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Date	May 2022	Marks available	2	Reference code	22M.1.SL.TZ1.1
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 1
Command term	Find	Question number	1	Adapted from	N/A

Question

Consider the points $A (- 2, 20)$ $A (- 2, 20)$ , $B (4, 6)$ $B (4, 6)$ and $C (- 14, 12)$ $C (- 14, 12)$ . The line $L$ $L$ passes through the point $A$ $A$ and is perpendicular to $[BC]$ $[BC]$ .

Find the equation of $L$ $L$ .

[3]

The line $L$ $L$ passes through the point $(k, 2)$ $(k, 2)$ .

Find the value of $k$ $k$ .

[2]

Markscheme

$m_{BC} = \frac{12 - 6}{- 14 - 4} (= - \frac{1}{3})$ $m_{BC} = \frac{12 - 6}{- 14 - 4} (= - \frac{1}{3})$ (A1)

finding $m_{L} = \frac{- 1}{m_{BC}}$ $m_{L} = \frac{- 1}{m_{BC}}$ using their $m_{BC}$ $m_{BC}$ (M1)

$m_{L} = 3$ $m_{L} = 3$

$y - 20 = 3 (x + 2), y = 3 x + 26$ $y - 20 = 3 (x + 2), y = 3 x + 26$ A1

Note: Do not accept $L = 3 x + 26$ $L = 3 x + 26$

[3 marks]

substituting $(k, 2)$ $(k, 2)$ into their $L$ $L$ (M1)

$2 - 20 = 3 (k + 2)$ $2 - 20 = 3 (k + 2)$ OR $2 = 3 k + 26$ $2 = 3 k + 26$

$k = - 8$ $k = - 8$ A1

[2 marks]

Examiners report

Finding the gradient of a line was well understood and many candidates also correctly found the perpendicular slope. Even with an error in their part (a), follow through marks in part (b) allowed many candidates to earn full marks for finding k despite their incorrect equation resulting in arithmetic of greater complexity.

[N/A]

Syllabus sections

Topic 2—Functions » SL 2.1—Equations of straight lines, parallel and perpendicular

22M.1.SL.TZ1.1a:
Find the equation of $L$ $L$ .
22M.2.SL.TZ2.3b:
Assuming Kaia’s annual salary can be approximately modelled by the equation $S = a x + b$ $S = a x + b$ , show that Kaia had a higher salary than Gemma in the year 2021, according to the model.
21N.1.SL.TZ0.5b:
Find $f (4)$ $f (4)$ .
18N.2.SL.TZ0.T_4a:
Sketch the graph of y = f (x), for −4 ≤ x ≤ 3 and −50 ≤ y ≤ 100.
18N.2.SL.TZ0.T_4b.iii:
Use your graphic display calculator to find the equation of the tangent to the graph of y = f (x) at the point (–2, 38.75).

Give your answer in the form y = mx + c.
18N.2.SL.TZ0.T_4c:
Sketch the graph of the function g (x) = 10x + 40 on the same axes.
21N.1.SL.TZ0.5a:
Write down the value of $f' (4)$ .
22M.1.SL.TZ2.7c:
Find the equation of $L$ .
17M.1.SL.TZ2.T_4c:
Find the $x$ -coordinate of point A.
21N.1.SL.TZ0.5c:
Find $h (4)$ .
17M.1.SL.TZ2.T_4b:
Find the equation of $L$ in the form $y = mx + c$ .
21N.1.SL.TZ0.5d:
Hence find the equation of the tangent to the graph of $h$ at $x = 4$ .

Topic 2—Functions

Question

Markscheme

Examiners report

Syllabus sections

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