year 8 maths

Chapter review
115
10 a The sum of three consecutive numbers is 39 . First write an equation and then find the
value of the smallest number.
b Four times a number less 5 is the same as double the number plus 3 . Write an equation to
find the number.
c The difference between a number and three times that number is 17 . What is the number?
11 Solve the following simple quadratic equations. Round to two decimal places where necessary.
a x 2 = 4 b x 2 = 100 c a 2 = 49
d x 2 = 8 e y 2 = 39 f b 2 = 914
12 State the number of solutions for x in these equations .
a 2x = 6 b x 2 = 16 c x 2 = 0
d 5x 2 = 0 e 4x − 1 = 3 f x 2 = −3
Extended-response questions
1 To upload an advertisement to the www.searches.com.au website it costs $20 and then
12 cents whenever someone clicks on it.
a Write a formula relating the total cost ( $S ) and the number of clicks ( n ) on the
advertisement.
b If the total cost is $23.60 , write and solve an equation to find out how many times the
advertisement has been clicked on.
c To upload to the www.yousearch.com.au website it costs $15 initially and then 20 cents
for every click. Write a formula for the total cost, $Y, when the advertisement has been
clicked n times.
d If a person has at most $20 to spend, what is the maximum number of clicks they can
afford for their advertisement at yousearch.com.au?
e Set up and solve an equation to find the minimum number of clicks for which the total
cost of posting an advertisement to searches.com.au is less than the cost of posting to
yousearch.com.au.
2 Mahni plans to spend the next 12 weeks saving some of her income. She will save $x a week
for the first 6 weeks and then $(2x − 30) a week for the following 6 weeks.
a Write an expression for the total amount Mahni saves over the 12 weeks.
b If Mahni managed to save $213 in the first 6 weeks, how much did she save:
i in the first week? ii in the 7 th week?
iii in total over the 12 weeks?
c If Mahni wishes to save a total of $270 , write and solve an equation to find out how much
she would have to save in the first week.
d If Mahni wishes to save the same amount in the first 6 weeks as in the last 6 weeks, how
much should she save each week?
e In the end Mahni decides that she does not mind exactly how much she saves but wants
it to be between $360 and $450 . State the range of x values that would achieve this goal,
giving your answer as an inequality.
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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