P(two tails).
  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
  14
  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
  ½×½=¼.
  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…”
21 · 2 Marks · Cost, income and break-even
Fixed R80, each costs R5, sell R15. Break-even items?
Formulas
break-even: income=cost
Break-even point
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: Fixed R80, each costs R5, sell R15. Break-even items?
Before any working — hunt first
Given
Numbers and units already in the sentence: R80 · R5 · R15. 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: Break-even items. Circle that word — that is the missing variable.
Find
We are required to find: Break-even items. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 8. Then substitute the given, one line at a time, to get Break-even items.
In other words — as if you have never seen this before
8
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R80 · R5 · R15. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
8
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R80 · R5 · R15. 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: Break-even items. Circle that word — that is the missing variable. Find: We are required to find: Break-even items. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 8. Then substitute the given, one line at a time, to get Break-even items.
  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: R80 · R5 · R15. 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
  8
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  Contribution 10. 8010=8.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 06 / 08
  Step G — Sense-check the size
  Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
  Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
7. 07 / 08
  Step F — Box the answer with its unit
  8
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
8
Copy onto your answer sheet — in this order
Answer: 8
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
22 · 2 Marks
An invoice in Polokwane shows R1400 excluding VAT. VAT is 15%. VAT amount?
Notes: An invoice in Polokwane shows R1400 excluding VAT. VAT is 15%. VAT 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: An invoice in Polokwane shows R1400 excluding VAT. VAT is 15%. VAT amount?
Before any working — hunt first
Given
Numbers and units already in the sentence: R1400 excluding · 15%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable.
Find
We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
In other words — as if you have never seen this before
VAT=0.15×1400=210.
2. What do we already know?
An invoice in Polokwane shows R1400 excluding VAT. VAT is 15%. VAT amount?
3. Which method — and why this one?
VAT=0.15×1400=210.
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: R1400 excluding · 15%. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable. Find: We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
  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
  An invoice in Polokwane shows R1400 excluding VAT. VAT is 15%. VAT amount?
  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
  VAT=0.15×1400=210.
  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
  VAT=0.15×1400=210.
  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
  R210.00
  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
R210.00
Copy onto your answer sheet — in this order
Answer: R210.00
6. Check it like a marker
VAT=0.15×1400=210.
7. A trap first-timers fall into
R1610.00
23 · 2 Marks · Simple and compound interest
R5 000 at 10% p.a. simple for 2 years. Amount A?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs 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 10% p.a. simple for 2 years. Amount A?
Before any working — hunt first
Given
Numbers and units already in the sentence: R5 · 000 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 = 5000(1+0. 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=5000(1+0.1×2)=6000.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R5 · 000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
A=5000(1+0.1×2)=6000.
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 · 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 = 5000(1+0. 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: R5 · 000 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=5000(1+0.1×2)=6000.
  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=5000(1+0.1×2)=6000.
  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
  R6 000
  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
R6 000
Copy onto your answer sheet — in this order
Answer: R6 000
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 · 2 Marks
An invoice in a national paper shows R400 excluding VAT. VAT is 15%. VAT amount?
Notes: An invoice in a national paper shows R400 excluding VAT. VAT is 15%. VAT 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: An invoice in a national paper shows R400 excluding VAT. VAT is 15%. VAT amount?
Before any working — hunt first
Given
Numbers and units already in the sentence: R400 excluding · 15%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable.
Find
We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
In other words — as if you have never seen this before
VAT=0.15×400=60.
2. What do we already know?
An invoice in a national paper shows R400 excluding VAT. VAT is 15%. VAT amount?
3. Which method — and why this one?
VAT=0.15×400=60.
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: R400 excluding · 15%. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable. Find: We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
  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
  An invoice in a national paper shows R400 excluding VAT. VAT is 15%. VAT amount?
  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
  VAT=0.15×400=60.
  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
  VAT=0.15×400=60.
  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
  R60.00
  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
R60.00
Copy onto your answer sheet — in this order
Answer: R60.00
6. Check it like a marker
VAT=0.15×400=60.
7. A trap first-timers fall into
R460.00
25 · 2 Marks
An elevation on a building plan is a view of the
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: An elevation on a building plan is a view of the
In other words — as if you have never seen this before
Front, back, north elevation: the standing walls.
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?
Front, back, north elevation: the standing walls.
4. Step-by-step working
1. 01 / 07
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 07
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
3. 03 / 07
  Step C — Name the method in words
  Front, back, north elevation: the standing walls.
  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
  Front, back, north elevation: the standing walls.
  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
  outside wall from one side
  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
outside wall from one side
Copy onto your answer sheet — in this order
Answer: outside wall from one side
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
Plan 30 mm, scale 1:100. Real length?
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: Plan 30 mm, scale 1:100. Real length?
Before any working — hunt first
Given
Numbers and units already in the sentence: 30 mm · 1 · 100. 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: Real length. Circle that word — that is the missing variable.
