1. Algebra 1
Level 6
1. Sequences
For each sequence below, tick ( ) the correct box to show if it is increasing,
decreasing or neither.
increasing decreasing neither
2
1
3
1
4
1
5
1
13
6
12
7
11
8
10
9
2
1
4
2
6
3
8
4
2
3
3
4
4
5
5
6
2 marks
2. nth term
Look at these pairs of number sequences.
The second sequence is formed from the first sequence by adding a number or
multiplying by a number.
Work out the missing nth terms.
(a) 5, 9, 13, 17, ... nth term is 4n + 1
6, 10, 14, 18, …
nth term is ..............................
1 mark
Brewood CE C Middle School 1

2. (b) 12, 18, 24, 30, ... nth term is 6n + 6
6, 9, 12, 15, …
nth term is ..............................
1 mark
(c) 2, 7, 12, 17, ... nth term is 5n – 3
4, 14, 24, 34, …
nth term is ..............................
1 mark
3. Functions
(a) A function maps the number n to the number n + 2
Complete the missing values.
n → n + 2
4 → .................
................. → 20
1 mark
Brewood CE C Middle School 2

3. (b) A different function maps the number n to the number 2n
Complete the missing values.
n → 2n
4 → .................
................. → 20
1 mark
(c) Many different functions can map the number 25 to the number 5
Complete the tables by writing two different functions.
n → ................. n → .................
25 → 5 25 → 5
2 marks
Brewood CE C Middle School 3

4. 4. Puzzle
You can often use algebra to show why a number puzzle works.
Fill in the missing expressions.
5
9
1 4
7
5
T h in k o f a n u m b e r
A d d 4
N o w a d d th e n u m b e r y o u
w e r e f ir s t t h in k in g o f
D iv id e b y 2
S u b t r a c t 2
n
n + 4
T h e a n s w e r is th e n u m b e r y o u w e r e f ir s t th in k in g o f
E x a m p le : A lg e b r a :
2 marks
Brewood CE C Middle School 4

5. 5. Making patterns
Uri makes a sequence of shapes using square tiles.
s h a p e
n u m b e r
1
s h a p e
n u m b e r
2
s h a p e
n u m b e r
3
The number of square tiles in shape number n is
2n + 1
Uri makes a different sequence of shapes.
In this sequence of shapes, the number of square tiles in shape number n is
3n + 1
Brewood CE C Middle School 5

6. Draw what the first 3 shapes might look like.
2 marks
Brewood CE C Middle School 6

7. Draw what the first 3 shapes might look like.
2 marks
Brewood CE C Middle School 6