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.Solve x² = 81.
(a)x = 6561
(b)x = 9
(c)x = 40.5
(d)x = 9 or x = −9
2.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.
(a)2
(b)4
(c)10
(d)0.5
3.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?
(a)y stays the same however large x becomes
(b)y decreases towards zero but never reaches it
(c)y increases towards a limit but never reaches it
(d)y decreases at a steady rate and reaches zero
4.A graph has equation y = x² − 6x + 5. A student says its turning point has x-coordinate 6, because that's the coefficient of x. Which statement corrects the student's mistake?
y = x² − 6x + 5
(a)The student is correct, because the turning point's x-coordinate always equals the coefficient of x.
(b)The turning point has x-coordinate −6, because the sign of the coefficient must be reversed.
(c)The turning point has x-coordinate 5, because that is the larger of the equation's two roots.
(d)The roots of x² − 6x + 5 = 0 are x = 1 and x = 5 (since it factorises to (x − 1)(x − 5)), so by symmetry the turning point has x-coordinate 3, not 6.
5.Solve 3x − 1 = 8
(a)x = 9
(b)x = 6
(c)x = 27
(d)x = 3
6.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.
(a)£7.20
(b)£22.20
(c)£9.70
(d)£10.20
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.Solve 2x² = 18.
(a)x = 9 or x = −9
(b)x = 4 or x = −4
(c)x = 6 or x = −6
(d)x = 3 or x = −3
9.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.
(a)20
(b)456
(c)0.05
(d)480
10.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.
(a)£50
(b)£120
(c)£60
(d)£40
11.Make x the subject of the formula y = 5x + 3.
y = 5x + 3
(a)x = (y + 3)/5
(b)x = (y − 3)/5
(c)x = y/5 − 3
(d)x = 5(y − 3)
12.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.
y = x²
(a)x = −1 and x = 2
(b)x = −3 and x = 4
(c)x = 0 and x = 1
(d)x = −2 and x = 3
13.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.
(a)8/3
(b)−3
(c)3
(d)1/3
14.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.
(a)29
(b)25
(c)28
(d)16
15.Write down the expression that means 5 more than half of n.
(a)(n + 5)/2
(b)5n/2
(c)2n + 5
(d)n/2 + 5

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