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Date May 2018 Marks available 2 Reference code 18M.1.SL.TZ1.S_4
Level Standard Level Paper Paper 1 Time zone Time zone 1
Command term Show that Question number S_4 Adapted from N/A

Question

Let f(x) = ax2 − 4xc. A horizontal line, L , intersects the graph of f at x = −1 and x = 3.

The equation of the axis of symmetry is x = p. Find p.

[2]
a.i.

Hence, show that a = 2.

[2]
a.ii.

Markscheme

METHOD 1 (using symmetry to find p)

valid approach      (M1)

eg   1 + 3 2

p = 1     A1 N2

Note: Award no marks if they work backwards by substituting a = 2 into  b 2 a to find p.

Do not accept  p = 2 a .

 

METHOD 2 (calculating a first)
(i) & (ii) valid approach to calculate a      M1

eg   a + 4 − c = a(32) − 4(3) − c,  f(−1) = f(3)

correct working      A1

eg   8a = 16

a = 2      AG N0

valid approach to find p      (M1)

eg    b 2 a , 4 2 ( 2 )

p = 1      A1 N2

[2 marks]

a.i.

METHOD 1

valid approach       M1

eg  b 2 a , 4 2 a  (might be seen in (i)), f' (1) = 0

correct equation     A1

eg  4 2 a = 1, 2a(1) − 4 = 0

a = 2      AG N0

 

METHOD 2 (calculating a first)
(i) & (ii) valid approach to calculate a      M1

eg   a + 4 − c = a(32) − 4(3) − c,  f(−1) = f(3)

correct working      A1

eg   8a = 16

a = 2      AG N0

[2 marks]

a.ii.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.

Syllabus sections

Topic 2—Functions » SL 2.5—Modelling functions
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Topic 2—Functions

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