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 rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.
(a)19
(b)21
(c)22
(d)16
2.Make x the subject of the formula y = 5x + 3.
y = 5x + 3
(a)x = (y + 3)/5
(b)x = (y − 3)/5
(c)x = y/5 − 3
(d)x = 5(y − 3)
3.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.
(a)16
(b)24
(c)84
(d)50
4.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.
(a)x = −2 and x = −5
(b)x = 2 and x = −5
(c)x = −2 and x = 5
(d)x = 2 and x = 5
5.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?
(a)Yes — the t² coefficient is negative, giving an n-shape.
(b)No — it is U-shaped, since height starts by increasing.
(c)No — the shape comes from the story, not the coefficient.
(d)Yes, but only because the rocket eventually lands.
6.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.
(a)£24
(b)£14
(c)£12
(d)£8
7.Solve the inequality x − 10 < −3.
(a)x < 13
(b)x > 7
(c)x < −13
(d)x < 7
8.Solve the inequality 6x ≥ 18.
(a)x ≥ 12
(b)x ≤ 12
(c)x ≥ 3
(d)x ≤ 3
9.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
10.A straight line has equation y = 4 − 3x. Work out the gradient of the line.
(a)4
(b)−4
(c)3
(d)−3
11.Solve the inequality 5x − 3 > 2x + 9.
(a)x > 4
(b)x > 2
(c)x < 4
(d)x > 36
12.Simplify (5x² + 3x − 2) − (2x² − x + 5)
(a)3x² + 4x + 3
(b)3x² + 2x + 3
(c)7x² + 2x + 3
(d)3x² + 4x − 7
13.Factorise fully 12x² + 18x.
(a)2x(6x + 9)
(b)6(2x² + 3x)
(c)6x(2x + 3)
(d)3x(4x + 6)
14.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.
(a)20
(b)26
(c)24
(d)23
15.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.
(a)34
(b)68
(c)55
(d)47

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