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 lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?
(a)w < 630
(b)w ≥ 630
(c)w > 630
(d)w ≤ 630
2.a = 3 and b = 5. Work out the value of a²b.
(a)45
(b)75
(c)14
(d)225
3.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.
(a)y = 6x − 4
(b)y = x/3 + 13
(c)y = 3x + 5
(d)y = 3x + 23
4.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.
(a)720
(b)184
(c)176
(d)45
5.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.
(a)2n + 4
(b)2n
(c)2n + 2
(d)2n − 2
6.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.
y = x
(a)8
(b)−6
(c)−8
(d)6
7.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.
y = x² − 6x + 5
(a)x = 1
(b)x = 5
(c)x = 6
(d)x = 3
8.Which of these points lies in the first quadrant?
(a)(−1, −4)
(b)(4, −1)
(c)(−2, 3)
(d)(3, 5)
9.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.
(a)8
(b)3
(c)11
(d)−8
10.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
(a)−6
(b)−3
(c)−1/3
(d)3
11.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.
(a)6.4
(b)4
(c)5.2
(d)3.5
12.Work out the gradient of the straight line with equation 3y = 12 − 6x.
(a)2
(b)4
(c)−2
(d)−6
13.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
14.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.
(a)2n + 2
(b)4n + 2
(c)4n − 2
(d)4n
15.Work out the value of (x − 4)/2 + 3 when x = 10
(a)0
(b)4.5
(c)6
(d)11

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