AQA Core 2 Algebra and functions

1 of 2 15/01/13 MEI

Section 1: Indices

Solutions to Exercise

1. (i) 43 3 3 3 3 81

(ii) 62 2 2 2 2 2 2 64

(iii) 1 24 4 2

(iv) 06 1

(v) 22

1 15

5 25

(vi) 1 3 364 64 4

(vii) 1 2 1 1

1616 4

(viii) 55 3 538 8 2 32

(ix)

3 2

3 3

1 1 136

6 21636

(x) 1

11 11 2 2 22

(xi)

1 2 1 / 29 925 3

9 25 25 5

(xii)

22 / 3 32 3 227 64 64 4 16

64 27 27 3 9

2. (i) 3 3 3 3 4 52 3 5 2 3 5 30a b ab b a a b b b a b

(ii) 2

2

2 2

4

a b

ab

a a b

2 4 a b b 2

a

b

(iii) 2 3

2

4 1212

9

p qr

pq r

p p q r

3 9

r r

p q q r

24

3

pr

q

(iv) 3

2 24

4 2xy x y x 2y

2 8 6x 5 3y 1 51

2x y

(v) ( 11 4 3 11 4 3 4a a a a a

(vi) 3 25 7 15 14 15 14p p p p p p

(vii) 3 3 1 3 12 2 2 2 2 2x x x x x x

(viii) 2 21 1

3 3 3 32

11y y y y y y

3. (i) 11 4 3 11 4 3 43 3 3 3 3 81

(ii) 3 25 7 15 14 15 14 12 2 2 2 2 2 2

AQA C2 Algebra 1 Exercise solutions

2 of 2 15/01/13 MEI

(iii) 6

6 5 3 2

5 3 2

5 1 15 5

5 5 5 25

(iv) 1 2 1 25 5 2 5 1

5 1 1 52 4 2 (2 ) 2 2 2 2 322 2 2

(v) 715

2 23 2 3 2 7 47 45 5 2 15 / 2 7 / 2 43 9 3 3 3 3 3 3 81

(vi) 1

4 81 5 5 523 3 3 3 3 6

4 3

1 3 8 3

xx x x x

x x

4. (i) 5 2 1 2 1 21 / 2 2

1 / 2 2

3 3 3 3 3

3 (3 1)

3 8

8 3

(ii) 1 2 3 2 5 2 1 / 2 1 / 2 1 1 / 2 2

1 / 2 2

2 2 2 2 2 2 2 2

2 (1 2 2 )

7 2

(iii) 1 2 1 2 11 yy y y

y y