Page 32 - MAT KS3 Y8 Cambridge CheckPoint

End-of-unit review

End-of-unit review

1 Write down the first three terms of each of the sequences described.
a first term is 7, term-to-term rule is ‘add 3’
b first term is 11, term-to-term rule is ‘subtract 5’
c position-to-term rule is term = 8 × position number
d position-to-term rule is term = 4 × position number − 3
2 The third term of a sequence is 9. The eighth term of the sequence is 19.
Which of these position-to-term rules is the correct one for the sequence?
Show how you worked out your answer.

A term = position number + 9 B term = 2 × position number + 3

C term = 3 × position number D term = 4 × position number − 3

3 For each sequence of numbers:
i write down the term-to-term rule ii write the sequence of numbers in a table
iii work out the position-to-term rule iv check your rule works for the first three terms.
a 6, 12, 18, 24, … … b 6, 11, 16, 21, … … c 8, 9, 10, 11, … …
4 This pattern is made from dots.
Pattern 1 Pattern 2 Pattern 3 Pattern 4

Alicia thinks that the nth term for the sequence of numbers of dots is 3n + 3.
Is Alicia correct? Explain how you worked out your answer.
5 a Copy and complete the table of values for each function machine.
i ii
x + 9 y x × 2 – 3 y

x 1 2 8 x 1 2
y 14 y 7 19

b Write each of the functions in part a as an equation.
6 Ahmad thinks of a number, x. Write an expression for the number Ahmad gets when he:
a multiplies the number by 4 b multiplies the number by 2 then adds 7
c divides the number by 3 then subtracts 10 d adds 4 to the number then multiplies by 5.
7 Work out the value of each expression.
a x + 7 when x = −12 b 3x − 4y when x = 2 and y = 7
c 3n + 1 when n = −6 d 30 − 5k when k = −2
2
3
e x − 10 when x = 3 f 4y when y = 2
8 Use the formula P = mgh to work out P when m = 5, g = 10 and h = 3.
2
2
9 Zalika uses the formula v = u + 2as.
When she substitutes v = 4, u = 3 and a = 7 into the formula she gets the equation 8 = 6 + 14s.
Is Zalika correct? Show how you worked out your answer.
30 2 Sequences, expressions and formulae