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4024/21 Oct/Nov 2021, Question 9: Equations That Become Quadratics

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 12 marks

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The question, in short

Solve an equation, an inequality, a rational equation and simplify an algebraic fraction involving x and y.

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

Part (a) · 2 marks

Find x from the linear equation 3x − 8 = 7.

  1. 13x = 7 + 8 = 15
  2. 2x = 5

Answer5

Part (b) · 2 marks

Find the solution set of the inequality 7x < 3(2 − x).

  1. 17x < 6 − 3x
  2. 210x < 6
  3. 3x < 3/5

Answerx < 3/5

Part (c) · 4 marks

Solve 3/(x − 2) + x/(x + 5) = 1 for x.

  1. 13(x + 5) + x(x − 2) = (x − 2)(x + 5)
  2. 23x + 15 + x² − 2x = x² − 2x + 5x − 10
  3. 3x + 15 = 3x − 10 → 2x = 25
  4. 4x = 25/2 = 12.5

Answer25/2 or 12 1/2 or 12.5

Part (d) · 4 marks

Simplify the fraction (2x² + 3x + 4xy + 6y)/(2x² + 11x + 12).

  1. 1Numerator: x(2x + 3) + 2y(2x + 3) = (x + 2y)(2x + 3)
  2. 2Denominator: 2x² + 11x + 12 = (2x + 3)(x + 4)
  3. 3Cancel (2x + 3): (x + 2y)/(x + 4)

Answer(x + 2y)/(x + 4)

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Also searched as: 4024/21/O/N/21 · 4024_w21_qp_21 · 4024 w21 21 · question 9.
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