Solving One Step Equations - Worksheets, Questions and Revision

20 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

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2.9 Solving One Step Equations

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Revision notes: Solving One Step Equations

A one-step equation needs only a single operation (add, subtract, multiply or divide) to find the value of the unknown letter. The rule is to do the SAME inverse operation to both sides of the equation, so the equation stays balanced.

Identify the operation that has been done to the letter (e.g. + 5, or x 3).
Apply the INVERSE operation to both sides: the inverse of + is -, the inverse of - is +, the inverse of x is division by the same number, the inverse of division is x by the same number.
Simplify both sides to leave the letter on its own on one side.
Check your answer by substituting it back into the original equation; both sides should be equal.

Worked example. Solve (a) x + 9 = 14, and (b) 5y = 35.

(a) The inverse of + 9 is - 9. Subtract 9 from both sides: x + 9 - 9 = 14 - 9, so x = 5.
Check: 5 + 9 = 14, correct.
(b) The inverse of x 5 is divide by 5. Divide both sides by 5: 5y / 5 = 35 / 5, so y = 7.
Check: 5 x 7 = 35, correct.

Answer: x = 5; y = 7.

Solve each equation.

(a)x + 4 = 9(1)

(b)x - 3 = 8(1)

(Total for Question 1 is 3 marks)

5x = 20

A) x = 4
B) x = 15
C) x = 25
D) x = 100

Circle the letter next to the correct solution to the equation.

A) x = 4
B) x = 15
C) x = 25
D) x = 100

(Total for Question 2 is 1 mark)

Solve each equation.

(a)x + 9 = 15(1)

(b)x - 5 = 2(1)

(Total for Question 3 is 2 marks)

Kwame thinks of a number, n. He adds 6 to it. His answer is 13.

Form an equation in terms of n and solve it to find Kwame's number.

(Total for Question 4 is 2 marks)

Solve each equation.

(a)x - 6 = -2(2)

(b)8 - x = 11(2)

(Total for Question 5 is 4 marks)

Solve each equation.

(a)3x = 21(2)

(b)4x = 18(2)

(Total for Question 6 is 4 marks)

Solve each equation.

(a)x / 4 = 5(2)

(b)x / 6 = -3(2)

(Total for Question 7 is 4 marks)

Match each equation to its solution. Each solution on the right is used exactly once: 7, 13, 10, 30

(a)x + 3 = 10(1)

(b)x - 3 = 10(1)

(d)x / 3 = 10(1)

(Total for Question 8 is 4 marks)

Solve each equation.

(a)x + 1.5 = 4(2)

(b)x - 2.5 = 6.5(2)

(Total for Question 9 is 4 marks)

Solve each equation.

(a)-x = 7(2)

(b)-2x = 10(2)

(Total for Question 10 is 4 marks)

Solve

20 / x = 4

(Total for Question 11 is 2 marks)

Tom buys a coffee and pays with a £10 note. He receives £3.55 change.

Form an equation for the cost of the coffee, c, and solve it to find c.

(Total for Question 12 is 2 marks)

Aisha is tiling a square patio with side length x metres.

The perimeter of the patio is 32 m.

Form an equation in terms of x and solve it to find the side length.

Diagram NOT accurately drawn

(Total for Question 13 is 2 marks)

Show that x = 4 is the solution to the equation

3x = 12

(Total for Question 14 is 2 marks)

Solve

7x = 3.5

(Total for Question 15 is 2 marks)

Solve

x - 2.7 = 5.3

(Total for Question 16 is 2 marks)

Solve

4x = -9

Give your answer as a decimal.

(Total for Question 17 is 2 marks)

Solve

x / (-3) = 6

(Total for Question 18 is 2 marks)

Solve

12 - x = 20

(Total for Question 19 is 2 marks)

The temperature in Leeds at 6 am was t degrees C. By 9 am the temperature had risen by 9 degrees C to reach 2 degrees C.

Form an equation and solve it to find t, the temperature at 6 am.

(Total for Question 20 is 3 marks)

Mark scheme · 2.9 Solving One Step Equations

Question 1

(a) B1 x = 5 cao
(a) Answer: x = 5
(b) B1 x = 11 cao
(b) Answer: x = 11
(c) B1 x = 4 cao
(c) Answer: x = 4

Question 2

B1 A circled, cao
Answer: A) x = 4

Question 3

(a) B1 x = 6 cao
(a) Answer: x = 6
(b) B1 x = 7 cao
(b) Answer: x = 7

Question 4

M1 correct equation formed, n + 6 = 13 oe
A1 n = 7 cao
Answer: n = 7

Question 5

(a) M1 6 added to both sides oe
(a) A1 x = 4 cao
(a) Answer: x = 4
(b) M1 8 subtracted from both sides oe, -x = 3 seen
(b) A1 x = -3 cao
(b) Answer: x = -3

Question 6

(a) M1 both sides divided by 3 oe
(a) A1 x = 7 cao
(a) Answer: x = 7
(b) M1 both sides divided by 4 oe
(b) A1 x = 4.5 oe cao
(b) Answer: x = 4.5

Question 7

(a) M1 both sides multiplied by 4 oe
(a) A1 x = 20 cao
(a) Answer: x = 20
(b) M1 both sides multiplied by 6 oe
(b) A1 x = -18 cao
(b) Answer: x = -18

Question 8

(a) B1 matched to 7 cao
(a) Answer: 7
(b) B1 matched to 13 cao
(b) Answer: 13
(c) B1 matched to 10 cao
(c) Answer: 10
(d) B1 matched to 30 cao
(d) Answer: 30

Question 9

(a) M1 1.5 subtracted from both sides oe
(a) A1 x = 2.5 cao
(a) Answer: x = 2.5
(b) M1 2.5 added to both sides oe
(b) A1 x = 9 cao
(b) Answer: x = 9

Question 10

(a) M1 both sides multiplied (or divided) by -1 oe
(a) A1 x = -7 cao
(a) Answer: x = -7
(b) M1 both sides divided by -2 oe
(b) A1 x = -5 cao
(b) Answer: x = -5

Question 11

M1 both sides multiplied by x, or 20 divided by 4, oe
A1 x = 5 cao
Answer: x = 5

Question 12

M1 correct equation formed, c + 3.55 = 10 oe
A1 c = 6.45 (or £6.45) cao
Answer: c = £6.45

Question 13

M1 correct equation formed, 4x = 32 oe
A1 x = 8 (m) cao
Answer: x = 8 m

Question 14

M1 x = 4 substituted into 3x, 3 x 4 = 12 seen
A1 12 = 12 stated, so x = 4 is a correct solution, cso
Answer: 3 x 4 = 12, which equals the right-hand side, so x = 4 is correct.

Question 15

M1 both sides divided by 7 oe
A1 x = 0.5 cao
Answer: x = 0.5

Question 16

M1 2.7 added to both sides oe
A1 x = 8 cao
Answer: x = 8

Question 17

M1 both sides divided by 4 oe
A1 x = -2.25 oe cao
Answer: x = -2.25

Question 18

M1 both sides multiplied by -3 oe
A1 x = -18 cao
Answer: x = -18

Question 19

M1 12 subtracted from both sides oe, -x = 8 seen
A1 x = -8 cao
Answer: x = -8

Question 20

M1 correct equation formed, t + 9 = 2 oe
A1 t = -7 cao
C1 correct interpretation stated, temperature at 6 am was -7 degrees C
Answer: t = -7 degrees C

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Solving One Step Equations - Worksheets, Questions and Revision

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2.9 Solving One Step Equations

Revision notes: Solving One Step Equations

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20