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 · 15 questions

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1.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.
y = x² + 1
(a)−3
(b)1
(c)5
(d)4
2.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.
(a)(L − 4)/6
(b)L/6 + 4
(c)4 − L/6
(d)L/6 − 4
3.Solve 7x − 5 = 3x + 11
(a)−4
(b)1.5
(c)0.6
(d)4
4.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.
(a)7
(b)8
(c)6
(d)9
5.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.
(a)y = 18
(b)y = 30
(c)y = 144
(d)y = 4
6.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.
(a)£50
(b)£120
(c)£60
(d)£40
7.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.
(a)15
(b)3
(c)−15
(d)−3
8.Solve x² + 7x = 0.
(a)x = 0 or x = 7
(b)x = 0 or x = −14
(c)x = 0 or x = −7
(d)x = −7
9.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.
(a)8n − 1
(b)8n + 15
(c)8n + 7
(d)7n + 8
10.Write down the first four terms of the sequence with nth term 6n − 5.
(a)0, 6, 12, 18
(b)6, 12, 18, 24
(c)1, 7, 13, 19
(d)5, 11, 17, 23
11.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.
(a)1
(b)−1
(c)3
(d)4
12.a = 2 and b = 5. Work out the value of ab².
(a)50
(b)10
(c)20
(d)100
13.Make m the subject of the formula w = m − 8.
(a)m = 8 − w
(b)m = w + 8
(c)m = w/8
(d)m = w − 8
14.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.
(a)36 km/h
(b)14.4 km/h
(c)6.25 km/h
(d)0.6 km/h
15.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.
y = x² + 2x − 15
(a)x = −3 and x = 5
(b)x = 5 and x = 3
(c)x = 3 and x = −5
(d)x = −15 and x = 1

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