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.Expand and simplify (x + 1)(x + 2)(x + 3).
(a)x³ + 6x² + 11x + 5
(b)x³ + 6x² + 6x + 6
(c)x³ + 5x² + 11x + 6
(d)x³ + 6x² + 11x + 6
2.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
(a)−6
(b)−3
(c)−1/3
(d)3
3.Solve 3(2x − 1) = 27
(a)4
(b)5
(c)4.5
(d)4 2/3
4.An allotment is in the shape of a rectangle. Its length is 5 m more than its width, x metres, and its area is 20 m². This gives x² + 5x − 20 = 0, which can be solved using the iterative formula xₙ₊₁ = 20 ÷ (xₙ + 5). Taking x₀ = 2, so that x₁ is the value found after the formula has been used once, work out x₂ correct to 2 decimal places.
(a)2.55
(b)−1.71
(c)2.00
(d)2.86
5.Solve 2x² − 32 = 0.
(a)x = 8
(b)x = 4
(c)x = 16
(d)x = 4 or x = −4
6.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.
(a)y = 6x − 4
(b)y = x/3 + 13
(c)y = 3x + 5
(d)y = 3x + 23
7.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.
(a)(−3.5, 3.5)
(b)(5, 3)
(c)(4, 5)
(d)(4, 8)
8.Simplify (x² − 9) ÷ (x² + 5x + 6).
(a)(x + 3)/(x + 2)
(b)(x − 3)/(x + 2)
(c)x − 3
(d)−9/(5x + 6)
9.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.
(a)s/f
(b)sf
(c)f/s
(d)s − f
10.Factorise x² − 3x − 10.
(a)(x − 10)(x + 1)
(b)(x − 5)(x + 2)
(c)(x + 5)(x − 2)
(d)(x − 5)(x − 2)
11.f(x) = 2x − 1. Work out ff(x).
y = 2x − 1
(a)4x² − 4x + 1
(b)4x − 2
(c)4x − 3
(d)4x − 1
12.A circular pond has equation x² + y² = 20, with lengths in metres from the centre of the garden. A straight path runs along the line y = 2x, entering the pond and leaving it again. Work out the coordinates of the two points where the path meets the edge of the pond.
y = 2x
(a)(2, 4)
(b)(2, 4) and (−2, −4)
(c)(2, 1) and (−2, −1)
(d)(2, −4) and (−2, 4)
13.Solve the simultaneous equations y = 3 − x and x² + y² = 9, giving both pairs of solutions.
(a)x = 0, y = 3 and x = 6, y = −3
(b)x = 0, y = 3 and x = −3, y = 6
(c)x = 0, y = 3 and x = 3, y = 0
(d)x = 0, y = 3
14.Simplify fully: (x + 2)/(3x) × 6x²/(x² − 4)
(a)2/(x − 2)
(b)2x/(x + 2)
(c)2x²/(x − 2)
(d)2x/(x − 2)
15.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.
(a)34
(b)68
(c)55
(d)47

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