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.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.
(a)39
(b)192
(c)768
(d)256
2.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?
(a)The two roots must both be positive.
(b)The graph has no roots at all.
(c)The graph must touch the x-axis at exactly one point.
(d)If the graph has two real roots, they are equal and opposite in value, so they sum to zero.
3.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.
(a)y = x + 2
(b)y = 2x − 1
(c)y = 2x + 1
(d)y = 2x + 3
4.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?
(a)It does not cross, since the minimum lies below the axis.
(b)It crosses the x-axis, since the minimum is below it.
(c)It touches the x-axis once, at (3, −4).
(d)It is impossible to tell without the full equation.
5.A number machine multiplies its input by 5. Work out the output when the input is −1.
(a)−5
(b)5
(c)4
(d)−6
6.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
7.y = 5x − 1. Work out the value of y when x = 3.
y = 5x − 1
(a)14
(b)16
(c)15
(d)10
8.Write down the gradient of the line with equation y = 6 + 4x.
(a)6
(b)24
(c)10
(d)4
9.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.
(a)5
(b)8
(c)7
(d)28
10.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.
(a)20
(b)26
(c)24
(d)23
11.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.
(a)9
(b)20
(c)45
(d)25
12.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
13.Solve 2x² − 32 = 0.
(a)x = 8
(b)x = 4
(c)x = 16
(d)x = 4 or x = −4
14.Solve 4x − (2x − 6) = 18
(a)x = 6
(b)x = 3
(c)x = 12
(d)x = 24
15.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.
(a)4
(b)1/5
(c)5
(d)13

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