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

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1.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.
(a)4
(b)2
(c)16
(d)8
2.Solve 5x − 9 = 16
(a)1.4
(b)5
(c)25
(d)3.2
3.Write down the number of terms in the expression 4x² − 7x + 3.
(a)2
(b)5
(c)4
(d)3
4.Solve x² = 49.
(a)x = 7
(b)x = 24.5
(c)x = −7
(d)x = 7 or x = −7
5.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.
y = -5x + 200
(a)(40, 0)
(b)(0, 40)
(c)(0, 200)
(d)(200, 0)
6.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
7.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
8.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.
y = 45x + 60
(a)£315
(b)£108
(c)£135
(d)£195
9.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.
(a)(−4, −7)
(b)(7, −4)
(c)(−4, 7)
(d)(4, 7)
10.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.
(a)20
(b)15
(c)5
(d)10
11.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.
(a)4.6
(b)7.4
(c)90
(d)6
12.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
13.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.
(a)(2, 5)
(b)(−5, −2)
(c)(−5, 2)
(d)(5, −2)
14.The diagram shows the graph of a function. Which equation could it represent?
(a) $y = x^{3} + 4 x$
(b) $y = x^{3} - 4 x$
(c) $y = - x^{3} + 4 x$
(d) $y = x^{2} - 4 x$
15.Make x the subject of the formula y = 2x − 9.
y = 2x − 9
(a)x = (y + 9) / 2
(b)x = (y − 9) / 2
(c)x = 2(y + 9)
(d)x = y / 2 + 9

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