Cambridge Additional Mathematics

(singke) #1
-1 1 x

y= 3 x

y

1

4

O

Surds, indices, and exponentials (Chapter 4) 127

15 The temperature of a dishtminutes after it is removed from the microwave, is given by
T=80£ 2 ¡^0 :^1 t ±C.
a Find the initial temperature of the dish.
b Find the temperature after: i 10 minutes ii 20 minutes.
c Draw the graph ofTagainsttfor t> 0.
d Find the time taken for the temperature of the dish to fall to 10 ±C.

Review set 4B

#endboxedheading
1 Simplify:
a (7 + 2

p
3)(5¡ 3

p
3) b (6 + 2

p
2)(6¡ 2

p
2)
2 Rationalise the denominator:
a
1
5 ¡

p
3

b

p
11
p
7 ¡ 2

c
8+

p
2
3 ¡

p
2

d
4+5

p
5
6 ¡ 3

p
5
3 Given the graph of y=3x shown, estimate
solutions to the exponential equations:
a 3 x=5
b 3 x=^12
c 6 £ 3 x=20

4 Write each of the following in the form

a (

p
2 ¡1)^2 b

p
2 ¡ 1
p
2+1
c
1
(
p
2+1)^2
d
1
3+2
p
2
5 Simplify using the laws of exponents:
a (a^7 )^3 b pq^2 £p^3 q^4 c
8 ab^5
2 a^4 b^4
6 Write the following as a power of 2 :
a 2 £ 2 ¡^4 b 16 ¥ 2 ¡^3 c 84
7 Write the following without brackets:

a (2m^3 )^2 b

μ
¡a^3
b

¶ 3
c
(3x^2 y)^2
3 x
d
(2a

1

(^2) b
1
(^5) ) 4
a
8 Simplify
2 x+1
21 ¡x
.
9 Write as powers of 5 in simplest form:
a 1 b 5
p
5 c
1
p 45 d 25
a+3
a§b
p
2 where a,b 2 Z+:
4037 Cambridge
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Y:\HAESE\CAM4037\CamAdd_04\127CamAdd_04.cdr Tuesday, 14 January 2014 10:29:07 AM BRIAN

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