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Expanding Single Brackets - Worksheets, Questions and Revision

25 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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This topic is chapter 5 of KS3 Maths: Algebra Practice Book 1.

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KS3 · Algebra

2.8 Expanding Single Brackets

AQA KS3.M-A8 · Calculators not allowed · about 65 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Expand the brackets and solve the linear equation 2(x + 3) + 5 = 3x + 1.
Solve 2(x + 3) + 5 = 3x + 1.
(2)
2
Expand the brackets and solve the linear equation -3(x - 2) + 4 = 2x.
Solve -3(x - 2) + 4 = 2x.
(2)
3
Expand and simplify, taking care with negative signs: -2(x + 3) - 3(x - 1).
Work out -2(x + 3) - 3(x - 1).
(2)
4
Expand the single bracket -2(x - 5), taking care with the negative sign.
Expand -2(x - 5).
(1)
5
Expand the single bracket 5(2x + 3).
Expand 5(2x + 3).
(1)
6
Expand and simplify the expression 2(x + 3) + x.
Work out 2(x + 3) + x.
(2)
7
Expand and simplify the expression 3(a + 2) + 2(a - 5).
Work out 3(a + 2) + 2(a - 5).
(2)
8
Expand and simplify the expression 3(x + 4) - 2(x - 1).
Work out 3(x + 4) - 2(x - 1).
(2)
9
Expand and simplify the expression 2(3x + 4) - 5x.
Work out 2(3x + 4) - 5x.
(2)
10
Expand 5(x + 2).
(1)
11
Expand and simplify 2(3x + 4) - 5.
(2)
12
Expand and simplify -3(x + 2) + 10.
(2)
13
Expand and simplify 4(x + 6) - 3(x - 2).
(2)
14
Expand and simplify 5(2x - 3) - 3(x + 4).
(3)
15
Expand the brackets and solve the equation 3(x + 4) = 2x + 19.
(3)
16
A rectangle has length (x + 5) cm and width 3 cm. The perimeter of the rectangle is 46 cm. Form and solve an equation to find x.
(3)
17
A gardener buys tomato seed packs costing (2x + 3) pounds each and pepper seed packs costing (x - 1) pounds each. He buys 3 tomato packs and 2 pepper packs.
(a)Write and simplify an expression, in terms of x, for the total cost in pounds.(2)
(b)Given that x = 5, work out the total cost in pounds.(2)
18
A triangle has perimeter 5(x + 2) cm. Two of its sides are (x + 3) cm and (x + 5) cm.
(a)Expand 5(x + 2) to write the perimeter without brackets.(1)
(b)Find and simplify an expression, in terms of x, for the length of the third side.(2)
(c)Given that x = 4, find the length of the third side.(2)
19
Expand -4(x + 3).
(1)
20
Expand -2(x - 7).
(1)
21
Expand 6(2x + 1).
(1)
22
Expand 7(3x - 2).
(1)
23
Expand -3(4x + 5).
(1)
24
Expand and simplify 3(x + 5) + 2x.
(2)
25
Expand and simplify 4(x - 3) + 7.
(2)
Mark scheme · 2.8 Expanding Single Brackets

Question 1

  • M1 expand and collect like terms: 2x + 6 + 5 = 3x + 1 or 2x + 11 = 3x + 1
  • A1 x = 10 cao
  • Answer: 10

Question 2

  • M1 expand to -3x + 6 + 4 = 2x or -3x + 10 = 2x and collect terms
  • A1 x = 2 cao
  • Answer: 2

Question 3

  • M1 expand both brackets: -2x - 6 and -3x + 3 or equivalent
  • A1 -5x - 3 cao
  • Answer: -5x - 3

Question 4

  • B1 -2x + 10 cao
  • Answer: -2x + 10

Question 5

  • B1 10x + 15 cao
  • Answer: 10x + 15

Question 6

  • M1 expand 2(x+3) to 2x + 6 or equivalent method
  • A1 3x + 6 cao
  • Answer: 3x + 6

Question 7

  • M1 expand both brackets: 3a + 6 and 2a - 10 shown
  • A1 5a - 4 cao
  • Answer: 5a - 4

Question 8

  • M1 expand both brackets: 3x + 12 and -2x + 2 or equivalent method
  • A1 x + 14 cao
  • Answer: x + 14

Question 9

  • M1 expand 2(3x+4) to 6x + 8 or equivalent method
  • A1 x + 8 cao
  • Answer: x + 8

Question 10

  • B1 5x + 10 cao
  • Answer: 5x + 10

Question 11

  • M1 expand 2(3x+4) to 6x + 8 or equivalent method
  • A1 6x + 3 cao
  • Answer: 6x + 3

Question 12

  • M1 expand -3(x+2) to -3x - 6 or equivalent method
  • A1 -3x + 4 cao
  • Answer: -3x + 4

Question 13

  • M1 expand both brackets: 4x + 24 and -3x + 6 or equivalent
  • A1 x + 30 cao
  • Answer: x + 30

Question 14

  • M1 expand 5(2x-3) to 10x - 15
  • M1 expand -3(x+4) to -3x - 12
  • A1 7x - 27 cao
  • Answer: 7x - 27

Question 15

  • M1 expand 3(x+4) to 3x + 12
  • M1 collect terms correctly, e.g. 3x + 12 = 2x + 19 leading to x = 19 - 12
  • A1 x = 7 cao
  • Answer: 7

Question 16

  • M1 form expression for perimeter, e.g. 2(x+5) + 2(3) or 2x + 16
  • M1 set expression equal to 46 and rearrange, e.g. 2x = 30
  • A1 x = 15 cao
  • Answer: 15

Question 17

  • (a) M1 expand both: 3(2x+3) = 6x + 9 and 2(x-1) = 2x - 2
  • (a) A1 8x + 7 cao
  • (a) Answer: 8x + 7
  • (b) M1 substitute x = 5 into 8x + 7
  • (b) A1 47 cao
  • (b) Answer: 47

Question 18

  • (a) B1 5x + 10 cao
  • (a) Answer: 5x + 10
  • (b) M1 subtract the two given sides from the perimeter, e.g. (5x+10) - (x+3) - (x+5)
  • (b) A1 3x + 2 cao
  • (b) Answer: 3x + 2
  • (c) M1 substitute x = 4 into 3x + 2
  • (c) A1 14 cm cao
  • (c) Answer: 14 cm

Question 19

  • B1 -4x - 12 cao
  • Answer: -4x - 12

Question 20

  • B1 -2x + 14 cao
  • Answer: -2x + 14

Question 21

  • B1 12x + 6 cao
  • Answer: 12x + 6

Question 22

  • B1 21x - 14 cao
  • Answer: 21x - 14

Question 23

  • B1 -12x - 15 cao
  • Answer: -12x - 15

Question 24

  • M1 expand 3(x+5) to 3x + 15 or equivalent method
  • A1 5x + 15 cao
  • Answer: 5x + 15

Question 25

  • M1 expand 4(x-3) to 4x - 12 or equivalent method
  • A1 4x - 5 cao
  • Answer: 4x - 5

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Question 1

2 marks

Question 2

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Question 3

2 marks

Question 4

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Question 5

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Question 6

2 marks

Question 7

2 marks

Question 8

2 marks

Question 9

2 marks

Question 10

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Question 11

2 marks

Question 12

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Question 13

2 marks

Question 14

3 marks

Question 15

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Question 16

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Question 17

4 marks
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Question 18

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Question 19

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Question 20

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Question 21

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Question 22

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Question 23

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Question 24

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Question 25

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