Maths Lit is not about being a maths person. It is about reading the real world, one document at a time.The GOAT Notes™
South African papers print money as R2 000,00: a decimal comma and a space between thousands. Some documents print 2,000.00; read both, but write the comma. A negative number is a direction: −10 °C is below freezing, and a negative bank balance is a debit (you owe the bank).
| You see | It means | Watch out |
|---|---|---|
| 2 306 000 | two million three hundred and six thousand | one million = 1 000 000; one billion = 1 000 000 000 |
| R1,5 million | R1 500 000 | move the comma six places |
| Room 1214 | unit 14 on floor 12 | a code: you cannot add or divide it |
| 4 overs in cricket | 4 × 6 = 24 balls | an over is 6 balls, not 10 |
Say credit or debit as well as the amount; the word is the opinion mark.
Always estimate first: round to friendly numbers, calculate, then check that the calculator answer is close. Multiply or divide by 10, 100 or 1 000 by moving the comma: 3,47 × 100 = 347 and 52 ÷ 1 000 = 0,052.
Typing 150 − 6 × 8 ÷ 4 in order on a basic calculator can give the wrong rung first. Do the brackets yourself.
Fractions add over a common denominator; multiply across; divide by flipping. Shortcuts use the distributive fact: 25 × 98 = 25 × 100 − 25 × 2 = 2 450. On a basic calculator the squares key gives 12,5² = 156,25, the √ key gives √2 025 = 45, and a cube is a number multiplied by itself twice (3³ = 27). M+ adds to memory, M− subtracts, MRC recalls it; C and CE clear entries, so learn which one wipes everything on yours.
Round off to the places the question states (5 or more goes up). The context can overrule that, and cash totals round to the nearest 5 cents.
Check: 900 + 1 500 = 2 400.
Check: 16,7 + 33,3 = 50 ml.
Direct: when one quantity doubles, so does the other; the graph is a straight line through the origin. Inverse: when one doubles, the other halves; the graph falls in a curve and never touches either axis.
A rate compares different units, and “/” means “per”: R/kg, litres/100 km, km/h. A constant rate never changes; an average rate smooths out a trip. Compare rates by writing each in unit form.
| Pack of Lekker Rice | Price | Price per kg |
|---|---|---|
| 2 kg | R41,99 | R21,00 |
| 5 kg | R98,50 | R19,70 |
| 10 kg | R189,90 | R18,99 |
Convert minutes to hours before you divide.
| Task | Calculation | Answer |
|---|---|---|
| 35% of R1 840 | 0,35 × 1 840 | R644,00 |
| R4 250 increased by 8% | 4 250 × 1,08 | R4 590,00 |
| R640 less 15% | 640 × 0,85 | R544,00 |
| 36 out of 48 as a % | 36 ÷ 48 × 100 | 75% |
| R1 380 includes 15%: original? | 1 380 ÷ 1,15 | R1 200,00 |
Dividing by the new rent gives 7,4%, which is wrong.
A report says a municipality has set aside R4,5 million to repair water pipes. Which amount is this written out in full?
Which of these shows two million, four hundred and five thousand and sixty in figures?
Zodwa’s bank statement shows a balance of −R312,60. What does this tell you?
A cricket coach records that his bowler bowled 8 overs in a match. How many balls is that?
Which one of these numbers is a code, so that adding it to another number of the same kind gives a meaningless answer?
Calculate 9 + 4 × 15 without a calculator.
Calculate 200 − 5 × 18 − 25.
Calculate 48 ÷ 6 × 2.
Calculate 3 + 2² × 5.
Calculate (18,5 − 6,5) × 3 + 40 ÷ 8.
Naledi tiles a floor of 23,6 m². One box of tiles covers 2,5 m². How many boxes must she buy to cover the whole floor?
Mandla has R450 to spend on pens that cost R38,50 each. What is the largest number of pens he can buy?
A till total is R127,43. Cash amounts are rounded to the nearest 5 cents. How much must the customer pay in cash?
A school trip takes 94 learners. Each minibus taxi seats 15 learners. How many taxis must be booked?
