Cambridge International Mathematics

Review set 23A

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1 Sketch the graphs of the following cubics, showing all axes intercepts:

a y=x(x¡2)(x+3) b y=¡2(x+1)^2 (x¡3)

2 Find the form of the cubic function which has:

a x-intercept¡ 1 , 0 and 2 and y-intercept 6

b x-intercepts 1 and 4 ,y-intercept¡ 4 , and passes through(3,¡4):

3

4 Find the inverse function of: a f(x)=4x¡ 1 b g(x)=

1

x+3

5 For the function f(x)=

2 x¡ 5

3

:

a find f¡^1 (x)

b sketch y=f(x), y=f¡^1 (x) and y=x on the same axes.

6 Solve forx, correct to 3 significant figures:

a 7 x=50 b 5 x^3 ¡

p

x=12 c 3 x^2 ¡5=2¡x

7 Find the coordinates of the points of intersection for:

aby=6¡ 2 x and y=(x¡3)^2 ¡

1

p

x

8 Suppose f(x)=

x^2 +4

x^2 ¡ 1

:

a Use technology to sketch the graph of y=f(x):

b Find the equations of the three asymptotes.

c Find the domain and range of f(x).

d If

x^2 +4

x^2 ¡ 1

=k has 2 solutions, find the range of possible values ofk.

9 Find, as accurately as possible, the gradient of the tangent to y=

4

x

at the point(2,2):

Review set 23B

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1 Use axes intercepts to sketch the graphs of:

a y=(x+ 3)(x¡4)(x¡2) b y=3x^2 (x+2)

y

x

-1 O

-6

3

Find the equation of the cubic with

graph given alongside.

Give your answer in factor form and

in expanded form.

y=(1:5)¡x and y=2x^2 ¡ 7

Further functions (Chapter 23) 481

IGCSE01

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Y:\HAESE\IGCSE01\IG01_23\481IGCSE01_23.CDR Monday, 27 October 2008 2:18:59 PM PETER