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 · 15 questions

MathsUKwww.geekhero.co.uk

1.Which expression is equivalent to 0.5(4x + 6) − x?
(a)3x + 3
(b)2x + 3
(c)x + 3
(d)x + 6
2.Which expression is equivalent to 3(x + 4) − 2(x − 1)?
(a)x + 14
(b)x + 10
(c)5x + 10
(d)x + 13
3.Solve the inequality 9 − 2x ≥ 1.
(a)x ≤ 5
(b)x ≥ 4
(c)x ≤ 4
(d)x ≤ −4
4.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.
(a)y = 2x
(b)y = 3x
(c)y = x²
(d)y = 3x − 2
5.A Fibonacci-type sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₁ = 5 and a₃ = 17, work out a₂.
(a)22
(b)11
(c)−12
(d)12
6.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.
(a)25
(b)24
(c)21
(d)23
7.Solve x² + 3x − 10 = 0.
(a)x = 2 or x = 5
(b)x = −2 or x = 5
(c)x = −5 or x = −2
(d)x = 2 or x = −5
8.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?
(a)3(w − 5) ≥ 16
(b)3w − 5 ≥ 16
(c)3w − 5 > 16
(d)3w − 5 ≤ 16
9.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.
(a)There is not enough information
(b)They are equally steep
(c)Line D
(d)Line C
10.The curve y = x² − 1 and the line y = 3x − 3 meet at two points. Work out the x-coordinates of those two points.
y = 3x − 3y = x² − 1
(a)x = −1 and x = −2
(b)x = −1 and x = 4
(c)x = 1 and x = −1
(d)x = 1 and x = 2
11.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.
(a)20 km
(b)10 km
(c)40 km
(d)3 km
12.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.
(a)24
(b)35
(c)5
(d)30
13.Make x the subject of the formula y = (x − 4)/5.
(a)x = 5(y + 4)
(b)x = 5y − 4
(c)x = y/5 + 4
(d)x = 5y + 4
14.Solve the inequality 4x + 1 > 2x + 9.
(a)x > 5
(b)x < 5
(c)x < 4
(d)x > 4
15.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.
(a)10
(b)−6
(c)4
(d)−2

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