Cambridge Additional Mathematics

126 Surds, indices, and exponentials (Chapter 4)

4 Let f(x)=3x.

a Write down the value of: i f(4) ii f(¡1)

b Find the value ofksuch that f(x+2)=kf(x), k 2 Z.

5 Write without brackets or negative exponents:

a x¡^2 £x¡^3 b 2(ab)¡^2 c 2 ab¡^2

6 Write as a single power of 3 :

a

27

9 a

b (

p

3)^1 ¡x£ 91 ¡^2 x

7 Evaluate:

a 8

2

(^3) b 27 ¡
2
3
8 Write without negative exponents:
a mn¡^2 b (mn)¡^3 c
m^2 n¡^1
p¡^2
d (4m¡^1 n)^2
9 Expand and simplify:
a (3¡ex)^2 b (
p
x+ 2)(
p
x¡2) c 2 ¡x(2^2 x+2x)
10 Find the positive solution of the equation (8 +
p
13)x^2 +(2¡
p
13)x¡1=0.
Give your solution in the form x=a+b
p
13 , where a,b 2 Q.
11 Solve forx:
a 2 x¡^3 = 321 b 9 x=27^2 ¡^2 x c e^2 x=
1
p
e
12 Match each equation to its corresponding graph:
a y=¡ex b y=3£ 2 x c y=ex+1 d y=3¡x e y=¡e¡x
ABC
DE
13 If f(x)=3£ 2 x, find the value of:
a f(0) b f(3) c f(¡2)
14 Consider the function f:x 7 !e¡x¡ 3.
a State the range of the function. b Find the value of f(0).
c Solve f(x)=
p
e¡ 3 e
e
.
1
2
x
y
O
y
x
1
O
y
x

• 1

O

y

x

3

O

y

x

• 1

O

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_04\126CamAdd_04.cdr Tuesday, 14 January 2014 10:29:04 AM BRIAN