Cambridge International Mathematics

144 Exponents and surds (Chapter 6)

3 Simplify:

a (¡2)^3 b ¡(¡1)^8 c (¡1)^3 £(¡2)^2 £¡ 33

4 Simplify, giving your answers in simplest rational form:

a 3 ¡^3 b

¡ 4

3

¢¡ 2

c 30 ¡ 31

5 Write 161 as a power of 2.

6 Simplify, using the exponent laws:

a 56 £ 5 b b^7 ¥b^2 c (x^4 )^3

7 Express in simplest form, without brackets:

a (4c^3 )^2 b (2a^2 b)^3 c

³ s

3 t^2

́ 4

8 Write in standard form:

a 9 b 34 900 c 0 : 0075

9 Write as an ordinary decimal number:

a 2 : 81 £ 106 b 2 : 81 £ 100 c 2 : 81 £ 10 ¡^3

10 Simplify, giving your answer in standard form:

a (6£ 103 )£(7: 1 £ 104 ) b (2: 4 £ 106 )¥(4£ 102 )

11 The Earth orbits around the Sun at a speed of approximately 1 : 07 £ 105 km/h. How far does the

Earth move, relative to the Sun, in:

a 1 day b 1 week c 1 year?

Give your answers in standard form with decimal part correct to 2 decimal places. Assume that

1 year= 365days.

12 a Simplify (3

p

2)^2 : b Simplify ¡ 2

p

3 £ 4

p

3 :

c Simplify 3

p

2 ¡

p

8 : d Write

p

48 in simplest surd form.

13 Expand and simplify:

a 2

p

3(4¡

p

3) b (3¡

p

7)^2 c (2¡

p

3)(2 +

p

3)

d (3 + 2

p

5)(2¡

p

5) e (4¡

p

2)(3 + 2

p

2)

14 Rationalise the denominator:

a

8

p

2

b

15

p

3

c

p

3

p

2

d

5

6 ¡

p

3

15 Write

q

1

7 in the form k

p

7.

16 Write in the form a+b

p

3 where a,b 2 Q:

a

p

3

2 +1

1 ¡

p

3

2

b

2+

p

3

2 ¡

p

3

¡

2

p

3

2+

p

3

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Y:\HAESE\IGCSE01\IG01_06\144IGCSE01_06.CDR Monday, 15 September 2008 3:25:03 PM PETER