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4024/21 Oct/Nov 2024, Question 5: Algebraic Fractions

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 13 marks

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The question, in short

Solve equations, evaluate and rearrange a formula, factorise a four-term expression, and combine three terms into one simplified fraction.

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

Part (ai) · 1 mark

Solve y/4 = 8 for y.

  1. 1y = 8 × 4 = 32

Answer32

Part (aii) · 2 marks

Solve 3 − 4x = 2x + 12 for x.

  1. 13 − 12 = 2x + 4x
  2. 2−9 = 6x
  3. 3x = −9/6 = −3/2

Answer−3/2

Part (bi) · 2 marks

Find w from w = 5x − 6y using x = 6.2 and y = −1.8.

  1. 1w = 5 × 6.2 − 6 × (−1.8)
  2. 2= 31 + 10.8 = 41.8

Answer41.8

Part (bii) · 2 marks

Rearrange w = 5x − 6y to make x the subject.

  1. 1w + 6y = 5x
  2. 2x = (w + 6y)/5

Answer(w + 6y)/5

Part (c) · 2 marks

Factorise 15y − x² − 3xy + 5x.

  1. 115y − x² − 3xy + 5x = 5(3y + x) − x(x + 3y)
  2. 2= (5 − x)(3y + x)

Answer(5 − x)(3y + x) or −(x − 5)(3y + x)

Part (d) · 4 marks

Write 2/(x − 3) − 4/(x + 3) + 1 as one fraction in simplest form.

  1. 1Common denominator (x − 3)(x + 3)
  2. 2[2(x + 3) − 4(x − 3) + (x − 3)(x + 3)]/((x − 3)(x + 3))
  3. 3Numerator = 2x + 6 − 4x + 12 + x² − 9 = x² − 2x + 9
  4. 4= (x² − 2x + 9)/((x − 3)(x + 3))

Answer(x² − 2x + 9)/((x − 3)(x + 3)) or (x² − 2x + 9)/(x² − 9)

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Also searched as: 4024/21/O/N/24 · 4024_w24_qp_21 · 4024 w24 21 · question 5.
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