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Mathematical Literacy

Grade 10 · Year Summary · CAPS-aligned
CAPS · Grade 10 · 2022–2026
Mathematical Literacy Gr 10 · Year SummaryDate: TopJournal

Maths Lit is not about being a maths person. It is about reading the real world, one document at a time.The GOAT Notes™

Papers 1 and 2 · no marks of its own · inside every Finance, Data, Measurement and Maps calculation
TERM 1 · NUMBERS AND CALCULATIONS NUMBERS AND CALCULATIONS

What you must be able to do

Core content · Number formats, words and conventions

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).

Numbers that are read, not just calculated
You seeIt meansWatch out
2 306 000two million three hundred and six thousandone million = 1 000 000; one billion = 1 000 000 000
R1,5 millionR1 500 000move the comma six places
Room 1214unit 14 on floor 12a code: you cannot add or divide it
4 overs in cricket4 × 6 = 24 ballsan over is 6 balls, not 10
Thandi's account shows −R185,40 on 3 March. On 5 March R600,00 is deposited. Is she in credit on 3 March, and what is the balance on 5 March? (3)
  • ✓ O: Negative balance, so she is in debit on 3 March.
  • ✓ M: −185,40 + 600,00
  • ✓ A: Balance = R414,60 (credit)

Say credit or debit as well as the amount; the word is the opinion mark.

A bowler bowls 7 overs. How many balls is that? Write R3,2 million in full. (3)
  • ✓ M: An over is 6 balls: 7 × 6
  • ✓ A: = 42 balls
  • ✓ A: R3,2 million = R3 200 000

Core content · Operations, order of operations and the calculator

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.

Calculate 150 − 6 × (4,5 + 3,5) ÷ 4 and estimate 4,9 × 19,8 first. (5)
  • ✓ M: Brackets: 4,5 + 3,5 = 8
  • ✓ M: 6 × 8 ÷ 4 = 48 ÷ 4 = 12
  • ✓ A: 150 − 12 = 138
  • ✓ S: Estimate: 5 × 20 = 100
  • ✓ A: 4,9 × 19,8 = 97,02, close to 100, so reasonable

Typing 150 − 6 × 8 ÷ 4 in order on a basic calculator can give the wrong rung first. Do the brackets yourself.

⚠️ COMMON MISTAKE Left to right is a trap. Working strictly left to right. 7 + 3 × 12 is 43, not 120. The × happens before the +.

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.

Calculate 2/5 + 1/3 as a fraction, and 3/4 of R860. (4)
  • ✓ M: 2/5 = 6/15 and 1/3 = 5/15
  • ✓ A: 6/15 + 5/15 = 11/15 = 0,73
  • ✓ M: 3/4 × 860 = 860 ÷ 4 × 3
  • ✓ A: = R645,00

Core content · Rounding in context

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.

A floor of 14,3 m² is tiled with boxes that cover 2,2 m² each and cost R189,95. How many boxes, and what do they cost? A cash total of R86,38 is rounded to the nearest 5c. (5)
  • ✓ M: 14,3 ÷ 2,2
  • ✓ A: = 6,50 boxes
  • ✓ R: Round UP: 7 boxes, because 6 boxes leave the floor bare
  • ✓ A: 7 × R189,95 = R1 329,65
  • ✓ R: R86,38 is nearer R86,40 than R86,35, so pay R86,40
💡 EASY MARK Name the unit and the rounding. Write the rounding you used and the unit (“7 boxes”, “R86,40”). The rounding mark is separate from the method mark.

Core content · Ratios

📖 KEY DEFINITION Ratio: a comparison of quantities of the same kind, written without units. 3 : 8 is also written 3/8; its unit form is 1 : 2,667 (8 ÷ 3). Equivalent ratios multiply or divide both sides by the same number.
R2 400 is shared in the ratio 3 : 5. Calculate each share. A plan has scale 1 : 50; a wall measures 7,5 cm on it. How long is the wall in metres? (6)
  • ✓ M: 3 + 5 = 8 parts
  • ✓ A: 1 part = 2 400 ÷ 8 = R300,00
  • ✓ A: Shares: 3 × 300 = R900,00 and 5 × 300 = R1 500,00
  • ✓ M: 7,5 × 50 = 375 cm
  • ✓ C: 375 ÷ 100
  • ✓ A: = 3,75 m

Check: 900 + 1 500 = 2 400.

⚠️ COMMON MISTAKE No units in a ratio. Writing units in a ratio (3 kg : 5 kg) or mixing units. Convert to one unit first, then drop it.
A hair mix uses tint and peroxide in the ratio 1 : 2. How much of each is in a 50 ml mix? (4)
  • ✓ M: 1 + 2 = 3 parts
  • ✓ M: 1 part = 50 ÷ 3 = 16,67 ml
  • ✓ A: Tint = 16,7 ml
  • ✓ A: Peroxide = 33,3 ml

Check: 16,7 + 33,3 = 50 ml.

