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

MathsUKwww.geekhero.co.uk

1.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.
(a)25
(b)20
(c)18
(d)21
2.Write down the gradient of the line with equation y = 7x − 2.
y = 7x − 2
(a)−7
(b)7
(c)2
(d)−2
3.y = x + 10. Work out the value of y when x = 0.
y = x + 10
(a)0
(b)10
(c)11
(d)−10
4.Which of these statements is an identity?
(a)x + 4 = 2x
(b)2(x + 4) = 20
(c)2(x + 4) ≡ 2x + 8
(d)2(x + 4) = 2x + 4
5.Work out the value of 2(x + 2) when x = −5
(a)−3
(b)−1
(c)−6
(d)−8
6.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
7.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.
(a)3n + 2
(b)2n + 3
(c)2n − 3
(d)5n
8.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.
(a)y = 4.5
(b)y = 7
(c)y = 9
(d)y = 11
9.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
(a)2
(b)−18
(c)−6
(d)−2
10.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.
(a)y = 2x
(b)y = 3x
(c)y = x²
(d)y = 3x − 2
11.Solve 6x + 4 = 28
(a)x = 4
(b)x = 144
(c)x = 24
(d)x = 18
12.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.
(a)25
(b)28
(c)27
(d)31
13.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.
(a)(1, 3)
(b)(−1, 3)
(c)(9, 4)
(d)(−1, 4)
14.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.
(a)16 cm
(b)24 cm
(c)84 cm
(d)28 cm
15.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?
(a)(2, 3)
(b)(2, 5)
(c)(2, 6)
(d)(3, 2)

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