π
∞
∑
∫
θ
E = mc²
y = mx+b
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λ
About this video
Ten study habits for maths, counted down: no excuses, master the previous grade's work, aim to understand 80–90%, ask the 'stupid' question, use resources and past papers, keep notes tailored to your own mistakes, practise daily, the Feynman technique, a study group, and the Annual Teaching Plan (ATP).
What it covers
- Master the previous grade's work — the topics link up
- Ask the question everyone else is afraid to ask
- Use your resources, above all past papers
- Notes tailored to you: find where you went wrong, and highlight it
- Practise daily, and test yourself every week
- The Feynman technique: learn it, teach it, fill the gaps
- Study groups, and the ATP: tick off every objective
Extra worked examples
✍️ Tip 5 in action: a learner wrote (x + 3)² = x² + 9. Find where it went wrong.
- 1(x + 3)² = (x + 3)(x + 3)A bracket with two terms is written twice — you may not square each term on its own.
- 2= x² + 3x + 3x + 9 = x² + 6x + 9FOIL: the two middle terms are what the learner lost.
- 3The mistake: squaring each term separatelyWrite THAT in your notes and highlight it — copying the right answer alone teaches nothing.
✍️ Tip 5 in action: a learner wrote −3² = 9. Find where it went wrong.
- 1−3² = −(3 × 3) = −9With no bracket, the square is on the 3 only; the minus waits.
- 2(−3)² = (−3)(−3) = 9Only a bracket puts the minus inside the square.
- 3The mistake: treating −3² as (−3)²Note it in your own words, next to the corrected working.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Spot the mistake: 2(x − 5) = 2x − 5
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The 2 multiplies BOTH terms in the bracket: 2(x − 5) = 2x − 10 - 2Spot the mistake: x² = 36, so x = 6
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A square root has two answers: x = 6 or x = −6 - 3Spot the mistake: −2x ≥ −8, so x ≥ 4
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Dividing by a NEGATIVE number flips the sign: x ≤ 4 - 4Spot the mistake: (2a³)² = 2a⁶
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The exponent outside the bracket is for EVERY factor inside: (2a³)² = 4a⁶ - 5Spot the mistake: simple interest on R10 000 at 9% per year for 30 months is (10 000 × 9 × 30) ÷ 100 = R27 000
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The time must be in YEARS: 30 ÷ 12 = 2,5, so the interest is (10 000 × 9 × 2,5) ÷ 100 = R2 250
