Printable · GCSE Higher · ages 14-16

Algebra worksheet — GCSE Higher

Fifteen questions across the algebra statements at Higher 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 Higher

Maths · GCSE Higher · Algebra · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A cyclist's velocity increases from 3 m/s to 11 m/s over 5 seconds, at a constant rate. Work out the cyclist's acceleration, in m/s².
(a)0.625 m/s²
(b)1.6 m/s²
(c)8 m/s²
(d)2.2 m/s²
2.f(x) = 3x − 2. Find f⁻¹(x).
y = 3x − 2
(a)(x − 2)/3
(b)(x + 2)/3
(c)3x + 2
(d)x/3 + 2
3.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.
(a)12 km/h
(b)9 km/h
(c)8 km/h
(d)0.2 km/h
4.One solution of the equation x² − (k + 1)x + k = 0 is x = 3. Work out the value of k.
(a)k = 3
(b)k = −3
(c)k = 4
(d)k = 1.5
5.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.
(a)6
(b)4
(c)12
(d)−6
6.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.
(a)Subtracting 4x gives 3 = 10, which is never true.
(b)x would have to be negative, but x must be positive.
(c)It's true for every x, so there are infinite solutions.
(d)x = 7, since 10 − 3 = 7.
7.Work out the period of the graph of y = cos x, in degrees.
y = cos(x)
(a)180°
(b)90°
(c)360°
(d)720°
8.Find the common ratio of the geometric sequence 5, 5√2, 10, 10√2, ... Give your answer in surd form.
(a)1.41
(b)√2
(c)5√2
(d)2
9.Solve the inequality 5 − x ≤ 2.
(a)x ≤ −3
(b)x ≥ −3
(c)x ≥ 3
(d)x ≤ 3
10.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.
11.The graph of y = f(x) has x-intercepts at x = −1 and x = 4. Which statement correctly describes the x-intercepts of y = f(2 − x)?
(a)Translate +2 in x only (no reflection); roots 1, 6
(b)Solved 2 − x = k as x = k − 2; roots −3, 2
(c)No overall change; roots −1, 4
(d)Reflect in the y-axis, +2 in x; roots 3, −2
12.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.
(a)3n + 2
(b)2n + 3
(c)2n − 3
(d)5n
13.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.
(a)n + 5
(b)5n + 4
(c)5n
(d)5n − 1
14.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).
y = -4x + 1
(a)y = −4x + 3
(b)y = (−1/4)x + 3
(c)y = 4x + 3
(d)y = (1/4)x + 3
15.Subtract, giving your answer as a single fraction in its simplest form: 4/(x − 1) − 2/(x + 3)
(a)(2x + 11)/((x − 1)(x + 3))
(b)(2x + 14)/((x − 1)(x + 3))
(c)2/((x − 1)(x + 3))
(d)(2x − 10)/((x − 1)(x + 3))

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