CAMBRIDGE LOWER SECONDARY MATHEMATICS 8: END OF UNIT 9 TEST

Name ___________________________________ Date _____________

Stage 8 End of Unit 9 Test

1 For each of these sequences, write down

i the term-to-term rule ii the next two terms.

1 3 1
3 , 3 , 4, 4 , . . . , . . .
a 2 4 4 i ___________________ ii ___________________

b 12, 11.6, 11.2, 10.8, . . . , . . . i ___________________ ii ___________________ [4]

2 The first three terms of a sequence are 6, 12, 30, . . .

a Which of these cards, A, B or C, shows the correct term-to-term rule? ____

Show how you worked out your answer.

A multiply by 4 B divide by 2 C subtract 2 then

then subtract 12 then add 9 multiply by 3

____________________________________________________________________________

____________________________________________________________________________

____________________________________________________________________________ [2]

b Which is the first term in this sequence to be greater than 300?

____________________________________________________________________________

____________________________________________________________________________

____________________________________________________________________________ [1]

3 Work out the first three terms in this sequence.

1
4
First term is 10, term-to-term rule is subtract 2 then multiply by 2.

____________________________________________________________________________

____________________________________________________________________________

First term: _______ Second term: _______ Third term: _______ [2]

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 8: END OF UNIT 9 TEST

4 This pattern is made from rectangles.

a Write down the sequence of the numbers of rectangles. __________________________ [1]

b Write down the term-to-term rule. ____________________________________________ [1]

c Draw the next pattern in the sequence.

[1]

d Complete the table to find the position-to-term rule.

Position number 1 2 3 4
term
___ × position number
___ × position number − ___

Position-to-term rule is: term = ___ × position number – ___ [3]

5 Work out the first three terms and the 10th term of the sequences with the given nth term.

a 2n + 7 ___________________________________________________________________

___________________________________________________________________ [2]

First three terms: ___, ___, ___ 10th term: ___

b 5n − 4 ___________________________________________________________________

___________________________________________________________________ [2]

First three terms: ___, ___, ___ 10th term: ___

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 8: END OF UNIT 9 TEST

6 Work out an expression for the nth term for each sequence.

a 5, 8, 11, 14, . . . ____________________________________________________________

_________________________________________________________________________

nth term is ______________________ [2]

b 19, 17, 15, 13, . . . __________________________________________________________

_________________________________________________________________________

nth term is ______________________ [2]

7 a Work out the missing values in the tables for these function machines.

i ii

1 1 8 15
x 2 6 x
2 4
1
y 11 23 y 2 11
2
[2]

b Write each function in part a as an equation.

i equation is: ______________________

ii equation is: ______________________ [2]

8 Complete these inverse function machines and equations.

a
equation: y = ________

inverse equation: x = ________ [2]

b
equation: y = ________

inverse equation: x = ________ [2]

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 CAMBRIDGE LOWER SECONDARY MATHEMATICS 8: END OF UNIT 9 TEST

9 Draw a line linking each function equation with its inverse equation.

A y = 5x B y= C y=x+5 D y = 2x + 5 E y= F y=

i x = 5y ii x = y – 5 iii x = 5(y + 2) iv x = 5y – 2 v x= vi x =

[3]

[TOTAL: 34 Marks]

END OF TEST

Cambridge Lower Secondary Mathematics 8 – Byrd, Byrd & Pearce © Cambridge University Press 2021 4