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.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?
(a)False — 4(2x − 3) = 8x − 12, not 8x − 3.
(b)True — 4(2x − 3) = 8x − 3 when the bracket is expanded.
(c)False — 4(2x − 3) = 2x − 12, only the −3 is multiplied.
(d)True — 4(2x − 3) = 8x − 3, since both are linear.
2.Work out the value of (x − 4)/2 + 3 when x = 10
(a)0
(b)4.5
(c)6
(d)11
3.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.
(a)5
(b)4
(c)6
(d)−5
4.Make x the subject of the formula y = x + 7.
y = x + 7
(a)x = y + 7
(b)x = y − 7
(c)x = 7 − y
(d)x = 7y
5.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.
(a)It touches the x-axis once, only at x = 4.
(b)It never touches the x-axis at all.
(c)It crosses twice, at x = 4 and x = −4.
(d)It crosses twice, at x = 2 and x = −2.
6.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.
(a)y + 1
(b)y − 4
(c)y − 9
(d)y + 9
7.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.
(a)6n + 1
(b)7n
(c)7n − 1
(d)7n + 6
8.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?
(a)An identity, true for every value of x
(b)A formula, relating two expressions
(c)An equation, because it has an equals sign
(d)An equation, solved by one value of x
9.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.
(a)1.5
(b)8
(c)3
(d)12
10.Solve 5x − 9 = 16
(a)1.4
(b)5
(c)25
(d)3.2
11.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
12.Which of these is an equation, rather than an expression, a formula or an identity?
(a)3x + 5
(b)A = πr²
(c)3x + 5 = 17
(d)3(x + 5) ≡ 3x + 15
13.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.
(a)20
(b)40
(c)35
(d)30
14.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
15.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

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