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0580/33 May/Jun 2021, Question 4: Substitution

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 13 marks

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The question, in short

Simplify an expression, evaluate a formula, factorise two expressions, rearrange a formula, and solve two equations.

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

Part (a) · 2 marks

Simplify 3a − 5b + 2a + b by collecting like terms.

  1. 13a + 2a = 5a and −5b + b = −4b
  2. 2= 5a − 4b

Answer5a − 4b

Part (b) · 3 marks

Given P = 3x² − xy, find y when P = 90 and x = 5.

  1. 190 = 3 × 5² − 5y
  2. 290 = 75 − 5y
  3. 390 − 75 = −5y, so 15 = −5y
  4. 4y = −3

Answer−3

Part (ci) · 1 mark

Factorise 6x − 18 completely.

  1. 16x − 18 = 6(x − 3)

Answer6(x − 3)

Part (cii) · 2 marks

Factorise 25x² + 10x completely.

  1. 1HCF of 25x² and 10x is 5x
  2. 225x² + 10x = 5x(5x + 2)

Answer5x(5x + 2)

Part (d) · 2 marks

Rearrange T = 8d − 3 to make d the subject.

  1. 1T + 3 = 8d
  2. 2d = (T + 3)/8

Answer(T + 3)/8

Part (ei) · 1 mark

Solve x/6 = 12 for x.

  1. 1x = 12 × 6 = 72

Answer72

Part (eii) · 2 marks

Solve 7x − 4 = 3x + 2 for x.

  1. 17x − 3x = 2 + 4
  2. 24x = 6
  3. 3x = 1.5

Answer1.5 or 1 1/2 or 3/2

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Also searched as: 0580/33/M/J/21 · 0580_s21_qp_33 · 0580 s21 33 · question 4.
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