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.Expand 2(x + 12)
(a)2x + 24
(b)2x + 14
(c)24x
(d)2x + 12
2.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.
(a)100/3
(b)25
(c)24
(d)50/3
3.Work out the value of 3n − 2 when n = 1
(a)5
(b)1
(c)3
(d)−1
4.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?
(a)It has an = sign, and equations always use =.
(b)3x + 5 cannot be simplified, so it must be an equation.
(c)Only x = 5 satisfies 3x + 5 = 20, not every value of x.
(d)A number on the right-hand side makes it an equation.
5.Solve the inequality 6x ≥ 18.
(a)x ≥ 12
(b)x ≤ 12
(c)x ≥ 3
(d)x ≤ 3
6.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.
(a)6
(b)9
(c)18
(d)12
7.Solve 5x + 2 = 17.
(a)3
(b)3.8
(c)15
(d)1.4
8.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
9.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.
(a)40
(b)92
(c)20
(d)28
10.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
11.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?
(a)30
(b)27
(c)28
(d)20
12.Solve the simultaneous equations 2x + y = 7 and x − y = 2.
(a)x = 1, y = 3
(b)x = 3, y = 2
(c)x = 3, y = 1
(d)x = 3, y = −1
13.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.
(a)(1, 3)
(b)(−1, 3)
(c)(9, 4)
(d)(−1, 4)
14.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.
(a)y = −2x + 3
(b)y = 2x + 3
(c)y = −2x − 3
(d)y = −x + 4
15.Which expression means 'add 3 to n, then multiply the result by 4'?
(a)4n + 3
(b)3(n + 4)
(c)4(n + 3)
(d)n + 3 × 4

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