Printable · GCSE Foundation · ages 14-16

Forming and solving equations from situations worksheet — GCSE Foundation

Fifteen questions on "forming and solving equations from situations" — DfE statement A21. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

Calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Forming and solving equations from situations worksheet — GCSE Foundation

Maths · GCSE Foundation · A21 · Forming and solving equations from situations · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.
(a)24
(b)35
(c)5
(d)30
2.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.
(a)£2.48
(b)£3.30
(c)£2.80
(d)£3.80
3.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.
(a)6 years
(b)12 years
(c)14 years
(d)28 years
4.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.
(a)9.5
(b)8
(c)17.5
(d)4.75
5.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.
(a)12
(b)8
(c)36
(d)6
6.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.
(a)12
(b)6
(c)7.5
(d)9
7.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.
(a)Subtracting 4x gives 3 = 10, which is never true.
(b)x would have to be negative, but x must be positive.
(c)It's true for every x, so there are infinite solutions.
(d)x = 7, since 10 − 3 = 7.
8.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.
(a)485
(b)1.1
(c)297.5
(d)110
9.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.
(a)y + 1
(b)y − 4
(c)y − 9
(d)y + 9
10.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.
(a)24
(b)18
(c)15
(d)12
11.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.
(a)−4.5
(b)50
(c)29.5
(d)8
12.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.
(a)6x + 12
(b)6x + 2
(c)x + 12
(d)8x
13.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.
(a)k + 5
(b)k − 5
(c)5k
(d)5 − k
14.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.
(a)No — it has never happened and never will
(b)Yes — when Harry is 20
(c)No — that moment has already passed
(d)Yes — when Harry is 16
15.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.
(a)b − 15
(b)b + 15
(c)b/15
(d)15b

Build your own mix at the worksheet builder.