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.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.
(a)x = 14, y = −4
(b)x = 7, y = 3
(c)x = 5, y = 5
(d)x = 7, y = 4
2.Solve (3x + 2)/5 = (x + 4)/3
(a)x = 3.5
(b)x = 4.5
(c)x = 10
(d)x = 1
3.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).
(a)(−10, −2)
(b)(−5, −2)
(c)(−4, −2)
(d)(5, −2)
4.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.
(a)y = 18
(b)y = 30
(c)y = 144
(d)y = 4
5.Solve 2x² − 32 = 0.
(a)x = 8
(b)x = 4
(c)x = 16
(d)x = 4 or x = −4
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.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.
(a)3x
(b)x − 3
(c)x/3
(d)x + 3
8.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.
y = x² − 2x − 8
(a)x = −1
(b)x = 3
(c)x = 2
(d)x = 1
9.Simplify (5x² + 3x − 2) − (2x² − x + 5)
(a)3x² + 4x + 3
(b)3x² + 2x + 3
(c)7x² + 2x + 3
(d)3x² + 4x − 7
10.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.
(a)7
(b)8
(c)6
(d)9
11.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.
(a)3n − 2
(b)3n + 1
(c)3n + 4
(d)n + 3
12.Expand 2(x + 12)
(a)2x + 24
(b)2x + 14
(c)24x
(d)2x + 12
13.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.
(a)2
(b)3
(c)−6
(d)18
14.Which expression means 'y squared, multiplied by 3'?
(a)3y²
(b)y³
(c)(3y)²
(d)3 + y²
15.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.

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