Page 30 - MAT KS3 Y8 Cambridge CheckPoint

2.6 Deriving and using formulae

3 This is part of Dakarai’s homework.
He has made a mistake in his working. Question Work out the value of
a Explain the mistake that he has made. x – 8 when x = –3.
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b Work out the correct answer for him. Answer x – 8 = (–3) – 8
2
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c Work out the value of y + 4 when y = −5. = –3 × –3 – 8
2
= –9 – 8
= –17
4 This is part of Oditi’s homework. She has made
a mistake in her working. Question Work out the value of
a Explain the mistake that she has made. 5x when x = –2.
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b Work out the correct answer.
3
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c Work out the value of 2y when y = −3. Answer 5x = 5 × (–2)
3
= (–10)
3
= –10 × –10 × –10
= –1000
5 a Write a formula for the number of months in any number of years, in:
i words ii letters.
b Use your formula in part a to work out the number of months in 8 years.
6 Use the formula v = u + 10t to work out the value of v when:
a u = 5 and t = 12 b u = 8 and t = 15 c u = 0 and t = 20.
7 Use the formula F = ma to work out F when:
a m = 6 and a = 2 b m = 18 and a = 3 c m = 8 and a = −4

8 In the UK the height of a horse is measured
in hands (H) and inches (I). C = 2.5(4H + I) where: C is the number of centimetres
Sasha has a horse with a height of 16 hands H is the number of hands
and 1 inch. She uses the formula to work out I is the number of inches.
the height of her horse, in centimetres.
Work out the height, in centimetres, of a horse with height:
a 14 hands and 2 inches b 15 hands and 3 inches C = 2.5(4 × 16 + 1)
c 13 hands and 1 inch d 17 hands and 2 inches = 2.5(64 + 1)
e 16 hands f 12 hands. = 2.5 × 65
= 162.5cm
16 hands exactly means 16 hands and 0 inches.

9 Xavier uses this formula
to work out the volume V = bhl where: V is the volume
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of a triangular prism. b is the base Remember that bhl means b × h × l.
h is the height
l is the length.

Xavier compares two prisms. Prism A has a base of 8 cm, height of 5 cm and length of 18 cm.
Prism B has a base of 9 cm, height of 14 cm and length of 6 cm.

Which prism has the larger volume? How much larger is it?

28 2 Sequences, expressions and formulae