4PM1/01R January 2020 Question 6: Solving Equations by Graphical Methods

Question 1

Fill in the missing y-values for y = x − 3/x² at the given x-values, rounding to one decimal place where needed.

Accepted Answer

x = 1: 1 − 3 = −2 x = 1.5: 1.5 − 3/2.25 = 0.17 → 0.2 x = 4: 4 − 3/16 = 3.81 → 3.8 x = 5: 5 − 3/25 = 4.88 → 4.9 Answer: x = 1: −2; x = 1.5: 0.2; x = 4: 3.8; x = 5: 4.9

Question 2

Draw the graph of y = x − 3/x² on the grid for x from 0.5 to 6.

Accepted Answer

Plot each point from the table within half a square Join with a smooth curve rising steeply at first then levelling off Answer: Smooth increasing curve through (0.5, −11.5), (1, −2), (1.5, 0.2), (2, 1.3), (3, 2.7), (4, 3.8), (5, 4.9), (6, 5.9)

Question 3

Draw a suitable straight line and use it to estimate, to one decimal place, both roots of 2x³ − 6x² + 3 = 0 for 0.5 ≤ x ≤ 6.

Accepted Answer

2x³ − 6x² + 3 = 0: divide by 2x² to get x − 3 + 3/(2x²) = 0 So 3/x² = 6 − 2x, and x − 3/x² = x − 6 + 2x = 3x − 6 Draw the line y = 3x − 6 on the grid Read the x-coordinates where it crosses the curve: x ≈ 0.8 and x ≈ 2.8 Answer: Draw y = 3x − 6; x ≈ 0.8 (or 0.9) and x ≈ 2.8 (or 2.9)

4PM1/01R Jan 2020, Question 6: Solving Equations by Graphical Methods

The question, in short

Part (a) · 2 marks

Part (b) · 2 marks

Part (c) · 5 marks

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