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.Make c the subject of the formula k = 6c.
(a)c = 6k
(b)c = k/6
(c)c = k − 6
(d)c = 6 − k
2.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?
(a)y = x² + 2
(b)y = 2x + 2
(c)y = 2/x
(d)y = x³ + 2
3.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.
(a)15 and 6
(b)15 and 21
(c)15 and 9
(d)18 and 6
4.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.
(a)n + 3
(b)3n + 5
(c)3n
(d)3n + 2
5.a = 3 and b = 5. Work out the value of a²b.
(a)45
(b)75
(c)14
(d)225
6.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?
(a)The cost, in pounds, for each extra 2 gigabytes of data used
(b)The fixed monthly fee, in pounds
(c)The cost, in pounds, for each extra gigabyte of data used
(d)The total number of gigabytes included in the plan
7.Solve x² − 100 = 0.
(a)x = 10 or x = −10
(b)x = 10
(c)x = 100 or x = −100
(d)x = 50
8.The point B has coordinates (−2, −2). In which quadrant is B?
(a)the fourth quadrant
(b)the second quadrant
(c)the first quadrant
(d)the third quadrant
9.Which of these is a formula, rather than an expression, an equation, or an identity?
(a)lwh
(b)lwh = 60
(c)2(l + w) ≡ 2l + 2w
(d)V = lwh
10.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.
(a)£13.20
(b)£15.50
(c)£34.20
(d)£16.70
11.The graph of y = (x − 4)(x + 1) crosses the x-axis. Which pair gives the correct roots and reasoning?
(a)x = −4 and x = −1, because the roots are always the negative of the numbers shown in the brackets.
(b)x = 4 and x = 1, because both brackets must be positive at the roots.
(c)x = 4 and x = −1, because the graph crosses the x-axis where x − 4 = 0 or x + 1 = 0.
(d)x = −4 and x = 1, because the signs inside the brackets must be reversed to solve them.
12.Solve 4x + 3 = 19
(a)3.75
(b)5.5
(c)4
(d)4.75
13.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.
(a)s/f
(b)sf
(c)f/s
(d)s − f
14.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.
y = 2x − 7
(a)(0, 7)
(b)(−7, 0)
(c)(2, −7)
(d)(0, −7)
15.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

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