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.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.
(a)4x = 20
(b)4x − 4 = 20
(c)4x − 4 = 2x + 20
(d)8x − 4 = 20
2.Which of these statements is an identity?
(a)x + 4 = 2x
(b)2(x + 4) = 20
(c)2(x + 4) ≡ 2x + 8
(d)2(x + 4) = 2x + 4
3.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?
(a)An equation, since it has an equals sign and unknown x.
(b)An identity, since both sides are equal for every x.
(c)A formula, since it relates two different quantities.
(d)An inequality, since the sides are equal sometimes.
4.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.
y = x² − 5x + 6
(a)x = −1 and x = −6
(b)x = 2 and x = −3
(c)x = 2 and x = 3
(d)x = −2 and x = −3
5.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.
(a)10
(b)16
(c)12
(d)13
6.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?
(a)The object was decelerating
(b)The object was travelling at a constant, non-zero speed
(c)The object was stationary (not moving)
(d)The object was travelling at its maximum speed
7.Factorise 6x² − 7x − 3.
(a)(x − 3)(6x + 1)
(b)(3x + 1)(2x − 3)
(c)(6x − 1)(x + 3)
(d)(3x − 1)(2x + 3)
8.Solve the inequality 9 − 2x ≥ 1.
(a)x ≤ 5
(b)x ≥ 4
(c)x ≤ 4
(d)x ≤ −4
9.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
10.The graph of y = sin x is reflected in the x-axis to give the graph of y = g(x). Work out the value of g(90), where x is measured in degrees.
y = sin(x)
(a)−1
(b)1
(c)−0.5
(d)0
11.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?
(a)w < 630
(b)w ≥ 630
(c)w > 630
(d)w ≤ 630
12.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.
y = 2x − 6
(a)(−3, 0)
(b)(6, 0)
(c)(0, −6)
(d)(3, 0)
13.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
14.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.
(a)2
(b)−0.5
(c)0.5
(d)−0.8
15.Simplify (5x² + 3x − 2) − (2x² − x + 5)
(a)3x² + 4x + 3
(b)3x² + 2x + 3
(c)7x² + 2x + 3
(d)3x² + 4x − 7

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