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4024/21 Oct/Nov 2020, Question 6: Simultaneous Equations by Elimination

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 12 marks

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The question, in short

Solve an inequality, form and solve simultaneous equations for notebook and pen costs, and rearrange and solve a quadratic equation to 2 decimal places.

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

Part (a) · 2 marks

Find the solution set of the inequality 6x − 7 > 5 − 2x.

  1. 16x + 2x > 5 + 7
  2. 28x > 12
  3. 3x > 1.5

Answerx > 1.5

Part (b) · 4 marks

Using 4 notebooks and 3 pens costing $17.50, and 2 notebooks and 5 pens costing $14, form simultaneous equations and find each item's cost.

  1. 14n + 3p = 17.50 and 2n + 5p = 14
  2. 2Double the second: 4n + 10p = 28
  3. 3Subtract: 7p = 10.50, so p = 1.50
  4. 42n + 7.50 = 14, so n = 3.25
  5. 5Notebook $3.25, Pen $1.50

AnswerNotebook $3.25, Pen $1.50

Part (ci) · 3 marks

Show that x/(x + 2) − 3/(x − 5) = 4 rearranges to 3x² − 4x − 34 = 0.

  1. 1Multiply by (x + 2)(x − 5): x(x − 5) − 3(x + 2) = 4(x + 2)(x − 5)
  2. 2x² − 5x − 3x − 6 = 4(x² − 3x − 10)
  3. 3x² − 8x − 6 = 4x² − 12x − 40
  4. 40 = 3x² − 4x − 34

AnswerCorrect completion to 3x² − 4x − 34 = 0

Part (cii) · 3 marks

Solve 3x² − 4x − 34 = 0, showing working, with answers to 2 decimal places.

  1. 1x = (4 ± √((−4)² − 4 × 3 × (−34)))/(2 × 3)
  2. 2= (4 ± √424)/6
  3. 3x = 4.10 or x = −2.77

Answer4.10, −2.77

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

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Also searched as: 4024/21/O/N/20 · 4024_w20_qp_21 · 4024 w20 21 · question 6.
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