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Date May 2017 Marks available 3 Reference code 17M.1.SL.TZ2.T_13
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Find Question number T_13 Adapted from N/A

Question

The diagram shows part of the graph of a function y = f ( x ) . The graph passes through point A ( 1 ,   3 ) .

M17/5/MATSD/SP1/ENG/TZ2/13

The tangent to the graph of y = f ( x ) at A has equation y = 2 x + 5 . Let N be the normal to the graph of y = f ( x ) at A.

Write down the value of f ( 1 ) .

[1]
a.

Find the equation of N . Give your answer in the form a x + b y + d = 0 where a , b , d Z .

[3]
b.

Draw the line N on the diagram above.

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

3     (A1)     (C1)

 

Notes:     Accept y = 3

 

[1 mark]

a.

3 = 0.5 ( 1 ) + c OR y 3 = 0.5 ( x 1 )     (A1)(A1)

 

Note:     Award (A1) for correct gradient, (A1) for correct substitution of A ( 1 ,   3 ) in the equation of line.

 

x 2 y + 5 = 0 or any integer multiple     (A1)(ft)     (C3)

 

Note:     Award (A1)(ft) for their equation correctly rearranged in the indicated form.

The candidate’s answer must be an equation for this mark.

 

[3 marks]

b.

M17/5/MATSD/SP1/ENG/TZ2/13.c/M     (M1)(A1)(ft)     (C2)

 

Note:     Award M1) for a straight line, with positive gradient, passing through ( 1 ,   3 ) , (A1)(ft) for line (or extension of their line) passing approximately through 2.5 or their intercept with the y -axis.

 

[2 marks]

c.

Examiners report

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

Syllabus sections

Topic 2—Functions » SL 2.3—Graphing
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