Page 52 - 新思维数学学生用书9 样章

2.6 Deriving and using formulae

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11 The formula for the area of a circle is A = π .
r
a Work out the area of a circle with radius 5 cm. Use the π button on your calculator.
Write your answer correct to 3 significant figures (3 s.f.).
b Make r the subject of the formula.
c Work out the radius of a circle with an area of 122.7 cm .
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Write your answer correct to 3 significant figures (3 s.f.).
12 Simon uses the formula V = to work out the volume of a cube.
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l
a Make l the subject of the formula.
b Simon works out that the volumes of two different cubes are 64 cm and 216 cm .
3
3
Work out the difference in the side length of the cubes.
13 Sasha uses the relationship shown to 5F = 9C + 160
change between temperatures in degrees where: F is the temperature in degrees

Fahrenheit (°F) and temperatures in Fahrenheit (°F)
degrees Celsius (°C). C is the temperature in degrees
Sasha thinks that 30 °C is higher than Celsius (°C).

82 °F.
Is she correct? Show how you worked out your answer.
14 A doctor uses the formula in the box to calculate m
a patient’s body mass index (BMI). BMI = h 2
A patient is described as underweight if their BMI where: m is the mass in kilograms

is below 18.5. h is the height in metres.
a Tina’s mass is 48.8 kg and her height is
1.56 m. Is she underweight?
Explain your answer. Show your working.

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.

Summary checklist

I can write and use formulae.
I can change the subject of a formula.

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