year 8 maths

2G
Formulas and relationships
93
12 The formula for the area of a trapezium is A = 1 h(a + b) .
2
a Find the area of the trapezium shown at right.
a
h
b
b Find the value of h if A = 20 , a = 3 and b = 7 .
8
6
12
c
Find the missing value in the trapezium shown at right.
7
Area = 72
8
13 Katy is a scientist who tries to work out the relationship between the volume of a gas, V mL , and
its temperature, T°C . She takes a few measurements.
V 10 20
T 10 15
a What is a possible rule between V and T ?
b Use your rule to find the volume at a temperature of 27°C .
(V − 10)2
c Prove that the rule T = + 10 would also work for Katy’s results.
20
14 Consider the rule G = 120 − 4p .
a If p is between 7 and 11 , what is the largest value of G ?
b If p and G are equal, what value do they have?
15 Marie is a scientist who is trying to discover the relationship between the volume of a gas, V , its
temperature, T, and its transparency, A . She takes a few measurements.
Test 1 Test 2
V 10 20
A 2 5
T 15 12
Which one or more of the following rules are consistent with the experiment’s results?
A T = 3V B T = V + 2A
C T = 17 − A
A
16 Temperatures in degrees Fahrenheit and degrees Celsius are related by the rule F = 1.8C + 32 .
a By substituting F = x and C = x , find a value such that the temperature in Fahrenheit and the
temperature in Celsius are equal.
b By substituting F = 2x and C = x , find a temperature in Celsius that doubles to give the
temperature in Fahrenheit.
c Prove that there are no Celsius temperatures that can be multiplied by 1.8 to give the
temperature in Fahrenheit.
?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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