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4024/22 Oct/Nov 2022, Question 8: Solving Quadratics by Factorising

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 12 marks

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The question, in short

Simplify expressions, solve equations, evaluate and rearrange a formula, and solve a quadratic with answers to 3 significant figures.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Simplify 6v + 3w − 5w − v by collecting like terms.

  1. 16v − v + 3w − 5w
  2. 2= 5v − 2w

Answer5v − 2w

Part (b) · 2 marks

Solve 5x − 7 = 10 for x.

  1. 15x = 10 + 7 = 17
  2. 2x = 17/5 = 3.4

Answer3.4 or 3 2/5 or 17/5

Part (ci) · 1 mark

Simplify a × a × a² using index laws.

  1. 1a¹ × a¹ × a² = a⁴

Answera⁴

Part (cii) · 1 mark

Simplify b³ ÷ b⁵, giving the result as a power of b.

  1. 1b³ ÷ b⁵ = b^(3 − 5) = b⁻²

Answerb⁻² or 1/b²

Part (di) · 1 mark

Find r from r = 4p − 3t when p = 7 and t = −5.

  1. 1r = 4 × 7 − 3 × (−5) = 28 + 15 = 43

Answer43

Part (dii) · 2 marks

Rearrange r = 4p − 3t to make p the subject.

  1. 1r + 3t = 4p
  2. 2p = (r + 3t)/4

Answer(r + 3t)/4

Part (e) · 3 marks

Solve 5x² + 3x − 6 = 0, showing working, with answers to 3 significant figures.

  1. 1x = (−3 ± √(3² − 4 × 5 × (−6)))/(2 × 5)
  2. 2= (−3 ± √129)/10
  3. 3x = 0.836 or x = −1.44 (3 s.f.)

Answer0.836 and −1.44

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Also searched as: 4024/22/O/N/22 · 4024_w22_qp_22 · 4024 w22 22 · question 8.
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