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 scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.
(a)6 years
(b)12 years
(c)14 years
(d)28 years
2.Which of these is a formula?
(a)4s + 7
(b)P = 4s
(c)4s > 20
(d)4s = 20
3.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)
4.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.
(a)b − 15
(b)b + 15
(c)b/15
(d)15b
5.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?
(a)The two roots must both be positive.
(b)The graph has no roots at all.
(c)The graph must touch the x-axis at exactly one point.
(d)If the graph has two real roots, they are equal and opposite in value, so they sum to zero.
6.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.
(a)6
(b)4
(c)12
(d)−6
7.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
8.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
9.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.
(a)An identity, because it is true for every value of x
(b)An identity, because the brackets can be expanded
(c)An equation, because solving it gives x = 3
(d)A formula, because it works out 4x + 12 from x
10.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
11.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.
(a)6n + 1
(b)7n
(c)7n − 1
(d)7n + 6
12.Solve 6x − 5 = 3x + 13.
(a)18
(b)2
(c)2.67
(d)6
13.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?
(a)An equation, since it has an equals sign and unknown x.
(b)An identity, since both sides are equal for every x.
(c)A formula, since it relates two different quantities.
(d)An inequality, since the sides are equal sometimes.
14.Simplify (5x² + 3x − 2) − (2x² − x + 5)
(a)3x² + 4x + 3
(b)3x² + 2x + 3
(c)7x² + 2x + 3
(d)3x² + 4x − 7
15.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.
(a)3
(b)40
(c)−3
(d)13

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