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4MA1/1HR Jan 2020, Question 18: Speed from a Curved Travel Graph

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 7 marks

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The question, in short

Using the given graph of y = f(x) for −4 ≤ x ≤ 12 with point P at x = 2, estimate the gradient at P, find the tangent equation there, and determine k values giving exactly two solutions.

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

Part (ai) · 3 marks

Estimate the gradient of the curve at point P, where x = 2, by using the graph.

  1. 1Draw a tangent at the point P where x = 2
  2. 2Measure the rise and run of the tangent line
  3. 3Calculate gradient: (change in y) / (change in x)
  4. 4−1.2 / 2 = −0.6

Answer−0.6

Part (aii) · 2 marks

Using your gradient from part (ai), find the tangent line equation at P in the form y = mx + c.

  1. 1Use the gradient from part (i): m = −0.6
  2. 2Identify a point on the tangent: (2, 2.4)
  3. 3Substitute into y = mx + c: 2.4 = −0.6 × 2 + c
  4. 42.4 = −1.2 + c
  5. 5c = 3.6
  6. 6y = −0.6x + 3.6

Answery = −0.6x + 3.6

Part (b) · 2 marks

Using the graph, find the two possible values of k for which f(x) = k has exactly two solutions for −4 ≤ x ≤ 12.

  1. 1Look for horizontal lines y = k that intersect the graph exactly twice
  2. 2One line crosses at the peak near y = 3
  3. 3Another line crosses at the trough near y = −1
  4. 4k = 3 and k = −1

Answer3, −1

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