4024/12 May/Jun 2022, Question 16: Solving Equations by Graphical Methods
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks
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The question, in short
Use the given graph of y = x³/5 − 3x + 2 to estimate a gradient from a tangent and to solve an equation by adding a straight line.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Draw a tangent to the curve at x = −1 and use it to estimate the gradient there.
- 1At x = −1, y = −1/5 + 3 + 2 = 4.8
- 2Draw the tangent touching the curve at (−1, 4.8); it passes through about (1, 0)
- 3Gradient = (0 − 4.8)/(1 − (−1)) = −4.8/2
- 4≈ −2.4
Answer−3 to −2
Part (b) · 3 marks
Draw a suitable straight line on the graph and use its intersections to find the solutions of x³/5 − 3x = 0.
- 1x³/5 − 3x = 0 is the same as x³/5 − 3x + 2 = 2
- 2Draw the line y = 2 and read off where it meets the curve
- 3x³/5 − 3x = x(x²/5 − 3) = 0 gives x = 0 or x² = 15
- 4x ≈ −3.87, x = 0, x ≈ 3.87
Answer−3.9 to −3.8, 0, 3.8 to 3.9
Stuck on a step? Read the free lesson: Solving Equations by Graphical Methods
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