Core content · Proportion: direct and inverse

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.

3 bags of plaster cover 18 m². How many bags for 45 m²? Four painters finish a hall in 9 days; how long do 6 painters take? (6)
  • ✓ M: Direct: 45 ÷ 18 = 2,5 times as much
  • ✓ A: 2,5 × 3 = 7,5 bags
  • ✓ R: Round UP: 8 bags
  • ✓ M: Inverse: 4 × 9 = 36 painter-days
  • ✓ M: 36 ÷ 6
  • ✓ A: = 6 days (more painters, fewer days)

Core content · Rates

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.

A shelf label read as a document: best buy = lowest price per unit
Pack of Lekker RicePricePrice per kg
2 kgR41,99R21,00
5 kgR98,50R19,70
10 kgR189,90R18,99
⭐ EXAM FAVOURITE Best buy. Divide each price by its mass or volume, compare the unit prices, then state which is cheapest. Here the 10 kg pack is R18,99/kg, so it is the best buy.
Use the table to find the best buy. A bakkie uses 9,2 litres per 100 km. How much petrol does a 350 km trip need, and what does it cost at R22,85 per litre? (6)
  • ✓ RT: Prices and masses read from the table
  • ✓ M: 98,50 ÷ 5 = 19,70 and 189,90 ÷ 10 = 18,99
  • ✓ O: 10 kg at R18,99/kg is cheapest: best buy
  • ✓ M: 350 ÷ 100 × 9,2
  • ✓ A: = 32,2 litres
  • ✓ A: 32,2 × 22,85 = R735,77
A taxi travels 276 km in 3 h 30 min. Calculate its average speed in km/h, to one decimal place. (4)
  • ✓ C: 30 min = 0,5 h, so time = 3,5 h
  • ✓ SF: Speed = distance ÷ time = 276 ÷ 3,5
  • ✓ A: = 78,8571… km/h
  • ✓ R: = 78,9 km/h

Convert minutes to hours before you divide.

Core content · Percentages

⚡ MUST MEMORISE Forms to know. 50% = 50/100 = 0,5. Percentage of an amount = % ÷ 100 × amount. Increase by 8%: × 1,08. Decrease by 20%: × 0,8. Percentage change = change ÷ original × 100.
Percentage tasks in one table
TaskCalculationAnswer
35% of R1 8400,35 × 1 840R644,00
R4 250 increased by 8%4 250 × 1,08R4 590,00
R640 less 15%640 × 0,85R544,00
36 out of 48 as a %36 ÷ 48 × 10075%
R1 380 includes 15%: original?1 380 ÷ 1,15R1 200,00
🔥 FREQUENTLY TESTED Percentage of an amount. A percentage of an amount, with a rand answer to two decimals. Discount, tax, wastage and marks all use it.
Rent rises from R3 850 to R4 158. Calculate the percentage increase. (3)
  • ✓ M: Increase = 4 158 − 3 850 = 308
  • ✓ M: 308 ÷ 3 850 × 100
  • ✓ A: = 8%

Dividing by the new rent gives 7,4%, which is wrong.

A jacket marked R1 299 is sold at 20% off. What is the sale price? A phone costs R1 380 including 15% VAT; what is the price before VAT? (5)
  • ✓ M: Sale price = 1 299 × 0,8
  • ✓ A: = R1 039,20
  • ✓ M: Price before VAT = 1 380 ÷ 1,15
  • ✓ A: = R1 200,00
  • ✓ O: Never take 15% off R1 380: 15% of the original is not 15% of the total.
⚠️ COMMON MISTAKE Wrong base. Taking a percentage increase off the new value. Always divide by the original, the amount you started with.
🧠 ACTIVE RECALL

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.

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.

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.

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.

ONE-MINUTE SUMMARY Every Finance, Data, Measurement and Maps question rests on these skills. Estimate first, follow the order of operations, round the way the context demands and only at the end, drop the units from a ratio, write a rate in unit form to find the best buy, and divide a percentage change by the original. Show each step and state the unit: the marks are in the working.
IN THE EXAM
  • Grade 10 sits two 75-mark papers; this topic has no question of its own but sits inside nearly every calculation in both.
  • Papers state the rounding or the number of decimal places, so follow the instruction and earn the R mark.
  • Best-buy, discount and percentage-change items are asked as short document questions of 2 to 4 marks.
  • Level 3 items ask you to verify a claim: calculate, compare, and write VALID or NOT VALID.
🔒 PATTERNS
🔒 FINANCE
🔒 MEASUREMENT
🔒 MAPS & PLANS
🔒 DATA HANDLING
🔒 PROBABILITY
🔒

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