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.

Non-calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Algebra worksheet — GCSE Higher

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

MathsUKwww.geekhero.co.uk

1.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
2.Work out the gradient of the straight line with equation 3y = 12 − 6x.
(a)2
(b)4
(c)−2
(d)−6
3.Factorise 6x² − 7x − 3.
(a)(x − 3)(6x + 1)
(b)(3x + 1)(2x − 3)
(c)(6x − 1)(x + 3)
(d)(3x − 1)(2x + 3)
4.A graph passes through the point (0, 1). As x increases through positive values, the graph rises more and more steeply, and as x decreases through negative values, the graph gets closer and closer to the x-axis without ever reaching it. Which of these could be the equation of the graph?
(a)y = 2ˣ
(b)y = x² + 1
(c)y = x³ + 1
(d)y = 1 − x²
5.Make x the subject of the formula y = x/2 − 5.
y = x
(a)x = (y + 5)/2
(b)x = 2y − 10
(c)x = 2y + 10
(d)x = 2y + 5
6.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.
(a)23
(b)27
(c)24
(d)20
7.Which of these equations represents the graph of y = 2ˣ translated by 3 units in the positive y-direction?
(a)y = 2ˣ + 3
(b)y = 2ˣ⁺³
(c)y = 2ˣ − 3
(d)y = 2(x + 3)
8.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.
(a)8 m
(b)24 m
(c)16 m
(d)12 m
9.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.
y = 3x + 6
(a)(2, 0)
(b)(−2, 0)
(c)(6, 0)
(d)(0, 6)
10.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.
y = 2x² + 1
(a)2x² − 4x + 2
(b)2x² − 1
(c)2x²
(d)2x² − 4x + 3
11.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.
y = x² + 2x − 15
(a)x = −3 and x = 5
(b)x = 5 and x = 3
(c)x = 3 and x = −5
(d)x = −15 and x = 1
12.The area under a speed-time graph between t = 0 and t = 6 seconds is estimated using three strips of equal width, using the speeds, in m/s, at t = 0, 2, 4 and 6: 0, 5, 9 and 12. Using the trapezium rule with these three trapezia, estimate the distance travelled.
(a)28 m
(b)80 m
(c)52 m
(d)40 m
13.Solve the inequality 2(3x − 1) ≥ 4x + 8.
(a)x ≥ 4.5
(b)x ≥ 5
(c)x ≥ 1
(d)x ≥ 20
14.A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₃ = 11 and a₅ = 29, work out a₁.
(a)4
(b)3
(c)7
(d)18
15.f(x) = (x + 1)/2. Find f⁻¹(x).
(a)2x − 1
(b)(x − 1)/2
(c)x/2 − 1
(d)2x + 1

Build your own mix at the worksheet builder.