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4024/21 Oct/Nov 2023, Question 7: Solving Quadratics by Factorising

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 11 marks

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The question, in short

Algebra question: simplify an expression, expand and simplify, solve a quadratic to 2 decimal places, and combine fractions.

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

Part (a) · 2 marks

Simplify 7a − 4b − 2a + b by collecting like terms.

  1. 17a − 2a = 5a and −4b + b = −3b
  2. 2= 5a − 3b

Answer5a−3b

Part (b) · 2 marks

Expand and simplify 3(2x − 3) + 5(x + 2).

  1. 16x − 9 + 5x + 10
  2. 2= 11x + 1

Answer11x + 1

Part (c) · 3 marks

Solve 6x² − 2x − 9 = 0, showing working, giving answers to 2 decimal places.

  1. 1x = (2 ± √((−2)² − 4 × 6 × (−9)))/(2 × 6)
  2. 2= (2 ± √220)/12
  3. 3x = (2 − 14.83…)/12 or (2 + 14.83…)/12
  4. 4x = −1.07 and 1.40

Answer−1.07 and 1.40

Part (di) · 1 mark

Write x/4 ÷ 2/y as a single fraction in simplest form.

  1. 1x/4 × y/2
  2. 2= xy/8

Answer(xy)/8

Part (dii) · 3 marks

Write 3/(x − 5) − 7/(2x + 1) as a single fraction in simplest form.

  1. 1(3(2x + 1) − 7(x − 5))/((2x + 1)(x − 5))
  2. 2= (6x + 3 − 7x + 35)/((2x + 1)(x − 5))
  3. 3= (38 − x)/((2x + 1)(x − 5))

Answer(38− x)/((2x +1)(x −5)) or (38− x)/(2x²−9x−5)

Stuck on a step? Read the free lesson: Solving Quadratics by Factorising

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Also searched as: 4024/21/O/N/23 · 4024_w23_qp_21 · 4024 w23 21 · question 7.
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