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 · Non-calculator · 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.Solve 2x² − 32 = 0.
(a)x = 8
(b)x = 4
(c)x = 16
(d)x = 4 or x = −4
3.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.
(a)(n − 5)/2
(b)n/2 − 5
(c)2(n − 5)
(d)(5 − n)/2
4.A tram sets off from a stop. Its velocity-time graph rises in a straight line from 0 m/s to 12 m/s over the first 8 seconds, then stays constant at 12 m/s for a further 10 seconds. Work out the total distance the tram travels in these 18 seconds, using the area under the graph.
(a)120 m
(b)216 m
(c)108 m
(d)168 m
5.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.
(a)4
(b)2
(c)16
(d)8
6.Solve 7x − 5 = 3x + 11
(a)−4
(b)1.5
(c)0.6
(d)4
7.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.
(a)4.6
(b)7.4
(c)90
(d)6
8.f(x) = 2x − 1. Work out ff(x).
y = 2x − 1
(a)4x² − 4x + 1
(b)4x − 2
(c)4x − 3
(d)4x − 1
9.Which of these values of x is a solution of x² + 2x − 15 = 0?
(a)x = 3
(b)x = 5
(c)x = 15
(d)x = −3
10.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
11.A circle has centre (0, 0) and passes through the point (7, 24). Work out the equation of the circle.
(a)x² + y² = 49
(b)x² + y² = 625
(c)x² + y² = 31
(d)x² + y² = 576
12.By completing the square, find the turning point of the curve y = x² + 6x + 2.
y = x² + 6x + 2
(a)x = 3, y = −7
(b)x = −3, y = −7
(c)x = −3, y = 7
(d)x = −6, y = −34
13.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.
(a)29
(b)25
(c)28
(d)16
14.A student attempts to prove that the product of two consecutive integers is always even: (i) Let the two consecutive integers be n and n + 1. (ii) Since n(n + 1) is even, one of n and n + 1 must be an even number. (iii) Therefore, n(n + 1) is even. At which statement does the proof first assume the very fact it is trying to prove?
(a)Statement (iii)
(b)Statement (i)
(c)Statement (ii)
(d)The proof does not assume anything it is trying to prove
15.Make x the subject of the formula y = x/2 − 5.
y = x
(a)x = (y + 5)/2
(b)x = 2y − 10
(c)x = 2y + 10
(d)x = 2y + 5

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