Equations with Brackets and Unknowns on Both Sides: Fluency and Exam Drill - Worksheets, Questions and Revision

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KS3 · Algebra

KS3.M-A11D Equations with Brackets and Unknowns on Both Sides: Fluency and Exam Drill

AQA KS3.M-A11 · Calculators not allowed · about 50 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Solve 3(x + 2) = 18.

(1)

Solve 4(x - 1) = 16.

(1)

Solve 2(x + 5) = 3x + 4.

(2)

Solve 3(x - 1) + 5 = 11.

(2)

Solve 5(x + 2) = 2x + 20.

(2)

Solve x/3 + 4 = 9.

(2)

Solve 2(3x - 2) = 4x + 6.

(2)

Solve -3(x - 2) = 15.

(2)

Solve 3(x + 4) = 4(x - 2) + 6.

(2)

Solve (2/3)x + 1 = 9.

(2)

Solve 2(x + 5) - 4 = x + 10.

(2)

Solve 4(x + 3) = 28.

(1)

Solve 5(x - 2) = 15.

(1)

Solve 4(x - 3) = 3(x + 1) + 2.

(2)

Deshi has x boxes of cards. Each box contains 6 cards and he also has 7 loose cards. Altogether he has 43 cards. Form an equation and solve it for x.

(3)

Aisha is 4 years older than twice Ben's age. Their ages add to 34. Write an equation using b for Ben's age and find both of their ages.

(3)

A cinema charges the same amount, x pounds, per ticket. Takings for 3(x + 4) tickets on Monday equalled takings of 4x tickets on Tuesday, minus 10 pounds. Form and simplify an equation, then solve it. (Start from 3(x + 4) = 4x - 10.)

(3)

Solve 3(2x - 1) = 5(x + 1). State the value of x.

(3)

Five equal boxes each contain x stickers, and there are 9 extra stickers. Altogether there are 79 stickers. Form an equation and solve it for x. Show your check.

(4)

Mark scheme · KS3.M-A11D Equations with Brackets and Unknowns on Both Sides: Fluency and Exam Drill

Question 1

B1 x = 4 cao
Answer: x = 4

Question 2

B1 x = 5 cao
Answer: x = 5

Question 3

M1 expands bracket: 2x + 10 = 3x + 4
A1 x = 6 cao
Answer: x = 6

Question 4

M1 expands bracket: 3x - 3 + 5 = 11
A1 x = 3 cao
Answer: x = 3

Question 5

M1 expands bracket: 5x + 10 = 2x + 20
A1 x = 10/3 cao
Answer: x = 10/3

Question 6

M1 correct first step, e.g. x/3 = 5
A1 x = 15 cao
Answer: x = 15

Question 7

M1 expands bracket: 6x - 4 = 4x + 6
A1 x = 5 cao
Answer: x = 5

Question 8

M1 expands bracket correctly: -3x + 6 = 15
A1 x = -3 cao
Answer: x = -3

Question 9

M1 expands both brackets: 3x + 12 = 4x - 8 + 6
A1 x = 14 cao
Answer: x = 14

Question 10

M1 correct first step, e.g. (2/3)x = 8
A1 x = 12 cao
Answer: x = 12

Question 11

M1 expands bracket: 2x + 10 - 4 = x + 10
A1 x = 4 cao
Answer: x = 4

Question 12

B1 x = 4 cao
Answer: x = 4

Question 13

B1 x = 5 cao
Answer: x = 5

Question 14

M1 expands both brackets: 4x - 12 = 3x + 3 + 2
A1 x = 17 cao
Answer: x = 17

Question 15

M1 forms 6x + 7 = 43
M1 correct rearrangement, e.g. 6x = 36
A1 x = 6 cao
Answer: x = 6

Question 16

M1 forms b + (2b + 4) = 34
M1 correct rearrangement, e.g. 3b = 30
A1 Ben = 10, Aisha = 24
Answer: Ben = 10, Aisha = 24

Question 17

M1 expands bracket: 3x + 12 = 4x - 10
M1 correct rearrangement, e.g. 22 = x
A1 x = 22 cao
Answer: x = 22

Question 18

M1 expands both brackets: 6x - 3 = 5x + 5
M1 correct rearrangement, e.g. x = 8
A1 x = 8 cao
Answer: x = 8

Question 19

M1 forms 5x + 9 = 79
M1 correct rearrangement, e.g. 5x = 70
A1 x = 14 cao
B1 check shown: 5(14) + 9 = 79
Answer: x = 14

Question 19

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Equations with Brackets and Unknowns on Both Sides: Fluency and Exam Drill - Worksheets, Questions and Revision

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KS3.M-A11D Equations with Brackets and Unknowns on Both Sides: Fluency and Exam Drill

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