Unit 8

9 marks · Easy

This question is about graphs and vectors. Answer each part, showing your methods.

(a)

Draw the graph of the curve for .

[2 marks]

(b)

Use your graph to solve the equation . Write down the values of correct to 1 decimal place.

[2 marks]

(c)

Let vector and vector .

Calculate the column vector .

[2 marks]

(d)

The point has coordinates . The vector represents the movement from to point .

Write down the coordinates of point .

[1 mark]

(e)

Find the magnitude of the vector from part (c). Give your answer to 2 decimal places.

[2 marks]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) A neatly plotted graph of for , points joined smoothly; axes labelled and scaled appropriately. · must show Curve passes through points (0,2), (1,-1),(2,-2),(3,-1), (4,2), (5,7), Axes labelled x and y

(b) x = 1.6, 2.4 (accept both values correct to 1 d.p.) · must show x=1.6, x=2.4

(d) Q = (5, 5) · must show (5,5)

(e) · must show 5.83

Common mistakes: Reading graph coordinates incorrectly; Adding vector components incorrectly; Misapplying magnitude formula

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Plots at least four correct points for and joins them smoothly.

A1 (a) · 1 mark · Axes correctly labelled and graph covers required domain, or at least 1 mark for good attempt.

M2 (b) · 1 mark · Attempts to read values where the curve crosses . (follow-through)

A2 (b) · 1 mark · Both values and given to 1 decimal place.

M3 (c) · 1 mark · Correct method: multiplies and adds vectors in column form.

A3 (c) · 1 mark · Correct answer as a column vector.

B1 (d) · 1 mark · Correct coordinates for Q: (5,5). (follow-through)

M4 (e) · 1 mark · Attempts magnitude using or equivalent. (follow-through)

A4 (e) · 1 mark · Correct magnitude 5.83 (to 2 d.p.). (follow-through)

Worked solution

a) Table of values for :

x	0	1	2	3	4	5
y	2	-1	-2	-1	2	7

Plot the six points (0,2), (1,-1), (2,-2), (3,-1), (4,2), (5,7) on axes and join smoothly with a curve.

b) To solve , set on the graph. The curve crosses at approximately and , correct to 1 d.p.

d) Q is found by adding to P's coordinates (3,2): (3+2, 2+3) = (5,5)

e) Magnitude = (2 d.p.).