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 − 3)²
(a)x² + 6x + 9
(b)x² − 9
(c)x² − 3x + 9
(d)x² − 6x + 9
2.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.
(a)£26.67
(b)£40
(c)£6.67
(d)£20
3.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.
(a)20
(b)40
(c)35
(d)30
4.An exponential model has equation y = A × bˣ, where b > 1. Its graph passes through the points (1, 135) and (2, 405). Work out the value of A.
(a)45
(b)1
(c)135
(d)3
5.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
6.x = 5. Work out the value of 3x² − 4.
(a)221
(b)75
(c)71
(d)3
7.Which of these quadratic graphs does NOT cross the x-axis at all?
(a)y = (x − 2)² + 3
(b)y = (x + 4)(x − 1)
(c)y = (x − 2)(x + 3)
(d)y = x² − 9
8.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.
(a)33
(b)65
(c)32
(d)17
9.A population of bacteria doubles every 3 hours. It starts at 800. Work out the population after 9 hours.
(a)409,600
(b)8
(c)6,400
(d)3,200
10.Solve (3x + 2)/5 = (x + 4)/3
(a)x = 3.5
(b)x = 4.5
(c)x = 10
(d)x = 1
11.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.
(a)(0, 16)
(b)(0, −2)
(c)(−8, −2)
(d)(5, 3)
12.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.
(a)2x
(b)x² + 49
(c)x² − 14x − 49
(d)x² − 49
13.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).
(a)y = −2x − 1
(b)y = −2x + 1
(c)y = −(1/2)x + 2
(d)y = 2x + 7
14.The equation x² + 2x − 5 = 0 can be solved using the iterative formula xₙ₊₁ = 5/(xₙ + 2). The starting value is x₀ = 1, so x₁ is the value after the formula has been used once. Work out x₂ correct to 2 decimal places.
(a)1.36
(b)1.49
(c)1.37
(d)1.67
15.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.
(a)6.4
(b)4
(c)5.2
(d)3.5

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