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Single Variable (Adding)
Harder mixed variables
Single Variable (Adding questions)
Harder mixed variables questions
Single Variable (Adding & Subtracting)
Teacher’s notes on quickfire questions
Single Variable (Adding & Subtracting questions)
Multiple variables (Adding)
Adding single variables
Adding & subtracting single
variables
Adding multiple variables
Multiple variables (Adding questions)
Multiple variables (Adding & subtracting)
Multiple variables (Adding & subtracting)
Questions
Multiple variables
Adding & subtracting multiple
variables
Multiple variables + & negative numbers
Harder mixed variables
(Adding & Subtracting : Negative numbers)
Multiple variables (Questions)
(Adding & Subtracting : Negative numbers)
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Algebra MENU
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Traffic Jam
x is the length of a single lorry.
x
x
x
+
x
x
4x
?
+
Lorry length + Lorry length +
x
x
+
Lorry length +
x
Lorry length
= 4x
Lorry lengths
3
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Traffic Jam
c is the length of a single car.
2c
3c
c
+ c
6c
?
2c
+
3c
2 car lengths
+
3 car lengths
+ 1 car length
= 6 Car
c lengths
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a is the cost of an apple
Total Cost = ?
4a
a
Cost of 1
apple
+
a
Cost of 1
apple
+
a
Cost of 1
apple
+
a
Cost of 1
apple
= Cost of 4 apples
= 4a
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a is the cost of an apple
Total Cost = ?
6a
3a
Cost of 3
apples
+
2a
Cost of 2
apples
+
a
Cost of 1
apple
= Cost of 6 apples
= 6a
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1 x +1x
3x + 5x
2x + 4x + 1x
3y + 6y
1 w +1 w + 4w
is the same as :
is the same as :
2x
8x
7x
9y
6w
is the same as :
is the same as :
is the same as :
7
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Simplify the following expressions
4h
3x
1) x + x + x
2) h + h + h + h
7e
3) 2e + 5e
8y
4) 3y + y + 4y
5w
5) 3w + 2w
5g
6) 2g + 2g + g
21h
7) h + 2h + 3h + 4h + 5h + 6h
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Answers
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x is the length of a single lorry.
5x- 2x = 3x
3x
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c is the length of a single car.
3c
+
4c
- 5c
= 2c
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a is the cost of an apple
Total Cost = ?
3a
5a - 2a = 3a
12
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c is the cost of a cherry
?
Total Cost = 6c
9c - 3c = 6c
13
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2x - 1x
5x - 2x
7x - 3x - 2x
9f - f - 3f
8w + 2w - 3w
8g - g + 3g - 4g
is the same as :
x
3x
2x
5f
7w
6g
is the same as :
is the same as :
is the same as :
is the same as :
is the same as :
14
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Simplify the following expressions
2h
3x
1) 5x - x - x
2) 7h - 2h - 3h
e
6y
3) 8e - 7e
4) 7y + y - 2y
8w
11g
5) 9w - w
6) 8g - 2g + 5g
7a
7) 7a + a - 4a - 2a + 5a
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Answers
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x is the length of a single lorry.
c is the length of a single car.
2x
+
3x
3c + x +
= 3x= +? 7c
+
4c
7c
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x is the length of a single lorry.
c is the length of a single car.
x +
3c
+
8
+
2x
+c
8 metre gap
= 3x + =4c? + 8
3x
+
4c
+ 8
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x is the length of a single lorry.
2x
+ 5 +
2x
+ 3+ x
5 metre gap
3 metre gap
= 5x
= ?+ 8
+
5x
8
8 metre gap
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a is the cost of an apple
p is the cost of a pear
Total Cost = ?
3a + 2p
a + a + a + p +
Cost of
Cost of
Cost of
Cost of
+
an apple +an apple +an apple + a pear
p
Cost of
a pear
= Cost of 3 apples + cost of 2 pears
= 3a + 2p
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s is the cost of a strawberry
c is the cost of a cherry
Total Cost = ?
4s + 6c
2s
+
Cost of 2
strawberries
3c
+
Cost of 3
cherries
2s
Cost of 2
strawberries
+
3c
Cost of 3
cherries
= Cost of 4 strawberries + cost of 6 cherries
= 4s + 6c
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s is the cost of a strawberry
?s + 10
Total Value = 6
4s
+ 10 +
2s
Value of 4
strawberries
10
Value of 2
strawberries
= Value of 6 strawberries + 10
= 6s + 10
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s is the cost of a strawberry
c is the cost of a cherry
Total Value = ?
