The document contains a math worksheet with 7 problems. Problem 1 involves finding the total number of hexagons in a pattern with 20 patterns. Problem 2 involves calculating costs for swimming based on number of visits and payment plans. Problem 3 provides rules for building huts out of matches and calculates number of matches and huts. Problem 4 matches math expressions to descriptions. Problem 5 provides rules for tile patterns and calculates tiles used. Problem 6 involves substituting numbers into equations. Problem 7 identifies rules for number chains.

1. Algebra 1
Level 5
1. Hexagon patterns
Look at this sequence of patterns made with hexagons.
p a tt e r n n u m b e r 1 p a tt e r n n u m b e r 2
p a tt e r n n u m b e r 3
To find the number of hexagons in pattern number n you can use these rules:
Number of grey hexagons = n + 1
Number of white hexagons = 2n
Brewood CE C Middle School 1

2. Altogether, what is the total number of hexagons in pattern number 20?
...............................
2 marks
2. Swimming
(a) You pay £2.40 each time you go swimming.
Complete the table.
Number of swims 0 10 20 30
Total cost (£) 0 24
1 mark
Brewood CE C Middle School 2

3. (b) Now show this information on the graph below.
Join the points with a straight line.
8 0
7 0
6 0
5 0
4 0
3 0
3 0
2 0
2 0
1 0
1 0
0
0
T o ta l
c o s t
( £ )
N u m b e r o f s w im s
2 marks
Brewood CE C Middle School 3

4. (c) A different way of paying is to pay a yearly fee of £22
Then you pay £1.40 each time you go swimming.
Complete the table.
Number of swims 0 10 20 30
Total cost (£) 22 36
1 mark
(d) Now show this information on the same graph.
Join these points with a straight line.
2 marks
(e) For how many swims does the graph show that the cost is the same for
both ways of paying?
...............................
1 mark
3. Huts
You can make ‘huts’ with matches.
1 h u t n e e d s
5 m a t c h e s
2 h u ts n e e d
9 m a t c h e s
3 h u ts n e e d
1 3 m a t c h e s
Brewood CE C Middle School 4

5. A rule to find how many matches you need is
m h= 4 + 1
m stands for the number of matches.
h stands for the number of huts.
(a) Use the rule to find how many matches you need to make 8 huts.
Show your working.
................ matches
2 marks
(b) I use 81 matches to make some huts.
How many huts do I make?
Show your working.
....................... huts
2 marks
(c) Andy makes different ‘huts’ with matches.
1 h u t n e e d s
6 m a t c h e s
2 h u ts n e e d
1 1 m a t c h e s
3 h u ts n e e d
1 6 m a t c h e s
Brewood CE C Middle School 5

6. Circle the rule below that shows how many matches he needs.
Remember: m stands for the number of matches.
h stands for the number of huts.
m = h + 5 m = 4h + 2 m = 4h + 3
m = 5h + 1 m = 5h + 2 m = h + 13
1 mark
Brewood CE C Middle School 6

7. 4. Matching expressions
A ruler costs k pence.
A pen costs m pence.
Match each statement with the correct expression for the amount in pence.
The first one is done for you.
T h e c h a n g e fr o m £ 5 ,
in p e n c e , w h e n y o u b u y 5 p e n s
H o w m u c h m o r e 5 p e n s c o s t
t h a n 5 r u le r s
T h e to t a l c o s t
o f 5 r u le r s a n d 5 p e n s
T h e to t a l c o s t
o f 5 r u le r s
S ta te m e n t
5 – 5k m
5 – 5m k
5 ( )k m+
5 +k m
5 0 0 – 5 m
5 – 5 m
5 m
5 k
E x p r e s s io n
3 marks
Brewood CE C Middle School 7

8. 5. Arms
Jeff makes a sequence of patterns with black and grey triangular tiles.
p a tt e r n
n u m b e r
1
p a t t e r n
n u m b e r
2
p a t t e r n
n u m b e r
3
The rule for finding the number of tiles in pattern number N in
Jeff's sequence is:
number of tiles = 1 + 3N
(a) The 1 in this rule represents the black tile.
What does the 3N represent?
1 mark
(b) Jeff makes pattern number 12 in his sequence.
How many black tiles and how many grey tiles does he use?
............................... black and ............................... grey tiles
1 mark
Brewood CE C Middle School 8

9. (c) Jeff uses 61 tiles altogether to make a pattern in his sequence.
What is the number of the pattern he makes?
pattern number ...................
1 mark
(d) Barbara makes a sequence of patterns with hexagonal tiles.
p a tt e r n
n u m b e r
1
p a tt e r n
n u m b e r
2
p a t t e r n
n u m b e r
3
Each pattern in Barbara's sequence has 1 black tile in the middle.
Each new pattern has 6 more grey tiles than the pattern before.
Write the rule for finding the number of tiles in pattern number N in Barbara's
sequence.
number of tiles = …………….. + ……………….
1 mark
Brewood CE C Middle School 9

10. (e) Gwenno uses some tiles to make a different sequence of patterns.
The rule for finding the number of tiles in pattern number N in Gwenno's
sequence is:
number of tiles = 1 + 4N
Draw what you think the first 3 patterns in Gwenno's sequence could be.
2 marks
6. Substituting
Write numbers in the boxes to make the statements true.
When x = then x + 3 =
When x = then 3x =
When x = then
3
x
=
2 marks
Brewood CE C Middle School 10

11. 7. Relationships
(a) The rule to get the next number in this number chain is multiply by 4 then
subtract 6
Fill in the two missing numbers in the number chain.
6
1 8
6 6
2 marks
(b) This number chain has a different rule.
2 . 7
5 . 4
1 0 .8
2 1 .6
4 3 . 2
Write what that rule might be.
............................................................
1 mark
Brewood CE C Middle School 11