4PM1/02R Jun 2020, Question 4: Solving Equations by Graphical Methods

Part (a) · 2 marks

Fill in the missing y-values in the table for y = 2x + 1 + 2/x², rounding to 2 decimal places where needed.

1. 1x = 0.5: 1 + 1 + 8 = 10
2. 2x = 1.5: 3 + 1 + 0.888… = 4.89
3. 3x = 2: 4 + 1 + 0.5 = 5.5
4. 4x = 3: 6 + 1 + 0.222… = 7.22

Answerx = 0.5: 10; x = 1.5: 4.89; x = 2: 5.5; x = 3: 7.22

Part (b) · 2 marks

Plot the graph of y = 2x + 1 + 2/x² on the grid for x from 0.5 to 3.5.

1. 1Plot the seven points from the table
2. 2Join them with a smooth curve

AnswerSmooth curve through (0.5, 10), (1, 5), (1.5, 4.89), (2, 5.5), (2.5, 6.32), (3, 7.22), (3.5, 8.16)

Part (c) · 2 marks

From your graph, estimate to 1 decimal place the roots of 2x + 2/x² = 7 for 0.5 ≤ x ≤ 3.5.

1. 1Add 1 to both sides: 2x + 1 + 2/x² = 8
2. 2Draw y = 8 and read off the intersections
3. 3x = 0.6 and x = 3.4

Answerx = 0.6 to 0.7 or x = 3.3 to 3.5

Part (d) · 5 marks

Draw a suitable straight line on the grid and use it to estimate, to 1 decimal place, the roots of 3x/2 + 2/x² = 5 for 0.5 ≤ x ≤ 3.5.

1. 1Add x/2 + 1 to both sides: 2x + 1 + 2/x² = x/2 + 6
2. 2Draw the line y = x/2 + 6
3. 3Read off the intersections: x = 0.7 and x = 3.2

Answerx = 0.7 and x = 3.2 (0.8 and 3.3 also accepted)

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