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 · Non-calculator · 15 questions

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1.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
2.Make p the subject of the formula n = p/3.
(a)p = n/3
(b)p = 3n
(c)p = 3/n
(d)p = n − 3
3.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.
(a)11 cm³
(b)24 cm³
(c)18 cm³
(d)36 cm³
4.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.
(a)20
(b)26
(c)24
(d)23
5.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.
(a)(1, 6)
(b)(−1, 6)
(c)(−1, −6)
(d)(6, −1)
6.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.
(a)7
(b)17
(c)12
(d)2
7.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.
(a)x = 2, y = 5
(b)x = 3, y = 2
(c)x = 2, y = 3
(d)x = −2, y = 11
8.Write down the gradient of the line with equation y = −x + 3.
y = −x + 3
(a)−3
(b)−1
(c)3
(d)1
9.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.
(a)9 m
(b)18 m
(c)37 m
(d)16 m
10.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.
(a)0
(b)12.5
(c)12
(d)6.25
11.Solve 2x + 1 = 9
(a)x = 8
(b)x = 16
(c)x = 4
(d)x = 5
12.Solve 3x + 14 = 8x − 6
(a)x = 15
(b)x = 2.5
(c)x = 4
(d)x = −1.6
13.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.
(a)30 US dollars
(b)25 US dollars
(c)19.20 US dollars
(d)120 US dollars
14.Solve x² − 2x − 24 = 0.
(a)x = 6 or x = −4
(b)x = −6 or x = 4
(c)x = −8 or x = 3
(d)x = −6 or x = −4
15.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.
(a)2
(b)−0.5
(c)0.5
(d)−0.8

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