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4024/22 Oct/Nov 2024, Question 7: Algebraic Fractions

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 13 marks

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The question, in short

Solve two linear equations, list integer solutions to a compound inequality, rearrange a formula for x, and simplify an algebraic fraction.

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

Part (a) · 2 marks

Find the value of x that makes 4x + 7 equal 16.

  1. 14x = 16 − 7 = 9
  2. 2x = 9/4

Answer9/4

Part (b) · 2 marks

Find the value of y that makes 5(4 − y) equal 30.

  1. 14 − y = 30 ÷ 5 = 6
  2. 2y = −2

Answer−2

Part (c) · 2 marks

List every integer x with −3/2 ≤ x < 3.

  1. 1−3/2 = −1.5, so integers from −1 up to 2
  2. 2−1, 0, 1, 2

Answer−1, 0, 1, 2

Part (d) · 3 marks

Make x the subject of y = (4y − x)/(3x).

  1. 13xy = 4y − x
  2. 23xy + x = 4y
  3. 3x(3y + 1) = 4y
  4. 4x = 4y/(3y + 1)

Answer4y/(3y + 1)

Part (e) · 4 marks

Reduce (12x² − 3y²)/(2x² + 8x − xy − 4y) to its simplest form.

  1. 1Numerator: 12x² − 3y² = 3(4x² − y²) = 3(2x + y)(2x − y)
  2. 2Denominator: 2x² + 8x − xy − 4y = 2x(x + 4) − y(x + 4) = (2x − y)(x + 4)
  3. 3Cancel (2x − y): 3(2x + y)/(x + 4)

Answer3(2x + y)/(x + 4) or (6x + 3y)/(x + 4)

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Also searched as: 4024/22/O/N/24 · 4024_w24_qp_22 · 4024 w24 22 · question 7.
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