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.Ben is asked to find the inverse of f(x) = 4 − 3x. He writes f⁻¹(x) = (4 − x)/3. Which statement about Ben's answer is correct?
(a)Wrong: sign kept, giving f⁻¹(x) = (−4 − x)/3
(b)Correct, but only because f is its own inverse
(c)Correct: 3y = 4 − x gives f⁻¹(x) = (4 − x)/3
(d)Wrong: correct inverse is f⁻¹(x) = (x − 4)/3
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.n is an integer. Which of these expressions is always an even number?
(a)n² + n
(b)n² − n + 1
(c)2n + 1
(d)n² + 1
4.A student claims: 'For every positive integer n, n² + n + 1 is a prime number.' Which value of n shows that this claim is false?
(a)n = 3
(b)n = 1
(c)n = 4
(d)n = 2
5.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.
(a)(2, 5)
(b)(−5, −2)
(c)(−5, 2)
(d)(5, −2)
6.Work out the value of m² + 3m when m = −2
(a)−10
(b)10
(c)−14
(d)−2
7.The table shows the speed, in m/s, of a car at times, in seconds, all 2 seconds apart: 0 at t = 0, 3 at t = 2, 8 at t = 4, 15 at t = 6, 24 at t = 8. A student uses the trapezium rule with these five readings to estimate the distance the car travels. By finding the second differences of the speed values, decide whether this trapezium estimate is an overestimate or an underestimate of the true distance.
(a)Underestimate — second differences are constant.
(b)Overestimate — the speed values are increasing.
(c)Underestimate — the curve bends upward (convex).
(d)Overestimate — the curve bends upward (convex).
8.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
9.Which expression means 'add 3 to n, then multiply the result by 4'?
(a)4n + 3
(b)3(n + 4)
(c)4(n + 3)
(d)n + 3 × 4
10.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.
(a)11
(b)4
(c)7.5
(d)22
11.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
12.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.
(a)28
(b)38
(c)32
(d)33
13.The 2nd term of a geometric sequence is 6 and the 4th term is 24. Given that all the terms of the sequence are positive, work out the common ratio.
(a)−2
(b)18
(c)2
(d)4
14.Factorise 6x² − 7x − 3.
(a)(x − 3)(6x + 1)
(b)(3x + 1)(2x − 3)
(c)(6x − 1)(x + 3)
(d)(3x − 1)(2x + 3)
15.The first five terms of a quadratic sequence are 4, 7, 12, 19, 28. Work out an expression, in terms of n, for the nth term.
(a)3n + 1
(b)2n² + 3
(c)n²
(d)n² + 3

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