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0580/42 May/Jun 2024, Question 7: Solving Linear Equations

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 11 marks

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The question, in short

Solve a linear equation, factorise two expressions fully, and work with functions f(x) = 1/(4x − 1) and g(x) = 3ˣ, finding values and an unknown.

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

Part (a) · 2 marks

Solve 3x − 8 = 6 − 4x for x.

  1. 13x + 4x = 6 + 8
  2. 27x = 14
  3. 3x = 2

Answer2

Part (b) · 2 marks

Factorise 10a² + 5a completely.

  1. 1The highest common factor of 10a² and 5a is 5a.
  2. 210a² ÷ 5a = 2a and 5a ÷ 5a = 1
  3. 310a² + 5a = 5a(2a + 1)

Answer5a(2a + 1)

Part (c) · 2 marks

Factorise (2x − 3)² − 9 completely.

  1. 1Difference of two squares: ((2x − 3) − 3)((2x − 3) + 3)
  2. 2= (2x − 6)(2x)
  3. 3= 4x(x − 3)

Answer4x(x − 3)

Part (di) · 1 mark

Find f(4) for f(x) = 1/(4x − 1).

  1. 1f(4) = 1/(4 × 4 − 1) = 1/15

Answer1/15

Part (dii) · 2 marks

Find gg(2), applying g twice with g(x) = 3ˣ.

  1. 1g(2) = 3² = 9
  2. 2gg(2) = g(9) = 3⁹ = 19 683

Answer19683

Part (diii) · 2 marks

Find k such that g(k) = f(7).

  1. 1f(7) = 1/(28 − 1) = 1/27
  2. 23ᵏ = 1/27 = 3⁻³
  3. 3k = −3

Answer−3

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Also searched as: 0580/42/M/J/24 · 0580_s24_qp_42 · 0580 s24 42 · question 7.
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