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y = mx+b
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About this video
A Grade 9 Term 1 practice test worked in full: fractions and decimals, squares and roots, scientific notation, a square root by prime factors, the HCF of three numbers, percentages, ratio, a rate problem, the exponent laws, compound interest, and buying a car with VAT, a trade-in and interest.
What it covers
- Fraction to decimal: make the denominator 100
- Scientific notation; a square root from prime factors
- The HCF of three numbers; increasing by a percentage; ratio
- A rate: break it down to 1 unit first
- Exponent laws with negative exponents
- Compound interest; VAT, a trade-in and a monthly instalment
Extra worked examples
✍️ Extra example: find √3 600 using prime factors
- 13 600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 2⁴ × 3² × 5²A factor tree, then count how often each prime repeats.
- 2√(3 600) = 2² × 3 × 5For a square root, HALVE every exponent.
- 3= 60Check: 60 × 60 = 3 600 ✓
✍️ Extra example: a car uses 6 ℓ per 100 km. How far can it travel on a 45 ℓ tank?
- 11 ℓ → 100 ÷ 6 = 16,67 kmBreak the rate down to ONE litre first.
- 245 ℓ → 45 × 16,666… = 750 kmMultiply by the litres in the tank — keep the full decimal in the calculator.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Write 7/20 as a decimal.
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7/20 = 35/100 = 0,35 (multiply the top and the bottom by 5) - 2Write 0,000062 in scientific notation.
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6,2 × 10−5 - 3Find the HCF of 36, 60 and 84.
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36 = 2² × 3², 60 = 2² × 3 × 5, 84 = 2² × 3 × 7 → the primes common to all three: HCF = 2² × 3 = 12 - 4R1 200 is invested at 6% per year compound interest for 3 years. Find the final amount.
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A = 1 200(1 + 6/100)3 = R1 429,22 - 5A bicycle costs R8 000 excluding VAT. Find the price including 15% VAT.
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VAT = 8 000 × 15/100 = R1 200, so the price is R9 200
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