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4.6F Forming and Solving Equations: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down an equation for the statement: "Seven more than a number x is 12" and then work out the value of x.

(a)Write an equation for the statement.(1)

(Total for Question 1 is 1 mark)

Solve the equation 3x = 15. Show your working.

(a)Find x.(1)

(Total for Question 2 is 1 mark)

Solve the equation x - 4 = 9. Give your answer.

(a)Find x.(1)

(Total for Question 3 is 1 mark)

The sum of a number y and 8 is 20. Form an equation and solve for y.

(a)Form an equation from the statement.(1)

(b)Solve the equation for y.(1)

(Total for Question 4 is 2 marks)

Amelia thinks of a number n. She doubles it and then adds 5 to make 17. Form an equation and find n.

(a)Form an equation to represent the situation.(1)

(b)Solve the equation and give n.(2)

(Total for Question 5 is 3 marks)

Form an equation and solve. "Five times a number p minus 7 equals 18."

(a)Write an equation for the statement.(1)

(b)Solve the equation for p.(2)

(Total for Question 6 is 3 marks)

Solve the equation 4x + 3 = 19. Show steps clearly.

(a)Find x.(2)

(Total for Question 7 is 2 marks)

Form and solve an equation. "Sarah has £2.50. She buys a drink costing d pounds and has £1.10 left. How much did the drink cost?"

(a)Form an equation in d to represent the situation.(1)

(b)Solve the equation and give the cost of the drink.(3)

(Total for Question 8 is 4 marks)

A rectangle has length equal to 3 more than twice its width. The perimeter of the rectangle is 60 cm. Form an equation and find the width and length.

(a)Let the width be w cm. Form an equation using w for the perimeter.(1)

(b)Solve your equation to find the width w.(3)

(c)Find the length.(1)

(Total for Question 9 is 5 marks)

A toy has an original price of x pounds. It is reduced by 20% in a sale and then a delivery charge of £1.50 is added. The final price paid is £7.50. Form an equation and work out the original price x.

(a)Write an equation in x to represent the sale reduction and delivery charge leading to the final price.(2)

(b)Solve your equation to find x. Show each step.(6)

(Total for Question 10 is 8 marks)

Mark scheme · 4.6F Forming and Solving Equations: Foundation Tier Practice

Question 1

(a) B1 x + 7 = 12 cao
(a) Answer: x + 7 = 12

Question 2

(a) B1 x = 5 cao
(a) Answer: 5

Question 3

(a) B1 x = 13 cao
(a) Answer: 13

Question 4

(a) M1 equation formed, e.g. y + 8 = 20 oe
(a) Answer: y + 8 = 20
(b) A1 y = 12 cao
(b) Answer: 12

Question 5

(a) M1 equation formed, e.g. 2n + 5 = 17 oe
(a) Answer: 2n + 5 = 17
(b) M1 subtract 5 then divide by 2 seen (2n = 12 -> n = 6) ft
(b) A1 n = 6 cao
(b) Answer: 6

Question 6

(a) M1 equation formed, e.g. 5p - 7 = 18 oe
(a) Answer: 5p - 7 = 18
(b) M1 add 7 then divide by 5 (5p = 25 -> p = 5) ft
(b) A1 p = 5 cao
(b) Answer: 5

Question 7

(a) M1 subtract 3 then divide by 4 seen (4x = 16 -> x = 4) ft
(a) A1 x = 4 cao
(a) Answer: 4

Question 8

(a) M1 equation formed, e.g. 2.50 - d = 1.10 oe
(a) Answer: 2.50 - d = 1.10
(b) M1 subtract 1.10 from both sides or rearrange (2.50 - 1.10 = d seen)
(b) M1 calculate correctly 2.50 - 1.10 = 1.40
(b) A1 d = 1.40 cao
(b) Answer: £1.40

Question 9

(a) M1 equation formed, e.g. 2( (2w + 3) + w ) = 60 oe
(a) Answer: 2((2w + 3) + w) = 60
(b) M1 substitute and simplify to linear form, e.g. 6w + 6 = 60 or equivalent
(b) M1 isolate w correctly, e.g. 6w = 54 seen
(b) A1 w = 9 cm cao
(b) Answer: 9 cm
(c) B1 length = 2w + 3 = 21 cm cao
(c) Answer: 21 cm

Question 10

(a) M1 recognise 20% reduction gives 0.8x or (1 - 0.2)x
(a) A1 equation 0.8x + 1.50 = 7.50 cao
(a) Answer: 0.8x + 1.50 = 7.50
(b) M1 subtract 1.50 from both sides, 0.8x = 6.00 seen
(b) M1 divide both sides by 0.8 seen
(b) M1 correct intermediate calculation 6.00 / 0.8 = 7.5 or equivalent
(b) A1 x = 7.50 cao
(b) C1 clear presentation of method leading to correct answer
(b) SC1 award if answer 7.5 is given with correct working shown in different equivalent form
(b) Answer: £7.50

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