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 number machine adds 6 to its input. Work out the output when the input is −4.
(a)10
(b)−10
(c)2
(d)−24
2.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.
(a)£1700
(b)£1500
(c)£2300
(d)£2000
3.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
4.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.
(a)R
(b)Q
(c)P
(d)S
5.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)
6.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.
(a)4.67
(b)−4
(c)2
(d)4
7.Which of these equations gives a straight-line graph when plotted?
(a)y = 3/x
(b)y = 2x − 3
(c)y = x³ − 3
(d)y = x² − 3
8.Make c the subject of the formula k = 6c.
(a)c = 6k
(b)c = k/6
(c)c = k − 6
(d)c = 6 − k
9.Work out the gradient of the straight line with equation y = (2x/5) − 3.
(a)2/5
(b)5/2
(c)−2/5
(d)−3
10.Solve x² = 49.
(a)x = 7
(b)x = 24.5
(c)x = −7
(d)x = 7 or x = −7
11.Work out the equation of the straight line through the points (−2, 1) and (0, 7).
(a)y = −3x + 7
(b)y = 3x + 1
(c)y = 3x + 7
(d)y = (1/3)x + 7
12.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
13.Write down the y-intercept of the line with equation y = 3x + 8.
y = 3x + 8
(a)−8
(b)11
(c)3
(d)8
14.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.
(a)11 — 6 and (4x + 3) are correct factors of 24x + 18.
(b)66 — 6 and (4x + 3) are not correct factors of 24x + 18.
(c)84 — 6 and (4x + 3) are correct factors of 24x + 18.
(d)66 — 6 and (4x + 3) are correct factors of 24x + 18.
15.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.
(a)s = P − 4
(b)s = P + 4
(c)s = P / 4
(d)s = 4P

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