Printable · GCSE Foundation · ages 14-16

Algebra worksheet — GCSE Foundation

Fifteen questions across the algebra statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Algebra worksheet — GCSE Foundation

Maths · GCSE Foundation · Algebra · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

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.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
3.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.
(a)2.6
(b)2.9
(c)2.4
(d)2.7
4.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.
(a)16
(b)24
(c)84
(d)50
5.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.
y = 0.15x + 20
(a)£50
(b)£30
(c)£203
(d)£320
6.A square tile has an area of 144 cm². Work out the side length of the tile.
(a)12 cm or −12 cm
(b)72 cm
(c)12 cm
(d)36 cm
7.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.
(a)6.6
(b)6.1
(c)6.3
(d)6.0
8.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?
(a)They always charge the same, since 3(2n + 4) = 6n + 12.
(b)It depends on the value of n, so it cannot be decided.
(c)Advert A is cheaper, since 3(2n + 4) = 6n + 4.
(d)Advert A is cheaper, since 3(2n + 4) = 2n + 7.
9.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.
(a)0.2 hours
(b)10 hours
(c)5 hours
(d)4.8 hours
10.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
11.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.
(a)£26.67
(b)£40
(c)£6.67
(d)£20
12.Work out the value of 4p² − 3 when p = 2.5
(a)97
(b)7
(c)22
(d)1
13.Which of these is an equation, rather than an expression, a formula or an identity?
(a)3x + 5
(b)A = πr²
(c)3x + 5 = 17
(d)3(x + 5) ≡ 3x + 15
14.Solve 2x² − 32 = 0.
(a)x = 8
(b)x = 4
(c)x = 16
(d)x = 4 or x = −4
15.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

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