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

MathsUKwww.geekhero.co.uk

1.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.
(a)28
(b)38
(c)32
(d)33
2.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.
(a)7n
(b)12n + 7
(c)7n + 12
(d)7n + 5
3.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.
(a)£7.20
(b)£22.20
(c)£9.70
(d)£10.20
4.Solve the inequality 3x + 6 ≤ 0.
(a)x ≤ 2
(b)x ≤ −2
(c)x ≥ −2
(d)x ≤ −18
5.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x
(a)−10
(b)5x − 10
(c)2
(d)−7
6.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.
(a)−7
(b)4
(c)−5
(d)7
7.The diagram shows part of the graph of a reciprocal function of the form $y = \frac{k}{x}$ , passing through the labelled point. Work out the value of k.
(a)5
(b)6
(c)9
(d)1.5
8.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.
(a)2.5
(b)0
(c)20
(d)5
9.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.
(a)There is not enough information
(b)They are equally steep
(c)Line D
(d)Line C
10.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
11.The diagram shows two curves drawn on the same grid. Curve A is the graph of $y = x^{2}$ . Which equation could represent curve B?
(a) $y = (x - 3)^{2}$
(b) $y = x^{2} - 3$
(c) $y = x^{2} + 3 x$
(d) $y = x^{2} + 3$
12.Work out the value of 5a + 2 when a = 3
(a)17
(b)10
(c)15
(d)25
13.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
14.Which of these is a formula?
(a)4s + 7
(b)P = 4s
(c)4s > 20
(d)4s = 20
15.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.
(a)8.5 kg
(b)8 kg
(c)6 kg
(d)7.5 kg

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