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 conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.
(a)16 km
(b)32 km
(c)23 km
(d)24 km
2.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.
(a)24
(b)18
(c)15
(d)12
3.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.
y = 12x + 20
(a)12
(b)3
(c)20
(d)5
4.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.
(a)5n + 2
(b)5n + 12
(c)5n + 7
(d)7n + 5
5.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.
(a)233 minutes
(b)158 minutes
(c)308 minutes
(d)218 minutes
6.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?
(a)It is an identity, because both sides begin with the term 3x, so they must be equivalent.
(b)It is not even an ordinary equation with a solution: expanding the left-hand side gives 3x − 12, and 3x − 12 = 3x − 4 would require −12 = −4, which is never true.
(c)It is not an identity, because the student forgot to multiply the 4 by 3 on both sides of the equation.
(d)It is not an identity, because the student needs to substitute a specific value of x before comparing the two sides.
7.Expand 2(x + 12)
(a)2x + 24
(b)2x + 14
(c)24x
(d)2x + 12
8.The diagram shows the graph of $y = x^{2} - x - 2$ , together with the horizontal line $y = 3$ . Use the graphs to estimate, to 1 decimal place, the two solutions of $x^{2} - x - 2 = 3$ .
(a)x = −1.8 and x = 2.8
(b)x = −3.0 and x = 4.0
(c)x = 1.8 and x = 2.8
(d)x = −1.0 and x = 2.0
9.Which of these equations describes a vertical line?
(a)y = 5x
(b)x = y
(c)x = 5
(d)y = 5
10.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.
(a)0
(b)8
(c)3
(d)1
11.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x
(a)−10
(b)5x − 10
(c)2
(d)−7
12.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
13.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.
(a)12a + 8
(b)8a + 6
(c)8a + 2
(d)5a
14.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
15.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) $y = x^{2} - 2 x - 3$

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