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About this video
A Grade 9 prep test worked through: kinds of numbers, HCF, ratio, time from speed, hire purchase with the months turned into years, the exponent laws, an integer word problem and algebraic fractions.
What it covers
- Natural and whole numbers; the constant ratio of a pattern
- HCF from factor trees; simplifying a ratio
- Time = distance ÷ speed; hire purchase (months → years)
- Exponent laws, with negative and zero exponents
- Integers in context: the difference between two temperatures
Extra worked examples
✍️ Extra example: a car costing R120 000 is bought on hire purchase over 48 months at 15% per year simple interest. Find the total paid.
- 1T = 48 ÷ 12 = 4 yearsThe formula needs YEARS — the trap many learners fall for.
- 2SI = (120 000 × 15 × 4) ÷ 100 = R72 000P × R × T ÷ 100.
- 3Total = R120 000 + R72 000 = R192 000If the monthly instalment were asked, divide by 48 — read what the question wants.
✍️ Extra example: it is −12 °C in Moscow and 18 °C in Cape Town. How much warmer is Cape Town?
- 118 − (−12)'How much warmer' is a difference: the warmer one minus the colder one.
- 2= 18 + 12 = 30 °CTwo minus signs next to each other make a plus. A difference in warmth is positive.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Which of these is a natural number: 0, −3, √2 or 7?
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7 — 0 is a whole number, but not a natural number - 2Find the HCF of 48 and 72 using prime factors.
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48 = 2⁴ × 3 and 72 = 2³ × 3², so the HCF = 2³ × 3 = 24 - 3A train travels 270 km at 90 km/h. How long does the trip take?
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time = distance ÷ speed = 270 ÷ 90 = 3 hours - 4Simplify 2−3 + 50.
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1/2³ + 1 = 1/8 + 8/8 = 9/8 - 5Simplify 18a³b²/6ab.
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3a²b — divide the numbers, subtract the exponents of the same letter
Practise this topic
Download matching Grade 9 papers and worksheets.
