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

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1.Solve 2x + 1 = 9
(a)x = 8
(b)x = 16
(c)x = 4
(d)x = 5
2.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.
(a)2
(b)5
(c)9
(d)−5
3.In the expression 5x² − 3x + 7, which of these is a single term of the expression?
(a)5x² − 3x
(b)5x² − 3x + 7
(c)5x²
(d)−3x + 7
4.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.
(a)12
(b)4
(c)8
(d)16
5.The diagram shows part of the graph of a reciprocal function of the form $y = \frac{k}{x}$ , passing through the labelled point. Work out the value of k.
(a)5
(b)6
(c)9
(d)1.5
6.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.
(a)3 km/h
(b)60 km/h
(c)195 km/h
(d)180 km/h
7.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.
(a)53
(b)41
(c)48
(d)47
8.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?
(a)3x = 12
(b)3x = 10
(c)3x + 2y = 12
(d)x = 12
9.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.
(a)9n + 6
(b)6n
(c)6n + 9
(d)6n + 3
10.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
11.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.
(a)k + 5
(b)k − 5
(c)5k
(d)5 − k
12.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.
(a)x ≥ 30
(b)x ≤ 50
(c)x ≤ 90
(d)x ≤ 30
13.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.
(a)25
(b)24
(c)21
(d)23
14.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?
(a)5x − 3 = 4x + 9
(b)6x − 3 = 4x + 9
(c)6x − 1 = 4x + 9
(d)6x − 4 = 4x + 9
15.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?
(a)3(w − 5) ≥ 16
(b)3w − 5 ≥ 16
(c)3w − 5 > 16
(d)3w − 5 ≤ 16

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