Ruth has 250 m of fencing wire. Each gate panel needs 6,5 m of wire. How many complete panels can she make?
Two friends share R7 500 in the ratio 2 : 3. How much does the friend with the bigger share receive?
A plan is drawn to a scale of 1 : 200. A room measures 4,5 cm on the plan. What is the real length of the room?
Five loaves of bread cost R82,50. At the same price per loaf, what do 8 loaves cost?
Six workers paint a school hall in 8 days. Working at the same speed, how long will 4 workers take?
A drink is made by mixing 750 ml of syrup with 3 litres of water. What is the ratio of syrup to water in simplest form?
A shop sells sunflower oil in three sizes: 750 ml for R34,50, 2 litres for R79,90 and 5 litres for R204,50. Which size is the best buy?
A car uses 7,8 litres of petrol per 100 km, and petrol costs R23,10 per litre. What does the petrol for a 450 km trip cost?
A taxi travels 285 km in 3 h 45 min. What is its average speed?
Tap A drips 450 ml in 3 hours. Tap B drips 1,2 litres in 10 hours. Which tap leaks faster, and why?
A shop sells sugar in a 2 kg pack for R41,98 and a 5 kg pack for R109,90. Which pack is the better buy, and by how much per kilogram?
A shop raises the price of a R800 jacket by 25%. In a sale it then lowers the new price by 25%. The manager says the jacket is back to R800. Which statement is correct?
A teacher’s salary rises from R12 500 to R13 750 a month. The union says this is a 10% increase. Which statement is correct?
A fridge costs R6 900 with 15% VAT included. The salesman says the VAT in this price is R1 035, which is 15% of R6 900. Which statement is correct?
A 2 kg pack of chicken costs R80 and a 2 kg pack of fish costs R56. An advert says: “Chicken costs 30% more than fish.” Which statement is correct?
A shirt is on sale for R340. The tag says: “15% off the marked price of R400.” Which statement is correct?
Explain the difference between a ratio and a rate, and give one everyday example of each.
A ratio compares two quantities of the same kind, such as the amount of tint with the amount of peroxide in a hair mix. A ratio is written without units, for example 1 : 2. A rate compares quantities of different kinds, so it has different units, for example distance and time. A rate is written with the word per or a slash, such as 80 km/h or R18,99/kg.
Shop A sells mealie meal in a 12,5 kg bag for R139,75. Shop B sells it in a 5 kg bag for R59,95. Calculate the price per kilogram at each shop and state which shop offers the better buy.
Price per kilogram = price ÷ mass, so for Shop A: R139,75 ÷ 12,5 kg = R11,18 per kg. For Shop B: R59,95 ÷ 5 kg = R11,99 per kg. Compare the unit prices: Shop A is the better buy, because R11,18 per kg is lower than R11,99 per kg, even though Shop B’s bag costs less in total.
A shop advertises: “Buy a 3 kg bag of oranges for R94,50 and save 30% compared with buying three 1 kg bags at R42,00 each.” Verify whether the claim is VALID or NOT VALID. Show your working.
The three 1 kg bags cost 3 × R42,00 = R126,00. The 3 kg bag costs R94,50, so the saving is R126,00 − R94,50 = R31,50. Percentage saving = saving ÷ original price × 100 = 31,50 ÷ 126 × 100 = 25%. The advert claims 30%, but the saving is only 25%, so the claim is NOT VALID.
Explain to a Grade 8 learner why a price that goes up by 20% and then comes down by 20% does not end where it started.
Explain to a Grade 8 learner how to decide whether to round up, round down or round off, using the number of minibus taxis for a school trip as one example.
Explain to a Grade 8 learner how to find the best buy when a small pack and a big pack of the same rice have different prices, and why the lowest shelf price can be the worse deal.
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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 | Life Sciences | Your weakest topic, notes + summary | ✓ |
| Tue 9 Jul | Life Sciences | Next topic + 10 practice questions | ✓ |
| Wed 10 Jul | Life Sciences | A full past paper under time | – |
| Thu 11 Jul | Life Sciences | Mark the paper, revise weak spots | – |
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|---|---|---|---|
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