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Date November 2019 Marks available 2 Reference code 19N.2.SL.TZ0.S_2
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Write down Question number S_2 Adapted from N/A

Question

Consider the lines L1L1 and L2L2 with respective equations

L1:y=23x+9L1:y=23x+9  and  L2:y=25x195L2:y=25x195.

A third line, L3L3, has gradient 3434.

Find the point of intersection of L1L1 and L2L2.

[2]
a.

Write down a direction vector for L3L3.

[1]
b.

L3L3 passes through the intersection of L1L1 and L2L2.

Write down a vector equation for L3L3.

[2]
c.

Markscheme

valid approach           (M1)

eg      L1=L2L1=L2x=12x=12y=1y=1

(121)(121)  (exact)         A1  N2

[2 marks]

a.

(43)(43)  (or any multiple of (43)(43))       A1  N1

[1 mark]

b.

any correct equation in the form r = a + ttb (accept any parameter for tt) where 
a is a position vector for a point on L1L1, and b is a scalar multiple of (43)(43)       A2  N2

eg       r =(121)+t(43)=(121)+t(43)

Note: Award A1 for the form a + tb, A1 for the form L = a + tb, A0 for the form r = b + ta.

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2—Functions » SL 2.10—Solving equations graphically and analytically
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Topic 2—Functions
Topic 3— Geometry and trigonometry

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