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.The diagram shows the graph of a quadratic function. Which equation could it represent?
(a) $y = x^{2} - x - 6$
(b) $y = x^{2} - x - 2$
(c) $y = x^{2} + 2 x - 3$
(d) $y = x^{2} - 2 x - 3$
2.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?
(a)The graph has only one branch, in quadrant 1
(b)The graph passes through the origin, (0, 0)
(c)The graph crosses the y-axis but never the x-axis
(d)The graph never crosses either axis
3.A number machine multiplies its input by 5. Work out the output when the input is −1.
(a)−5
(b)5
(c)4
(d)−6
4.A number machine adds 5 to its input. Work out the output when the input is 0.
(a)5
(b)−5
(c)0
(d)6
5.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
6.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.
(a)88 km/h
(b)180 km/h
(c)45 km/h
(d)92 km/h
7.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.
(a)−2 and 2
(b)0 and 2
(c)−4 and 4
(d)−2 and 3
8.Which of these quadratic graphs does NOT cross the x-axis at all?
(a)y = (x − 2)² + 3
(b)y = (x + 4)(x − 1)
(c)y = (x − 2)(x + 3)
(d)y = x² − 9
9.Expand and simplify (x − 3)²
(a)x² + 6x + 9
(b)x² − 9
(c)x² − 3x + 9
(d)x² − 6x + 9
10.Solve 2x + 1 = 9
(a)x = 8
(b)x = 16
(c)x = 4
(d)x = 5
11.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.
(a)n + 3
(b)3n + 5
(c)3n
(d)3n + 2
12.Solve 4x² − 9 = 0.
(a)x = 3/2 or x = −3/2
(b)x = 3/2 only
(c)x = 3 or x = −3
(d)x = 9/4 or x = −9/4
13.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.
y = 45x + 60
(a)£315
(b)£108
(c)£135
(d)£195
14.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.
(a)25
(b)24
(c)21
(d)23
15.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.
(a)216
(b)36
(c)180
(d)250

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