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4024/22 Oct/Nov 2021, Question 5: Simultaneous Equations by Elimination

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 11 marks

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The question, in short

Solve four unrelated algebra tasks: a simultaneous-equation word problem about card and envelope masses, a factorisation, a formula rearrangement, and combining two algebraic fractions.

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

Part (a) · 4 marks

Using 4 cards plus 3 envelopes weigh 85 g and 2 cards plus 5 envelopes weigh 67 g, set up two equations and solve for the mass of one card and one envelope.

  1. 14c + 3e = 85 and 2c + 5e = 67
  2. 2Double the second: 4c + 10e = 134
  3. 3Subtract: 7e = 49, so e = 7
  4. 44c + 21 = 85, so c = 16
  5. 5Card = 16 g, Envelope = 7 g

AnswerCard = 16, Envelope = 7

Part (b) · 1 mark

Write x² − 25 as a product of two brackets.

  1. 1x² − 25 = x² − 5²
  2. 2= (x + 5)(x − 5)

Answer(x + 5)(x − 5)

Part (c) · 3 marks

Change r = 2t/(t − 5) so that t is expressed in terms of r.

  1. 1r(t − 5) = 2t
  2. 2rt − 5r = 2t
  3. 3rt − 2t = 5r
  4. 4t(r − 2) = 5r
  5. 5t = 5r/(r − 2)

Answert = 5r/(r − 2) or −5r/(2 − r)

Part (d) · 3 marks

Combine 4/(x − 5) − 3/(2x + 1) into one fraction and simplify it.

  1. 1Common denominator (x − 5)(2x + 1)
  2. 2Numerator: 4(2x + 1) − 3(x − 5)
  3. 3= 8x + 4 − 3x + 15 = 5x + 19
  4. 4Answer (5x + 19)/((x − 5)(2x + 1))

Answer(5x + 19)/((x − 5)(2x + 1)) or (5x + 19)/(2x² − 9x − 5)

Stuck on a step? Read the free lesson: Simultaneous Equations by Elimination

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Also searched as: 4024/22/O/N/21 · 4024_w21_qp_22 · 4024 w21 22 · question 5.
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