Cambridge Additional Mathematics

-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