Cambridge International AS and A Level Mathematics Pure Mathematics 1

Exercise 1A

P^

1

2 Factorise the following expressions.

(i) 4 x + 8 y (ii) 12 a + 15 b – 18c

(iii) 72 f − 36 g − 48 h (iv) p^2 − pq + pr

(v) 12 k^2 + 144 km − 72 kn

3 Simplify the following expressions, factorising the answers where possible.

(i) 8(3x + 2 y) + 4(x + 3 y)

(ii) 2(3a − 4 b + 5 c) − 3(2a − 5 b − c)

(iii) 6(2p − 3 q + 4 r) − 5(2p − 6 q − 3 r) − 3(p − 4 q + 2 r)

(iv) 4(l + w + h) + 3(2l − w − 2 h) + 5 w

(v) 5 u − 6(w − v) + 2(3u + 4 w − v) − 11 u

4 Simplify the following expressions, factorising the answers where possible.

(i) a(b + c) + a(b − c) (ii) k(m + n) − m(k + n)

(iii) p(2q + r + 3 s) − pr − s(3p + q) (iv) x(x − 2) − x(x − 6) + 8

(v) x(x − 1) + 2(x − 1) − x(x + 1)

5 Perform the following multiplications, simplifying your answers.

(i) 2 xy × 3 x^2 y (ii) 5 a^2 bc^3 × 2 ab^2 × 3 c

(iii) km × mn × nk (iv) 3 pq^2 r × 6 p^2 qr × 9 pqr^2

(v) rs × 2 st × 3 tu × 4 ur

6 Simplify the following fractions as much as possible.

(i) abac (ii) 42 ef (iii) xx

2

5

(iv) 4

2

ab^2

ab

(v) 6

3

23

332

pqr

pqr

7 Simplify the following as much as possible.

(i) a

b

b

c

c

a

× × (ii)

3

2

8

3

5

4

x

y

y

z

z

× × x (iii)

p

q

q

p

22

×

(iv) 2

16

4

4

32

12

23

3

fg

h

gh

fh

fh

f

× ×^ (v)^ kmn

n

km

3 km

6

(^32)
23
× 3
8 Write the following as single fractions.
(i) xx 23 + (ii) 253 xx– +^34 x (iii) 38 zz+− 122 524 z
(iv) 234 xx− (v)
yy y
2

5

8

4

– + 5

9 Write the following as single fractions.

(i) (^35) xx+ (ii) (^11) xy+ (iii) (^4) x+xy
(iv)
p
q
q
p

• (v) 11 1
  ab c

– +