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9.4 Deriving and using formulae

3 Use the formula v = u + at to work out the value of:
a v when u = 7, a = 10, t = 8 b v when u = 0, a = 5, t = 25 c u when v = 75, a = 4, t = 12
d u when v = 97, a = 6, t = 8.5 e t when v = 80, u = 20, a = 6 f a when v = 72, u = 34, t = 19.

4 Amy is x years old. Tom is 2 years older than Amy.
a Write an expression for Tom’s age in terms of x.
b Write a formula for the total age, T, of Amy and Tom.
c Use your formula in part b to work out T when x = 19.
d Rearrange your formula in part b to make x the subject.
e Use you formula in part d to work out x when T = 48.

5 Adrian buys and sells paintings.
He uses the formula on the right to work Percentage profi t = sellingprice –costprice × 100

out the percentage profit he makes. cost price

Work out Adrian’s percentage profit on
each of these paintings.
a Cost price $250, selling price $300
b Cost price $120, selling price $192
c Cost price $480, selling price $1080

6 In some countries the mass of a person is measured in stones (S) and pounds (P).
The formula to convert a mass from stones and
pounds into kilograms is shown opposite.
+
(
Work out the mass, in kilograms, of a person K = 514SP ) where: K is the number of kilograms
11
with a mass of: S is the number of stones
a 10 stones and 3 pounds P is the number of pounds.
b 7 stones and 10 pounds
c 15 stones and 1 pound 9 stones exactly means 9 stones and 0 pounds
d 9 stones

7 Sasha uses the relationship shown to change between temperatures in degrees Fahrenheit (°F) and
temperatures in degrees
Celsius (°C). 5F = 9C + 160 where: F is the temperature in degrees Fahrenheit (°F)
Sasha thinks that 30 °C is C is the temperature in degrees Celsius (°C)
higher than 82 °F.
Is she correct? Show how you worked out your answer.

8 A doctor uses the formula in the box to calculate
patients’ body mass index (BMI). BMI = m 2 where: m is the mass in kilograms
A patient is described as underweight if their BMI is h h is the height in metres.
below 18.5.
a Tina’s mass is 48.8 kg and her height is 1.56 m. Is she underweight? Explain your answer.
b Stephen’s height is 1.80 m and his mass is 68.5 kg. He wants to have a BMI of 20.
How many kilograms must he lose to reach a BMI of 20? Show your working.

90 9 Expressions and formulae