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Date May 2018 Marks available 7 Reference code 18M.1.sl.TZ2.10
Level SL only Paper 1 Time zone TZ2
Command term Find Question number 10 Adapted from N/A

Question

Consider a function f. The line L1 with equation y=3x+1 is a tangent to the graph of f when x=2

Let g(x)=f(x2+1) and P be the point on the graph of g where x=1.

Write down f(2).

[2]
a.i.

Find f(2).

[2]
a.ii.

Show that the graph of g has a gradient of 6 at P.

[5]
b.

Let L2 be the tangent to the graph of g at P. L1 intersects L2 at the point Q.

Find the y-coordinate of Q.

[7]
c.

Markscheme

recognize that f(x) is the gradient of the tangent at x     (M1)

eg   f(x)=m

f(2)=3  (accept m = 3)     A1 N2

[2 marks]

a.i.

recognize that f(2)=y(2)     (M1)

eg  f(2)=3×2+1

f(2)=7     A1 N2

[2 marks]

a.ii.

recognize that the gradient of the graph of g is g(x)      (M1)

choosing chain rule to find g(x)      (M1)

eg  dydu×dudx,u=x2+1,u=2x

g(x)=f(x2+1)×2x     A2

g(1)=3×2     A1

g(1)=6     AG N0

[5 marks]

 

 

b.

 at Q, L1L2 (seen anywhere)      (M1)

recognize that the gradient of L2 is g'(1)  (seen anywhere)     (M1)
eg  m = 6

finding g (1)  (seen anywhere)      (A1)
eg  g(1)=f(2),g(1)=7

attempt to substitute gradient and/or coordinates into equation of a straight line      M1
eg  yg(1)=6(x1),y1=g(1)(x7),7=6(1)+b

correct equation for L2 

eg  y7=6(x1),y=6x+1     A1

correct working to find Q       (A1)
eg   same y-intercept, 3x=0

y=1     A1 N2

[7 marks]

 

c.

Examiners report

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

Syllabus sections

Topic 2 - Functions and equations » 2.2 » The graph of a function; its equation y=f(x) .
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