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 · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.f(x) = x³ − 3x − 20, and the equation f(x) = 0 has exactly one solution. Work out the pair of consecutive integers between which that solution lies.
y = x
(a)2 and 3
(b)3 and 4
(c)4 and 5
(d)6 and 7
2.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
3.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?
(a)y stays the same however large x becomes
(b)y decreases towards zero but never reaches it
(c)y increases towards a limit but never reaches it
(d)y decreases at a steady rate and reaches zero
4.A circle has centre (0, 0) and passes through the point (12, 35). Work out the equation of the circle.
(a)x² + y² = 1225
(b)x² + y² = 1369
(c)x² + y² = 144
(d)x² + y² = 2209
5.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
6.The mass of a chemical sample decays by 15% every hour. It starts at 500 g. Work out the mass remaining after 3 hours, correct to 1 decimal place.
(a)192.9 g
(b)275.0 g
(c)307.1 g
(d)361.3 g
7.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.
(a)No — it has never happened and never will
(b)Yes — when Harry is 20
(c)No — that moment has already passed
(d)Yes — when Harry is 16
8.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.
(a)1 hour 12 minutes
(b)1 hour 48 minutes
(c)1 hour 40 minutes
(d)1 hour 32 minutes
9.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.
(a)12
(b)6
(c)7.5
(d)9
10.The point (20, 21) lies on the circle x² + y² = 841, which has centre O(0, 0). The tangent to the circle at (20, 21) crosses the x-axis at P and the y-axis at Q. Work out the area of triangle OPQ, correct to 1 decimal place.
(a)842.0
(b)2.0
(c)1684.0
(d)580.7
11.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.
(a)£7.20
(b)£22.20
(c)£9.70
(d)£10.20
12.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
13.Points A(−1, 2) and B(5, 8) are the endpoints of a line segment. Work out the equation of the perpendicular bisector of AB.
(a)x + y = 4
(b)x + y = 12
(c)x − y = −3
(d)x + y = 7
14.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.
(a)(3, 5)
(b)(−3, 9)
(c)(3, 9)
(d)(3, 7)
15.The equation x³ − 5x − 3 = 0 can be rearranged to give an iterative formula of the form xₙ₊₁ = ∛(…). Work out which one of these is a correct rearrangement.
(a)xₙ₊₁ = ∛(5xₙ + 3)
(b)xₙ₊₁ = ∛(5xₙ − 3)
(c)xₙ₊₁ = (5xₙ + 3) ÷ 3
(d)xₙ₊₁ = ∛(3xₙ + 5)

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