4s + 3c + 30
Value of 2
strawberries
+
10
+
Value of 3
Value of 2
cherries strawberries
+
+
20
= Value of 4 strawberries + value of 3 cherries + 30
= 4s + 3c + 30
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+ 2x + 4x + 3y + 2y is the same as : 6x + 5y
+ 3x + 5y + 6x + 7y is the same as : 9x + 12y
4w + 3h + w + 2w is the same as : 7w + 3h
3x + 5y + 2a + 4x + 4y + a
4a + 3a + 5
is the same as :
3x + 5 + 4x + 2 + 5y + 1
is the same as :
7x + 9y + 3a
7a + 5
is the same as :
7x + 5y + 8
The sign BEFORE the term belongs to the term !
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Simplify the following expressions
10x + 5y
1)
4f + 5w
4x + 6x + 3y + 2y
2)
9h + 11c
3)
6g + 3t
7h + 3c + 2h + 8c
4)
9a + 6k
5)
8a + 4k + 2k + a
6)
a+b+a+b
4x + 1
3x + 2 + 2x + 1
8)
5h + 5g + 7
9)
5g + g + 3t
2a + 2b
5x + 3
7)
4f + 3w + 2w
x + 1 + x + 2x
9 + 2x + y
5h + 3g + 7 + 2g
10)
7+x+x+y+2
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Answers
26
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x is the length of a single lorry.
c is the length of a single car.
+
4x
3x
3x + c
3c
- x - 2c
+c
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a is the cost of an apple
p is the cost of a pear
5a
+
3p - 4a - p
= a + 2p
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Menu
+ 5x – 3x + 3y + 2y is the same as : 2x + 5y
+ 8x + 5y – 3x – 2y is the same as : 5x + 3y
4w + 3h – w – 2w is the same as : w + 3h
9x + 5y + 2a – 3x – 4y + a
7a – 3a + 5
is the same as :
8x + 5 – x – 2 + 5y + 1
is the same as :
6x + y + 3a
4a + 5
is the same as :
7x + 5y + 4
The sign BEFORE the term belongs to the term !
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Simplify the following expressions
2x + 2y
1)
7a + 2b
7x + 2y – 5x
2)
2h + 3a
6c + t
3)
4c + 2c + 6t – 5t
4)
5g + 6w – g – 6w
6)
f
7)
5 + 4f – 3f – 4 – 1
h + 4a + h – a
3x + 4
4g
5)
8a – a + 3b – b
4x + 7 – x – 2 – 1
7k + 3m
8)
5k + k + k + 4m – m
3a + 8b + 5
9)
10)
3a + 6b + 7 – a + 2b – 2 + a
3 + 4x + 6y
7 + x – 3 + 5y + 3x – y + 2y – 1
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Answers
31
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-4 -3 -2 -1
0
1
Subtract
2
3
4
Add
3x + 2y – 2x – 5y
is the same as :
x - 3y
2x + 4y – 5x – 8y
is the same as :
- 3x - 4y
4a – 2b – a – 2b
is the same as :
3a - 4b
3h – 4r + h – 2r – 1 + r + 3
is the same as :
4h - 5r + 2
The sign BEFORE the term belongs to the term !
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Menu
Simplify the following expressions
3a – 4b
-x+y
1)
4x - 5x + 3y - 2y
2)
5g – 3y + 8
3)
5)
7)
2a – 3b – b + a
4g – 4w
6g – g + 8 – 3y
4)
3x – 4
3g + g – 3w – w
2a + 1
4x + 3 – x – 7
6)
c
6c + 2 + 2c – 2 – 7c
8)
4t + 1 – 4t + 2a
6 – 3x – 4y
6 – 2x – 5y – x + y
- 5h – 3 + 3f
9)
4h + 3 – h + 3f – 9h – 5 + h – 1
0
10)
1 – x + y – 2x – 2y – 1 + 3x + y
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Answers
34
Menu
When adding or subtracting in order to simplify the
expression the terms must be IDENTICAL to each other
!
