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4PM1/01R Jun 2020, Question 2: Simultaneous Equations with a Curve

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 11 marks

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The question, in short

Complete the square for x² + 4x − 8, solve the simultaneous equations with y = 2x + 7 algebraically, then sketch the curve and line showing turning point and intersection coordinates.

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

Part (a) · 2 marks

Rewrite x² + 4x − 8 as (x + a)² + b, finding the constants a and b.

  1. 1x² + 4x − 8 = (x + 2)² − 4 − 8
  2. 2= (x + 2)² − 12

Answer(x + 2)² − 12, a = 2, b = −12

Part (b) · 5 marks

Solve algebraically the simultaneous equations y = x² + 4x − 8 and y = 2x + 7.

  1. 1x² + 4x − 8 = 2x + 7
  2. 2x² + 2x − 15 = 0
  3. 3(x − 3)(x + 5) = 0 ⇒ x = 3 or −5
  4. 4x = 3, y = 13; x = −5, y = −3

Answerx = 3, y = 13 and x = −5, y = −3

Part (c) · 4 marks

On one set of axes sketch C and L, marking the turning point of C and the intersection points.

  1. 1C is a U-shaped parabola with turning point (−2, −12) from part (a)
  2. 2L is a straight line with gradient 2 and y-intercept 7
  3. 3Label the intersections (−5, −3) and (3, 13) from part (b)

AnswerU-shaped parabola with minimum (−2, −12); straight line with positive gradient and positive y-intercept 7; they intersect at (−5, −3) and (3, 13)

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