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.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.
(a)130
(b)13
(c)65
(d)490
3.The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at (6, 8).
(a)−3/4
(b)−4/3
(c)3/4
(d)4/3
4.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.
(a)11
(b)16
(c)96
(d)48
5.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.
(a)4
(b)7.5
(c)5.75
(d)2.71
6.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
7.The table shows the speed, in m/s, of a cyclist at times, in seconds, 1 second apart: 0 at t = 0, 7 at t = 1, 12 at t = 2, 15 at t = 3, 16 at t = 4, 14 at t = 5, 9 at t = 6. Using the trapezium rule with strip width 1 second, estimate the distance the cyclist travels between t = 2 and t = 5 only.
(a)68.5 m
(b)39 m
(c)28.5 m
(d)44 m
8.The equation x³ = 6x + 20 can be solved using the iterative formula xₙ₊₁ = ∛(6xₙ + 20). Taking x₀ = 3, x₁ = 3.3620 correct to 4 decimal places. Using the full unrounded value of x₁, work out x₂ correct to 3 decimal places.
(a)3.362
(b)2.722
(c)0.556
(d)3.425
9.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)
10.Expand and simplify (x − 3)²
(a)x² + 6x + 9
(b)x² − 9
(c)x² − 3x + 9
(d)x² − 6x + 9
11.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.
(a)8 cm³
(b)5 cm³
(c)15 cm³
(d)20 cm³
12.Make x the subject of the formula y = 3(x + 2).
(a)x = (y − 2)/3
(b)x = y/3 − 2
(c)x = 3y − 2
(d)x = y/3 + 2
13.The equation x² − 5x − 2 = 0 can be solved using the iterative formula xₙ₊₁ = √(5xₙ + 2). The starting value is x₀ = 2, so x₁ is the value after the formula has been used once. Work out x₃ correct to 3 decimal places.
(a)4.897
(b)4.396
(c)5.146
(d)3.464
14.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.
(a)£0.20
(b)£2.00
(c)£3.20
(d)£1.80
15.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.
(a)−14
(b)−2
(c)−8
(d)88

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