Find
We are required to find: Real length. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3 000 mm. Then substitute the given, one line at a time, to get Real length.
In other words — as if you have never seen this before
3 000 mm
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 30 mm · 1 · 100. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3 000 mm
4. Step-by-step working
1. 01 / 08
  Step A — Read the question twice
  Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 30 mm · 1 · 100. 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: Real length. Circle that word — that is the missing variable. Find: We are required to find: Real length. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 3 000 mm. Then substitute the given, one line at a time, to get Real length.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 30 mm · 1 · 100. 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
  3 000 mm
  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
  30×100=3 000 mm=3 m.
  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
  3 000 mm
  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
3 000 mm
Copy onto your answer sheet — in this order
Answer: 3 000 mm
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 · Inflation and exchange rates
A loaf was R20. After 8% inflation it is
Formulas
new price=old price×(1 + inflation rate)
One-year inflation
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 loaf was R20. After 8% inflation it is
Before any working — hunt first
Given
Numbers and units already in the sentence: R20 · 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: After 8% inflation it is. Circle that word — that is the missing variable.
Find
We are required to find: After 8% inflation it is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 20 × 1. Then substitute the given, one line at a time, to get After 8% inflation it is.
In other words — as if you have never seen this before
20×1.08=21.60.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R20 · 8%. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
20×1.08=21.60.
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: R20 · 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: After 8% inflation it is. Circle that word — that is the missing variable. Find: We are required to find: After 8% inflation it is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 20 × 1. Then substitute the given, one line at a time, to get After 8% inflation it 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: R20 · 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
  20×1.08=21.60.
  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
  20×1.08=21.60.
  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
  R21.60
  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
R21.60
Copy onto your answer sheet — in this order
Answer: R21.60
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
1 m³ of water is
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 1 m³ of water is
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 m³. 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: 1 m³ of water is. Circle that word — that is the missing variable.
Find
We are required to find: 1 m³ of water is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 1 m³ = 1 000 ℓ. Then substitute the given, one line at a time, to get 1 m³ of water is.
In other words — as if you have never seen this before
1 m³=1 000 ℓ.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 m³. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
1 m³=1 000 ℓ.
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 m³. 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: 1 m³ of water is. Circle that word — that is the missing variable. Find: We are required to find: 1 m³ of water is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 1 m³ = 1 000 ℓ. Then substitute the given, one line at a time, to get 1 m³ of water 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 m³. 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
  1 m³=1 000 ℓ.
  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
  1 m³=1 000 ℓ.
  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
  1 000 litres
  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
1 000 litres
Copy onto your answer sheet — in this order
Answer: 1 000 litres
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 · Cost, income and break-even
Fixed R100, variable R8 each, sell at R20. Break-even n?
Formulas
break-even: income=cost
Break-even point
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: Fixed R100, variable R8 each, sell at R20. Break-even n?
Before any working — hunt first
Given
Numbers and units already in the sentence: R100 · R8 each · R20. 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: Break-even n. Circle that word — that is the missing variable.
Find
We are required to find: Break-even n. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Profit R12 each. Then substitute the given, one line at a time, to get Break-even n.
In other words — as if you have never seen this before
Profit R12 each. 10012=8.33, so 9 items.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R100 · R8 each · R20. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Profit R12 each. 10012=8.33, so 9 items.
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: R100 · R8 each · R20. 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: Break-even n. Circle that word — that is the missing variable. Find: We are required to find: Break-even n. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Profit R12 each. Then substitute the given, one line at a time, to get Break-even n.
  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: R100 · R8 each · R20. 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
  Profit R12 each. 10012=8.33, so 9 items.
  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
  Profit R12 each. 10012=8.33, so 9 items.
  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
  9
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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
9
Copy onto your answer sheet — in this order
Answer: 9
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
30 · 2 Marks
An invoice in Mahikeng shows R600 excluding VAT. VAT is 15%. VAT amount?
Notes: An invoice in Mahikeng shows R600 excluding VAT. VAT is 15%. VAT 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: An invoice in Mahikeng shows R600 excluding VAT. VAT is 15%. VAT amount?
Before any working — hunt first
Given
Numbers and units already in the sentence: R600 excluding · 15%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable.
Find
We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
In other words — as if you have never seen this before
VAT=0.15×600=90.
2. What do we already know?
An invoice in Mahikeng shows R600 excluding VAT. VAT is 15%. VAT amount?
3. Which method — and why this one?
VAT=0.15×600=90.
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: R600 excluding · 15%. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: VAT amount. Circle that word — that is the missing variable. Find: We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
  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
  An invoice in Mahikeng shows R600 excluding VAT. VAT is 15%. VAT amount?
  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
  VAT=0.15×600=90.
  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
  VAT=0.15×600=90.
  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
  R90.00
  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
R90.00
Copy onto your answer sheet — in this order
Answer: R90.00
6. Check it like a marker
VAT=0.15×600=90.
7. A trap first-timers fall into
R690.00