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About this video
The Gauteng 2023 Grade 9 June control test (75 marks, 1½ hours) worked through: number properties, LCM, ratio and indirect proportion, simple versus compound interest, integers, exponents and roots, patterns, flow diagrams, algebraic expressions, factorising and equations.
What it covers
- The additive inverse, LCM by prime factors, the zero exponent
- A ratio with three parts; indirect proportion
- Simple versus compound interest — and saying which is cheaper
- Roots and powers, one step at a time
- Patterns: the general term; flow diagrams
- Factorising: common factor, taking out a negative, trinomials
- Equations: x² = 25 has two answers; the zero product rule
Extra worked examples
✍️ Extra example: 3 painters take 8 hours to paint a hall. How long would 4 painters take?
- 13 × 8 = 24 hours of work in totalIndirect proportion — more painters, fewer hours — so multiply first, don't divide.
- 224 ÷ 4 = 6 hoursShare the total work among the 4 painters.
✍️ Extra example: factorise fully 3x² − 12x − 36
- 13(x² − 4x − 12)Take out the common factor first — it earns its own mark.
- 2Factors of 12 with a difference of 4: 6 and 2The last term is negative, so the signs differ; the bigger number takes the middle term's sign.
- 33(x − 6)(x + 2)Check: (x − 6)(x + 2) = x² − 4x − 12 ✓
Exercises to try
Work each one out, then click to reveal the answer.
- 1Share 2 400 trees in the ratio 1 : 3 : 4.
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8 parts → 1/8 × 2 400 = 300, 3/8 × 2 400 = 900, 4/8 × 2 400 = 1 200 - 2R20 000 is borrowed for 2 years at 10% per year. Which is cheaper: simple or compound interest?
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Simple: A = 20 000(1 + 10/100 × 2) = R24 000. Compound: A = 20 000(1 + 10/100)2 = R24 200. Simple interest is cheaper — say so in words. - 3Calculate 3√16 + ∛27 − (−2)².
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3 × 4 + 3 − 4 = 11 - 4A pattern is 7; 11; 15; 19; … Find Tn and T20.
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d = 4 and c = 7 − 4 = 3, so Tn = 4n + 3; T20 = 4(20) + 3 = 83 - 5Solve: (a) x² = 49 (b) (x − 5)(x + 3) = 0
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(a) x = ±7 — a square root has two answers (b) x = 5 or x = −3 (zero product rule)
Practise this topic
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