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END OF UNIT BOOKLET
ALGEBRA
LEVEL 4-6
BOOKLET 1
NON-CALCULATOR
Wellsway School.
1
1.
Thinking of rules
(a)
I can think of three different rules to change 6 to 18
6
18
Complete these sentences to show what these rules could be.
1 mark
first rule: add ..................
1 mark
second rule: multiply by ......................
1 mark
third rule: multiply by 2 then ........................
(b)
Now I think of a new rule.
The new rule changes 10 to 5 and it changes 8 to 4
10
5
8
4
Write what the new rule could be.
.......................................
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2.
Track
Kerry makes a pattern from grey tiles and white tiles.
You cannot see all of the pattern but it continues in the same way.
(a)
Kerry uses 30 grey tiles.
How many white tiles does she use?
..................................... white tiles
1 mark
(b)
Tim makes a pattern like Kerry’s but he uses 64 white tiles.
How many grey tiles does Tim use?
..................................... grey tiles
1 mark
3.
Number sequence
Here is part of a number sequence.
7
11
19
35
To get the next number you
multiply by 2 then subtract 3
Fill in the two missing numbers in the sequence.
7
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19
35
3
2 marks
4.
Tiles
Daniel has some parallelogram tiles.
He puts them on a grid, in a continuing pattern.
He numbers each tile.
The diagram shows part of the pattern of tiles on the grid.
y
6
3
x
4
2
x
2
1
0
x
2
4
6
8
x
Daniel marks the top right corner of each tile with a 
The co-ordinates of the corner with a  on tile number 3 are (6, 6)
(a)
What are the co-ordinates of the corner with a  on tile number 4?
(…………… , ……………)
1 mark
(b)
What are the co-ordinates of the corner with a  on tile number 20?
(…………… , ……………)
1 mark
Explain how you worked out your answer.
1 mark
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(c)
Daniel says:
One tile in the pattern has a
in the corner at (25 , 25)
Explain why Daniel is wrong.
1 mark
(d)
Daniel marks the bottom right corner of each tile with a X
Fill in the table to show the co-ordinates of each corner with a X
tile number
co-ordinates of the corner with a X
1
(...2..., ...1...)
2
(……, ……)
3
(……, ……)
4
(……, ……)
1 mark
Fill in the missing numbers below.
(e)
Tile number 7 has a X in the corner at (………… , …………)
1 mark
(f)
Tile number ……………….. has a X in the corner at (20, 19)
1 mark
Total 7 marks
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5.
Magic square
One way to make a magic square is to substitute numbers into this algebra grid.
(a)
a+b
a–b+c
a–c
a–b–c
a
a+b+c
a+c
a+b–c
a–b
Complete the magic square below using the values
a = 10
b=3
c=5
5
10
15
2 marks
(b)
Here is the algebra grid again.
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a+b
a–b+c
a–c
a–b–c
a
a+b+c
a+c
a+b–c
a–b
6
I use different values for a, b and c to complete the magic square.
20
21
7
3
16
29
25
11
12
What values for a, b and c did I use?
a = …………………
b = …………………
c = …………………
2 marks
6.
Solve these equations.
Show your working.
3t + 4 = t + 13
t = ................................
2 marks
2(3n + 7) = 8
n = ................................
1 mark
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7.
Bags
Ali, Barry and Cindy each have a bag of counters.
They do not know how many counters are in each bag.
They know that
Barry has two more counters than Ali.
Cindy has four times as many counters as Ali.
(a)
Ali calls the number of counters in her bag a
Write expressions using a to show the number of counters in Barry’s bag and
in Cindy’s bag.
Ali's bag
Barry's bag
Cindy's bag
a
1 mark
(b)
Barry calls the number of counters in his bag b
Write expressions using b to show the number of counters in Ali’s bag and
in Cindy’s bag.
Ali's bag
Barry's bag
Cindy's bag
b
2 marks
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(c)
Cindy calls the number of counters in her bag c
Ali's bag
Barry's bag
Cindy's bag
c
Which of the expressions below shows the number of counters in Barry’s bag?
Circle the correct one.
4c + 2
4c  2
c
+2
4
c
2
4
c2
4
c–2
4
1 mark
8.
Simplify
Write each expression in its simplest form.
7 + 2t + 3t
…………………
1 mark
b + 7 + 2b + 10
…………………
1 mark
(3d + 5) + (d – 2)
…………………
1 mark
3m – (– m)
…………………
1 mark
Total 4 marks
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9.
Jigsaw
A jigsaw has three different sorts of piece.
Corner pieces,
with 2 straight sides
(a)
Edge pieces,
with 1 straight side
This jigsaw has 24 pieces
altogether, in 4 rows of 6.
Middle pieces,
with 0 straight sides
Complete the table below to show
how many of each sort of piece
this jigsaw has.
Corner pieces: ..........
Edge pieces: ..........
Middle pieces: ..........
Total:
24
1 mark
(b)
Another jigsaw has 42 pieces
altogether, in 6 rows of 7.
Complete the table below to
show how many of each sort
of piece this jigsaw has.
7 pieces
6
pieces
Corner pieces: ..........
Edge pieces: ..........
Middle pieces: ..........
Total:
42
2 marks
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(c)
A square jigsaw has 64 middle pieces.
64
middle
pieces
Complete the table below to show how many of each sort of piece the square jigsaw
has, and the total number of pieces.
Remember that the total must be a square number.
Corner pieces: ..........
Edge pieces: ..........
64
Middle pieces: ..........
Total:
2 marks
Wellsway School.
