year 8 maths

1C Adding and subtracting terms 17
12 Add the missing expressions to the puzzle to make all six equations true.
5x + = 7x
+ + +
y + =
= = =
+ = 7x + 3y
13 In how many ways could the blank boxes be filled if all the coefficients must be positive integers?
□ a + □ b + □ a = 10a + 7b
14 Simplify a − 2a + 3a − 4a + 5a − 6a + … + 99a − 100a.
15 Prove that 10x + 5y + 7x + 2y is equivalent to 20x − 3x + 10y − 3y . (Hint: simplify both expressions.)
16 a Make a substitution to prove that 4a + 3b is not equivalent to 7ab .
b Is 4a + 3b ever equal to 7ab ? Try to find some values of a and b to make 4a + 3b = 7ab a true
equation.
c Is 4a + 3a ever not equal to 7a ? Explain your answer.
17 a Decide whether 7x − 3x is equivalent to 7x + (−3x) . Explain why or why not.
b Fill in the missing numbers to make the following equivalence true.
14a + 3b + 2ab + □ a + □ b + □ ba = a
ENRICHMENT
– –
18
Missing expressions
18 a Fill in the missing expressions to make all eight equations true.
5a + + 4a = 10a + 3
+ + + +
2b + 4 + a + =
+ + + +
+ + −3a = 1
= = = =
+ 3a + 8 + = 10a + 2b + 8
b Design your own ‘missing values’ puzzle like the one in part a. It should have only one possible
solution.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.