Page 31 - Mathematics Coursebook

End of unit review

End of unit review

1 For each of these infinite sequences, work out:
i the term-to-term rule ii the next two terms iii the tenth term.
a 6, 8, 10, 12, …, … b 9, 15, 21, 27, …, … c 28, 25, 22, 19, …, …

2 Write down the first four terms of the sequence that has a first term

of 5 and a term-to-term rule of: ‘Multiply by 3 then subtract 5.’
3 Sally is trying to solve this problem.
Work out the answer to the problem. The third term of a sequence is 19 and
Explain how you solved the problem. the fifth term is 11.
the fifth term is 11.
The term-to-term rule is: ‘Subtract a
The term-to-term rule is: ‘Subtract a
mystery number.’
mystery number.’
What is the first term of the sequence?
What is the mystery number?
4 This pattern is made from squares.
Pattern 1 Pattern 2 Pattern 3

a Draw the next pattern in the sequence.
b Copy and complete the table to show the number of squares in each pattern.
Pattern number 1 2 3 4 5

Number of squares 5 10

c Write down the term-to-term rule.
d How many squares will there be in Pattern 10?

5 Copy these function machines and work out the missing inputs and outputs.

Inputt
Output
Output
a
a a Inpu Output b b Inpub Inputt Output
11 ... ... 22 ... ...
33 + 4 + 4 ... ... 44 × 3 × 3 – 4 – 4 ... ...
... ... 12 12 ... ... 20 20
6 Ahmad looks at this function machine.
Input Output
2 6 I think the function is: ‘Divide by 2 then add 5.’
6 ... ... 8
10 10

Is Ahmad correct? Explain your answer.
7 Nimrah thinks of a number, n.
Write an expression for the number Nimrah gets each time.
a She multiplies the number by 4. b She subtracts 6 from the number.
c She multiplies the number by 3 then adds 5. d She divides the number by 6 then subtracts 1.

8 Work out the value of each expression.
a a + 3 when a = 8 b p + 3q when p = 3 and q = 4.
30 2 Sequences, expressions and formulae