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.

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Forming and solving equations from situations worksheet — GCSE Foundation

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

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1.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
2.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.
3.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
4.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
5.A square has sides of length y cm. Write down an expression for the perimeter of the square.
(a)2y
(b)y + 4
(c)y²
(d)4y
6.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
7.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.
(a)3x
(b)x − 3
(c)x/3
(d)x + 3
8.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.
(a)11
(b)4
(c)7.5
(d)22
9.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.
(a)2b
(b)b + 2
(c)2b + 2
(d)b/2
10.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
11.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.
(a)6c
(b)6 + c
(c)c ÷ 6
(d)c − 6
12.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.
(a)7.4
(b)1.25
(c)5
(d)4
13.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.
(a)27
(b)22.5
(c)18
(d)36
14.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
15.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

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