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10.
Interpreting algebra
Look at this table.
Age (in years)
Ann
a
Ben
b
Cindy
c
Write in words the meaning of each equation below.
The first one is done for you.
b = 30
Ben is 30 years old
a + b = 69
b = 2c
a + b +c
= 28
3
3 marks
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11.
Using rods
Look at these rods.
k
a
b
c
Use the rods to help you decide whether each equation is true or false.
Write T (true) or write F (false) for each question.
The first one is done for you.
T (true) or F (false)
k=a+b+c
T
k=b+c+a
b+c=k–a
a=k–b–c
c=k–a+b
c = k – (a + b)
3 marks
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12.
Marbles
(a)
Elin has a bag of marbles.
You cannot see how many marbles
are inside the bag.
Call the number of marbles which
Elin starts with in her bag n.
Elin puts 5 more marbles into her
bag.
Write an expression to show the
total number of marbles in Elin’s
bag now.
1 mark
(b)
Ravi has another bag of marbles.
Call the number of marbles which
Ravi starts with in his bag t.
Ravi takes 2 marbles out of his
bag.
Write an expression to show the
total number of marbles in Ravi’s
bag now.
1 mark
(c)
Jill has 3 bags of marbles.
Each bag has p marbles inside.
Jill takes some marbles out.
Now the total number of marbles in Jill’s 3 bags is 3p – 6
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Some of the statements below could be true.
Put a tick () by each statement which could be true.
Jill took 2 marbles out of one of the
bags, and none out of the other bags.
Jill took 2 marbles out of each of the
bags.
Jill took 3 marbles out of one of the
bags, and none out of the other bags.
Jill took 3 marbles out of each of two of
the bags, and none out of the other bag.
Jill took 6 marbles out of one of the
bags, and none out of the other bags.
Jill took 6 marbles out of each of two of
the bags, and none out of the other bag.
2 marks
13.
Rearrange
Rearrange the equations.
b+4=a
b = …………………………
1 mark
4d = c
d = …………………………
1 mark
m – 3 = 4k
m = …………………………
1 mark
14.
Solve these equations.
8k  1 = 15
k = .........................
1 mark
2m + 5 = 10
m = .........................
1 mark
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15.
The diagram shows a square drawn on a square grid.
y
B
2
1
C
–2
–1
0
A
0
1
2
x
–1
–2
D
The points A, B, C and D are at the vertices of the square.
Match the correct line to each equation.
One is done for you.
Line through C and D
y=0
Line through A and C
x=0
x+y=2
Line through A and D
Line through B and D
Line through B and C
x + y = –2
Line through A and B
2 marks
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16.
Solving
(a)
When x = 5, work out the values of the expressions below.
2x + 13 = ........................
5x – 5 = ..........................
3 + 6x = ........................
2 marks
(b)
When 2y + 11 = 17, work out the value of y
Show your working.
y = .................
2 marks
(c)
Solve the equation 9y + 3 = 5y + 13
Show your working.
y = .................
2 marks
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17.
Straight lines
The graph shows a straight line. The equation of the line is y = 3x
y
14
12
y = 3x
10
8
6
4
2
–4
–2
0
0
2
4
6
x
–2
–4
Does the point (25, 75) lie on the straight line y = 3x?
Tick (
) Yes or No.
Yes
No
Explain how you know.
1 mark
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Does the point (25, 75) lie on the straight line y = 3x?
Tick (
) Yes or No.
Yes
No
Explain how you know.
1 mark
18.
Thinking Equations
(a)
Solve this equation.
7 + 5k = 8k + 1
k = ……….…………
1 mark
(b)
Solve this equation. Show your working.
10y + 23 = 4y + 26
y = ……….…………
2 marks
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19.
Puzzle
(a)
Two numbers multiply together to make –15
They add together to make 2
What are the two numbers?
………………… and …………………
1 mark
(b)
Two numbers multiply together to make –15
but add together to make –2
What are the two numbers?
………………… and …………………
1 mark
(c)
Two numbers multiply together to make 8
but add together to make – 6
What are the two numbers?
………………… and …………………
1 mark
(d)
The square of 5 is 25
The square of another number is also 25
What is that other number?
…………………
1 mark
Total 4 marks
Wellsway School.
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20.
Areas
(a)
The diagram shows a rectangle 18cm long and 14cm wide.
It has been split into four smaller rectangles.
Write the area of each small rectangle on the diagram.
One has been done for you.
10cm
8cm
............... cm 2
............... cm 2
40cm 2
............... cm 2
10cm
4cm
1 mark
What is the area of the whole rectangle?
......…………....... cm2
1 mark
What is 18 × 14?
18 × 14 = .…………….
1 mark
(b)
The diagram shows a rectangle (n + 3) cm long and (n + 2) cm wide.
It has been split into four smaller rectangles.
Write a number or an expression for the area of each small rectangle on the
diagram.
One has been done for you.
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n cm
3cm
............... cm 2
3n cm2
............... cm 2
............... cm 2
n cm
2cm
1 mark
What is (n + 3) (n + 2) multiplied out?
(n + 3) (n + 2) = .................................................
1 mark
Total 5 marks
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21.
Lines
Look at this diagram:
y
F
A
10
E
B
5
D
C
0
0
(a)
5
10
x
The line through points A and F has the equation y = 11
What is the equation of the line through points A and B?
1 mark
(b)
The line through points A and D has the equation y = x + 3
What is the equation of the line through points F and E?
1 mark
(c)
What is the equation of the line through points B and C?
1 mark
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