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0580/43 May/Jun 2022, Question 6: Rearranging Formulas

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 14 marks

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The question, in short

Five-part algebra exercise: simplify an expression, expand and simplify, combine fractions, solve an equation, and rearrange a formula to make x the subject.

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

Part (a) · 2 marks

Collect like terms in a − 2b − 3a + 7b to give the simplest form.

  1. 1a − 3a = −2a, −2b + 7b = 5b
  2. 2= 5b − 2a

Answer5b − 2a

Part (b) · 2 marks

Multiply out 4(x − 5) − (3 − 2x) and collect terms.

  1. 14x − 20 − 3 + 2x
  2. 2= 6x − 23

Answer6x − 23

Part (c) · 3 marks

Combine 3/(x − 5) − 7/(2x) into one fraction, fully simplified.

  1. 1Common denominator 2x(x − 5)
  2. 2(3 × 2x − 7(x − 5))/(2x(x − 5))
  3. 3= (6x − 7x + 35)/(2x(x − 5)) = (35 − x)/(2x(x − 5))

Answer(35 − x)/(2x(x − 5)) or (35 − x)/(2x² − 10x)

Part (d) · 3 marks

Find the value of x satisfying (13 − 4x)/3 = 6 − x.

  1. 113 − 4x = 3(6 − x) = 18 − 3x
  2. 2−4x + 3x = 18 − 13
  3. 3−x = 5, x = −5

Answer−5

Part (e) · 4 marks

Rearrange y = (5(p − 2x))/x so that x is expressed in terms of y and p.

  1. 1xy = 5(p − 2x) = 5p − 10x
  2. 2xy + 10x = 5p
  3. 3x(y + 10) = 5p
  4. 4x = 5p/(y + 10)

Answer5p/(y + 10)

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Also searched as: 0580/43/M/J/22 · 0580_s22_qp_43 · 0580 s22 43 · question 6.
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