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.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
2.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.
(a)(3, 5)
(b)(−3, 9)
(c)(3, 9)
(d)(3, 7)
3.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
4.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.
(a)7
(b)8
(c)6
(d)9
5.y = 5 − 2x. Work out the value of x when y = 11.
(a)8
(b)3
(c)6
(d)−3
6.Which expression is equivalent to 6x − (2x − 5)?
(a)8x + 5
(b)8x − 5
(c)4x − 5
(d)4x + 5
7.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.
(a)8
(b)100
(c)7
(d)6
8.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.
(a)3 km/h
(b)60 km/h
(c)195 km/h
(d)180 km/h
9.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.
(a)t = 4
(b)t = 8
(c)t = 10
(d)t = 5
10.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
11.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.
y = x² − 2x − 8
(a)x = −2
(b)x = −1 or x = 3
(c)x = −2 or x = 4
(d)x = 0 or x = −8
12.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.
(a)29
(b)25
(c)28
(d)16
13.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.
(a)18 cm²
(b)6 cm²
(c)12 cm²
(d)36 cm²
14.Solve x² + 3x − 10 = 0.
(a)x = 2 or x = 5
(b)x = −2 or x = 5
(c)x = −5 or x = −2
(d)x = 2 or x = −5
15.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.
(a)8/3
(b)−3
(c)3
(d)1/3

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