x2 + x2 + x is the same as : 2x2 + x
ab + ab + a is the same as : 2ab + a
xy + yx is the same as : 2xy or 2yx
x
×
y
is the same as y × x
8a + 4ab – 3a – b + 1
3x + 5xy – x + xy + 4
is the same as : 2x + 6xy + 4
is the same as :
5a + 4ab – b + 1
2 × 3 is the same as 3 × 2
6x2 – 5xy + x2 – yx + y
is the same as :
7x2 – 6xy + y
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Simplify the following expressions
fg – f
5xy + 3x
1)
4xy + 3x + xy
2)
4fg – f – 3fg
3)
5 + x + 5x – 2x2
4)
9a3 + 2a2 + a3 – a
5)
6km – 7 – 9km + mk – 1 + m2
5 + 6x – 2x2
- 2km – 8 + m2
10a3 + 2a2 – a
3abc
6)
abc + cba + bca
7)
5wxy + 8w2xy – 5wxy – 8w2x
8)
7ax + 5 – 12xa + 3a – 4x + a – x
9)
4πr2 + 8πr2 + 4ad – 12ad + 5
10)
6πr + 9r – πr + πd – πr3
8w2xy – 8w2x
- 5ax + 4a – 5x + 5
12πr2 – 8ad + 5
5πr + 9r + πd – πr3
36
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Answers
Teacher’s Notes on quickfire questions
Quickfire questions are designed as a straight forward starter
where pupils quickly work out the answers (possibly in the backs
of their books).
The teacher should then review each question giving out the
answers and reminding pupils of the techniques / ideas behind the
topic.
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Menu
38
Question 1
Simplify :
2x + 3 + 2
Menu
39
Question 2
Simplify :
2x + 4x + 3
Menu
40
Question 3
Simplify :
3x + 2x + 1 + 4
Menu
41
Question 4
Simplify :
5x – 3x + 2y – 3
Menu
42
Question 5
Simplify :
8x + 3m – 2x – m
Menu
43
Question 6
Simplify :
6x + y – 2x + 1 –
3y
Menu
44
Question 7
Simplify :
2x – 1 – 4 + x
Menu
45
Question 8
Simplify :
5x – 3 + x + 1
Menu
46
Question 9
Simplify :
4 + 2x – x + y
Menu
47
Question 10
Simplify :
5 – 3x – 2x + 3
Menu
48
Menu
49
Question 1
2x + 4x
Menu
50
Question 2
3x + 5x
Menu
51
Question 3
x + 2x
Menu
52
Question 4
2x + 3x + 4x
Menu
53
Question 5
3x + x + x
Menu
54
Question 6
2w + 4w + 2w
Menu
55
Question 7
h + 2h + 3h
Menu
56
Question 8
m + m + 4m
Menu
57
Question 9
3y + 2y + y
Menu
58
Question 10
c + 2c + 3c + 4c
Menu
59
Menu
60
Question 1
5x – 2x
Menu
61
Question 2
7x – 6x
Menu
62
Question 3
8x – x
Menu
63
Question 4
6x – 2x – 3x
Menu
64
Question 5
8w + 3w – 2w
Menu
65
Question 6
9y + 3y – 4y
Menu
66
Question 7
12c – 8c + 3c
Menu
67
Question 8
9h + 3h – 11h
Menu
68
Question 9
8g + 2g – g – 3g
Menu
69
Question 10
10e – 3e – 2e – 5e
Menu
70
Menu
71
Question 1
5x + 2y + 3x
Menu
72
Question 2
3x + x + 4y + y
Menu
73
Question 3
5g + 4 + 2g + 1
Menu
74
Question 4
x+1+y+x
Menu
75
Question 5
6x + 4x + y + 2y
Menu
76
Question 6
3+x+y+2
Menu
77
Question 7
x+y+x+1
Menu
78
Question 8
4h + 3g + g + h
Menu
79
Question 9
3+x+2+x
Menu
80
Question 10
2e + e + 2e + f
Menu
81
Menu
82
Question 1
3x + 2y – x – y
Menu
83
Question 2
6x + 3x + 8y – 2y
Menu
84
Question 3
8m + 3n – m – n
Menu
85
Question 4
5h + 3 – h + 2
Menu
86
Question 5
8e + 4f + 3 – e – 3
Menu
87
Question 6
g + 2 + g + 3 – 2h
Menu
88
Question 7
3p – p + 5 – 2q
Menu
89
Question 8
12x – 5x – x + 1 – x
Menu
90
Question 9
a+b–a+b–1
Menu
91
Question 10
5h + k – 5h + 2k
Menu
92
Menu
93
Question 1
5ab + 3a + 4ab
Menu
94
Question 2
2
x
+
Menu
2
x
+x
95
Question 3
2
a +
3+
Menu
2
2a
–1
96
Question 4
2
5m
–
2
m
Menu
– 6a + a
97
Question 5
2ef + fe + 2 – 5ef
Menu
98
Question 6
2
3ax
+ 4ax +
Menu
2
xa
99
Question 7
2
2a
+1–
Menu
2
2
ab
+3
100
Question 8
abc + cba – ab
Menu
101
Question 9
3
2
ab
+
3
2
2a b
Menu
–
3
a
102
Question 10
2
8πr
+
Menu
2
πr -
πr
103
End of Collecting Like Terms Presentation.
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