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.Solve 3x + 14 = 8x − 6
(a)x = 15
(b)x = 2.5
(c)x = 4
(d)x = −1.6
2.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.
(a)15 and 6
(b)15 and 21
(c)15 and 9
(d)18 and 6
3.A coastguard radar at the origin covers a circular region modelled by x² + y² = 400, where each unit represents 1 kilometre. A boat travels along the straight line that touches the boundary of the region at the point (12, 16). Work out the equation of the line the boat travels along.
(a)y = −3x/4 − 25
(b)y = −3x/4 + 25
(c)y = −4x/3 + 32
(d)y = 3x/4 + 7
4.Solve the inequality x² − 5x + 6 < 0.
(a)−3 < x < −2
(b)x < 2 or x > 3
(c)2 < x < 3
(d)2 ≤ x ≤ 3
5.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.
(a)h = b/(2A)
(b)h = 2A/b
(c)h = A/(2b)
(d)h = 2Ab
6.Solve x² − 5x + 6 = 0 by factorising.
(a)x = −2 or x = −3
(b)x = 1 or x = 6
(c)x = 2 or x = 3
(d)x = 5 or x = 6
7.The graph of y = cos x is transformed onto the graph of y = cos(x − 90°). State the direction of the translation and which standard graph the image is.
y = cos(x)
(a)Positive x-direction, 90°; image is y = sin x.
(b)Negative x-direction, 90°; image is y = sin x.
(c)Positive x-direction, 90°; image is y = −sin x.
(d)Positive y-direction, 90°; image is y = sin x.
8.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.
(a)2.5
(b)0
(c)20
(d)5
9.a = 2 and b = 5. Work out the value of a²b.
(a)9
(b)20
(c)100
(d)50
10.The graph of y = f(x) crosses the x-axis at x = −3 and x = 7, and crosses the y-axis at (0, 21). A second graph crosses the x-axis at x = −7 and x = 3, and crosses the y-axis at the same point, (0, 21). The second graph is y = g(x). Which of these could be the equation of g(x)?
(a)y = f(x) − 4
(b)y = f(−x)
(c)y = −f(x)
(d)y = −f(−x)
11.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.
(a)Tuesday, by 2 km/h
(b)Tuesday, by 8 km/h
(c)Tuesday, by 3 km/h
(d)Monday, by 2 km/h
12.Which of these pairs of lines are perpendicular to each other?
(a)y = 2x and y = 2x + 1
(b)y = 2x and y = −(1/2)x + 1
(c)y = 2x and y = −2x + 1
(d)y = 2x and y = (1/2)x + 1
13.The diagram shows part of the graph of a reciprocal function of the form $y = \frac{k}{x}$ , passing through the labelled point. Work out the value of k.
(a)5
(b)6
(c)9
(d)1.5
14.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.
(a)27
(b)22.5
(c)18
(d)36
15.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
(a)3 and 2n + 5 are the two terms of 6n + 15
(b)6n and 15 are the factors of 6n + 15
(c)3 and 2n + 5 are both factors of 6n + 15
(d)3 is the only factor of 6n + 15

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