Cambridge International Mathematics

Exponents and surds (Chapter 6) 145

Review set 6B

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1 Find the integer equal to: a 73 b 32 £ 52

2 Write as a product of primes in index form: a 42 b 144

3 Simplify:

a ¡(¡1)^7 b ¡ 43 c (¡2)^5 £(¡3)^2

4 Simplify, giving your answers in simplest rational form:

a 6 ¡^2 b

¡

(^112)
¢¡ 1
c
¡ 3
5
¢¡ 2
5 Simplify, using the exponent laws:
a 32 £ 36 b a^5 ¥a^5 c (y^3 )^5
6 Write as powers of 2 , 3 or 5 :
a^1625 b^4081 c 180 d (^1119)
7 Express in simplest form, without brackets or negative indices:
a (5c)¡^1 b 7 k¡^2 c (4d^2 )¡^3
8 Write in standard form:
a 263 : 57 b 0 :000 511 c 863 400 000
9 Write as an ordinary decimal number:
a 2 : 78 £ 100 b 3 : 99 £ 107 c 2 : 081 £ 10 ¡^3
10 Simplify, giving your answer in standard form:
a (8£ 103 )^2 b (3: 6 £ 105 )¥(6£ 10 ¡^2 )
11 How many kilometres are there in 0 : 21 millimetres? Give your answer in standard form.
12 Simplify:
a 2
p
3 £ 3
p
5 b (2
p
5)^3 c 5
p
2 ¡ 7
p
2
d ¡
p
2(2¡
p
2) e (
p
3)^4 f
p
3 £
p
5 £
p
15
13 Write in simplest surd form: a
p
75 b
q
20
9
14 Expand and simplify:
a (5¡
p
3)(5 +
p
3) b ¡(2¡
p
5)^2
c 2
p
3(
p
3 ¡1)¡ 2
p
3 d (2
p
2 ¡5)(1¡
p
2)
15 Express with integer denominator:
a

14

p

2

b

p

2

p

3

c

p

2

3+

p

2

d

¡ 5

4 ¡

p

3

16 Write in the form a+b

p

5 wherea,b 2 Q:

a

1+

p

5

2 ¡

p

5

b

3 ¡

p

5

3+

p

5

¡

4

3 ¡

p

5

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Y:\HAESE\IGCSE01\IG01_06\145IGCSE01_06.CDR Wednesday, 5 November 2008 2:15:20 PM PETER