Every distinction begins with one topic at a time.- start now
To round OFF, look at the digit just after your rounding place. 5 or more rounds up, 4 or less stays. Example: R47,678 to the nearest cent is R47,68.
Some contexts force the direction. Round UP when you may not fall short (how many taxis, how many tins of paint). Round DOWN when you cannot go over (how many items you can afford).
| Situation | What to do | Example |
|---|---|---|
| Money answer | round off to the nearest cent (2 decimals) | R12,3456 → R12,35 |
| Number of taxis for 47 people, 10 per taxi | round UP | 4,7 → 5 taxis |
| Apples at R7 each with R100 | round DOWN | 14,28 → 14 apples |
Simplify a ratio by dividing every part by the same number, after making the units match. To share an amount in a ratio, add the parts to get the total, divide the amount by the total parts to get one part, then multiply.
Q: Write 250 g to 1 kg as a ratio in simplest form. (Invented for practice.)
Make units match: 1 kg = 1000 g, so the ratio is 250 : 1000.
Divide both parts by 250: 250 ÷ 250 : 1000 ÷ 250 = 1 : 4.
∴ 250 g : 1 kg = 1 : 4
Q: Three cousins share R1 200 in the ratio 2 : 3 : 5. How much does each receive? (Invented for practice.)
Total parts = 2 + 3 + 5 = 10.
One part = R1 200 ÷ 10 = R120.
Shares: 2 × R120 = R240, 3 × R120 = R360, 5 × R120 = R600.
Check: R240 + R360 + R600 = R1 200. ✓
∴ they receive R240, R360 and R600
Q: A 2 litre bottle of juice costs R32,90 and a 1 litre bottle costs R18,50. Which is the better buy? (Invented for practice.)
Unit rate = price ÷ litres.
2 litre bottle: R32,90 ÷ 2 = R16,45 per litre.
1 litre bottle: R18,50 ÷ 1 = R18,50 per litre.
∴ the 2 litre bottle is cheaper per litre, so it is the better buy
Q: A minibus travels 210 km in 3 hours. What is its average speed? (Invented for practice.)
Speed = distance ÷ time = 210 km ÷ 3 h = 70 km/h.
∴ the average speed is 70 km/h
| Type | How the quantities move | Everyday example |
|---|---|---|
| Direct proportion | both grow together, both shrink together | more litres of petrol cost more rand |
| Inverse proportion | one grows while the other shrinks | more workers finish the job in less time |
Percentage of an amount: percent ÷ 100 × amount.
Percentage change: (new − old) ÷ old × 100. A positive answer is an increase, a negative answer is a decrease.
Add 15% VAT: multiply the exclusive price by 1,15. To find VAT alone, take 15% of the exclusive price.
Discount of d%: multiply by (100 − d) ÷ 100. Mark-up adds a percentage of the cost price to get the selling price.
Q: A workshop charges R1 400 for a service before VAT. What is the VAT-inclusive price at 15%? (Invented for practice.)
VAT-inclusive = R1 400 × 1,15 = R1 610,00.
Check the VAT amount: 15% of R1 400 = R210, and R1 400 + R210 = R1 610. ✓
∴ the price including VAT is R1 610,00
Q: A loaf of bread rose from R16,00 to R18,40. By what percentage did the price increase? (Invented for practice.)
Change = new − old = R18,40 − R16,00 = R2,40.
Percentage change = R2,40 ÷ R16,00 × 100 = 15%.
∴ the price increased by 15%
A number without its unit is only half an answer: rands, litres and kilometres per hour are part of the mark.- on writing full answers
Round off with the next digit (5 or more up), but let the context decide: up for taxis and tins, down for what you can afford, and to the nearest cent for money. Match units before simplifying a ratio, and share an amount by finding one part first. A rate compares different units, so use price per unit for best buys and distance over time for speed. Direct proportion grows together, inverse proportion trades one for the other. For percentages, use percent over 100 times the amount, multiply by 1,15 for VAT, and use (new minus old) over old times 100 for a percentage change. Keep units and show every step.
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Exam stress is completely normal. Here are a few things that actually work. None of this replaces a doctor or a trusted adult.
Box breathing: 4 counts in, 4 hold, 4 out, 4 hold. Do it four times.
Look at the worked example below first, then make your own. Tick off each topic as you finish it.
Example (already filled in)
| Date | Subject | Topic | Done |
|---|---|---|---|
| Mon 8 Jul | Mathematical Literacy | Your weakest topic, notes + summary | ✓ |
| Tue 9 Jul | Mathematical Literacy | Next topic + 10 practice questions | ✓ |
| Wed 10 Jul | Mathematical Literacy | A full past paper under time | – |
| Thu 11 Jul | Mathematical Literacy | Mark the paper, revise weak spots | – |
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|---|---|---|---|
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A winner is a loser who tried one more time.- keep going, all the way to the exam