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End-of-unit review

End-of-unit review

1 Simplify each expression.
a x × x b y × y 4 c z × z d 3m × 5m 2 e 6n × n f 2p × 3p
3
8
6
7
3
8
9
2
g q ÷ q h r ÷ r 4 i t ÷ t j 12u 5 k 18v 9 l 7w 9
7
8
2
10
5
6u 3 6v 3 w 8
2 Write an expression for the perimeter of each shape.
Write each expression in its simplest form.
a b b + 3 c 2c d 5z – 2
a a
5 d d 3z + 1
a
3c
3 Write an expression for the area of each shape.
Write each expression in its simplest form.
a a b 8c c w d 3e
b 5d w 3e

4 Work out the value of each expression when a = −4, b = 5, c = −2 and d = 8.
a b + d b 3d − b c 5b + 3a d d + bc
2
e a + b f ac + bd g bd c − h 7(d − b)
2 a
a
i b + d j c − k 100 − 4c l d + b(3c + a)
2
2
2
24
5 Use the formula x = y + 5z to work out the value of:
a x when y = 4 and z = 3 b x when y = 16 and z = −4 c y when x = 100 and z = 7
d y when x = 20 and z = −8 e z when x = 40 and y = 30 f z when x = 25 and y = −5.
6 Factorise each expression.
a 2x + 6 b 4y − 12 c 9a − 3 d 20 − 10x e 24 + 30z f 50 − 30b
g 5x + x h 3a − 5a i 32y − 8x j 6xy − 3y k 18m + 8mn l 24n − 27n 2
2
2
7 Simplify each expression.
Give each answer as a fraction in its simplest form.

x
a x + b x + x 2 c 4x − x d y − y e 3y + 9y f 4y − 5y
3 3 5 5 7 7 5 15 4 8 9 18
y
b
b
g x + h 3x − y i a + j 3a + 2b k 5a − l 4a − 2b
4 4 5 20 3 5 4 5 6 8 7 3
8 Expand and simplify each expression.
a (x + 2)(x + 5) b (x − 3)(x + 4) c (x + 6)(x − 9)
d (x − 10)(x − 4) e (x − 8)(x + 8) f (x − 6) 2

9 Read what Hassan says.
Show that he is correct. When I expand 4(2x + 5) + 3(8x − 4), then collect like terms
and fi nally factorise the result, I get the expression 8(4x + 1).

96 9 Expressions and formulae