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Date May 2018 Marks available 5 Reference code 18M.1.AHL.TZ2.H_11
Level Additional Higher Level Paper Paper 1 Time zone Time zone 2
Command term Express Question number H_11 Adapted from N/A

Question

It is given that log2y+log4x+log42x=0log2y+log4x+log42x=0.

Show that logr2x=12logrxlogr2x=12logrx where r,xR+.

[2]
a.

Express y in terms of x. Give your answer in the form y=pxq, where p , q are constants.

[5]
b.

The region R, is bounded by the graph of the function found in part (b), the x-axis, and the lines x=1 and x=α where α>1. The area of R is 2.

Find the value of α.

[5]
c.

Markscheme

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

METHOD 1

logr2x=logrxlogrr2(=logrx2logrr)     M1A1

=logrx2     AG

[2 marks]

 

METHOD 2

logr2x=1logxr2     M1

=12logxr     A1

=logrx2     AG

[2 marks]

 

a.

METHOD 1

log2y+log4x+log42x=0

log2y+log42x2=0     M1

log2y+12log22x2=0     M1

log2y=12log22x2

log2y=log2(12x)     M1A1

y=12x1     A1

Note: For the final A mark, y must be expressed in the form pxq.

[5 marks]

 

METHOD 2

log2y+log4x+log42x=0

log2y+12log2x+12log22x=0     M1

log2y+log2x12+log2(2x)12=0     M1

log2(2xy)=0     M1

2xy=1     A1

y=12x1     A1

Note: For the final A mark, y must be expressed in the form pxq.

[5 marks]

 

b.

the area of R is α112x1dx     M1

=[12lnx]α1     A1

=12lnα     A1

12lnα=2     M1

α=e2     A1

Note: Only follow through from part (b) if y is in the form y=pxq

[5 marks]

c.

Examiners report

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

Syllabus sections

Topic 1—Number and algebra » SL 1.5—Intro to logs
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