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 sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
(a)38
(b)36
(c)64
(d)14
2.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.
y = x² + 1
(a)−3
(b)1
(c)5
(d)4
3.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.
(a)4x² + 2x − 20
(b)6x + 6
(c)6x + 14
(d)3x + 3
4.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.
(a)9.78
(b)8.39
(c)5.32
(d)7
5.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.
(a)6 s
(b)8 s
(c)32 s
(d)12 s
6.Solve the inequality 3x + 6 ≤ 0.
(a)x ≤ 2
(b)x ≤ −2
(c)x ≥ −2
(d)x ≤ −18
7.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.
(a)£0.20
(b)£2.00
(c)£3.20
(d)£1.80
8.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.
y = 0.15x + 20
(a)£50
(b)£30
(c)£203
(d)£320
9.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?
(a)False — 4(2x − 3) = 8x − 12, not 8x − 3.
(b)True — 4(2x − 3) = 8x − 3 when the bracket is expanded.
(c)False — 4(2x − 3) = 2x − 12, only the −3 is multiplied.
(d)True — 4(2x − 3) = 8x − 3, since both are linear.
10.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.
y = x² + 2x − 15
(a)x = −3 and x = 5
(b)x = 5 and x = 3
(c)x = 3 and x = −5
(d)x = −15 and x = 1
11.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.
(a)h = b/(2A)
(b)h = 2A/b
(c)h = A/(2b)
(d)h = 2Ab
12.Write down the expression that means the same as p + p + p + q.
(a)3p + q
(b)3(p + q)
(c)p³ + q
(d)3pq
13.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.
(a)18 − 3n
(b)3n − 21
(c)−3n
(d)21 − 3n
14.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
15.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.
(a)y = 84 + 14x
(b)y = 84 − 14x
(c)y = 14 − 84x
(d)y = 14x − 84

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