Date May 2017 Marks available 1 Reference code 17M.2.sl.TZ1.10
Level SL only Paper 2 Time zone TZ1
Command term Write down Question number 10 Adapted from N/A
Question
Markscheme
Let and , for .
The graph of can be obtained from the graph of by two transformations:
f
(
x
) = ln
x g
(
x
) = 3 + ln
( )
x
2
x
> 0
g f
a horizontal stretch of scale factor
q
followed by
a translation of
(
h
k
)
.
Let , for . The following diagram shows the graph of and the line .
The graph of intersects the graph of at two points. These points have coordinates 0.111 and 3.31 correct to three significant figures.
h
(
x
) =
g
(
x
) × cos(0.1
x
) 0 <
x
< 4
h y
=
x
h h
−1
x
Write down the value of ;
q
[1]a.i.
Write down the value of ;
h
[1]a.ii.
Write down the value of .
k
[1]a.iii.
Find .
∫
3.31
0.111 (
h
(
x
) −
x
) d
x
[2]b.i.
Hence, find the area of the region enclosed by the graphs of and .
h h
−1
[3]b.ii.
Let be the vertical distance from a point on the graph of to the line . There is a point on the graph of where is a
maximum.
Find the coordinates of P, where .
d h y
=
x
P(
a
,
b
)
h d
0.111 <
a
< 3.31
[7]c.
A1 N1
q
= 2
a.i.
