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3.14F Solving Equations: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out the value of x.
x + 7 = 13

(Total for Question 1 is 1 mark)

Solve the equation.
5x = 20

(Total for Question 2 is 1 mark)

Work out x.
2x + 3 = 11

(Total for Question 3 is 2 marks)

Solve the equation. Give your answer as a fraction if needed.
3x = 7

(Total for Question 4 is 2 marks)

Work out x. Show all steps.
4x - 5 = 11

(Total for Question 5 is 3 marks)

Solve the equation. Give your answer to 1 decimal place if needed.
2.5x + 1.5 = 6.5

(Total for Question 6 is 3 marks)

Solve the equation. Show your method.
6 = 3x + 9

(Total for Question 7 is 3 marks)

Work out x. Give exact answer.
7x - 4 = 3x + 12

(Total for Question 8 is 4 marks)

Solve the equation. Check your answer.
2(x + 3) = 10

(Total for Question 9 is 4 marks)

Solve the pair of equations by substitution. Show your steps.
Equation 1: y = 2x + 1
Equation 2: 3x + 2y = 18

(Total for Question 10 is 5 marks)

Solve the equation and state whether the solution is an integer. Show full working.
5(x - 2) = 3x + 4

(Total for Question 11 is 7 marks)

A bag contains some counters. Emma says there are n counters. After she adds 4 more counters, there are twice as many counters as she originally thought there were. Write an equation and solve it for n.
(Explain your steps.)

(Total for Question 12 is 5 marks)

Mark scheme · 3.14F Solving Equations: Foundation Tier Practice

Question 1

B1 x = 6 cao
Answer: 6 (x = 6).

Question 2

B1 x = 4 cao
Answer: 4 (x = 4).

Question 3

M1 subtract 3 then divide by 2 shown, e.g. 2x = 8
A1 x = 4 cao
Answer: 4 (x = 4).

Question 4

M1 divide both sides by 3 shown
A1 x = 7/3 cao
Answer: 7/3 (x = 7/3).

Question 5

M1 add 5 to both sides shown: 4x = 16
M1 divide both sides by 4 shown
A1 x = 4 cao
Answer: 4 (x = 4).

Question 6

M1 subtract 1.5 from both sides: 2.5x = 5.0
M1 divide both sides by 2.5 shown
A1 x = 2.0 (or 2 to 1 dp) cao
Answer: 2.0 (x = 2.0).

Question 7

M1 subtract 9 from both sides: 3x = -3
M1 divide both sides by 3 shown
A1 x = -1 cao
Answer: -1 (x = -1).

Question 8

M1 collect x terms: 7x - 3x = 12 + 4 or equivalent
M1 simplify to 4x = 16
M1 divide by 4 shown
A1 x = 4 cao
Answer: 4 (x = 4).

Question 9

M1 expand or divide both sides: 2x + 6 = 10 or x + 3 = 5
M1 solve to get x = 2
M1 substitute back shown: 2(x+3)=2(2+3)=10
A1 x = 2 cao with check
Answer: 2 (x = 2).

Question 10

M1 substitute y = 2x + 1 into 3x + 2y = 18 shown
M1 obtain 3x + 2(2x+1) = 18 or 3x + 4x + 2 = 18
M1 simplify and solve for x: 7x = 16, x = 16/7
M1 substitute x into y = 2x + 1 to find y
A1 x = 16/7, y = 2*(16/7)+1 = 32/7+7/7 = 39/7 cao
Answer: x = 16/7, y = 39/7.

Question 11

M1 expand left side: 5x - 10 = 3x + 4
M1 collect x terms: 5x - 3x = 4 + 10 or equivalent
M1 simplify to 2x = 14
M1 divide by 2 shown
M1 state x = 7
M1 substitute back shown: 5(7-2)=5*5=25 and RHS 3*7+4=21+4=25
A1 conclude x = 7 and solution is an integer cao
Answer: x = 7; yes, the solution is an integer.

Question 12

M1 form equation: n + 4 = 2n (student shows relationship)
M1 rearrange to get 4 = 2n - n or equivalent
M1 simplify to n = 4 shown
M1 interpret and state solution with working
A1 n = 4 cao
Answer: n = 4. (Equation n + 4 = 2n gives 4 = n so n = 4; Emma originally thought there were 4 counters.)

Solving Equations: Foundation Tier Practice - Worksheets, Questions and Revision