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.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.
y = x² + 12x + 40
(a)−6
(b)36
(c)4
(d)40
2.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.
(a)5/L − 3
(b)(L − 3)/5
(c)L/5 − 3
(d)L − 3/5
3.Solve x² − 6x = 0.
(a)x = 0
(b)x = 3
(c)x = 6
(d)x = 0 or x = 6
4.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.
(a)9x − 40y = 1681
(b)9x + 40y = 1681
(c)40x + 9y = 1681
(d)9x + 40y = 41
5.A tap's flow rate, in litres per minute, is plotted against time, in minutes, on a graph. What are the units of the area under this graph?
(a)Litres
(b)Litres per minute squared
(c)Litres per minute
(d)Minutes
6.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
(a)−6
(b)−3
(c)−1/3
(d)3
7.A proof that the product of two consecutive even numbers is always a multiple of 8 begins: Let the two consecutive even numbers be 2n and 2n + 2, so their product is 2n(2n + 2) = 4n(n + 1). Which line correctly completes the proof?
(a)4n(n + 1) is a multiple of 4, and because n and n + 1 are consecutive integers, it must be a multiple of 8.
(b)Expanding gives 4n(n + 1) = 4n² + 4n, which is clearly a multiple of 8.
(c)4n is always a multiple of 4 for any integer n, so 4n(n + 1) is a multiple of 4 as well, which means it is a multiple of 8.
(d)n and n + 1 are consecutive integers, so one of them must be even; this makes n(n + 1) even, so 4n(n + 1) is 4 × an even number, which is a multiple of 8.
8.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.
(a)18 cm²
(b)6 cm²
(c)12 cm²
(d)36 cm²
9.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.
(a)6n + 1
(b)7n
(c)7n − 1
(d)7n + 6
10.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.
(a)6.6
(b)6.1
(c)6.3
(d)6.0
11.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.
(a)s/f
(b)sf
(c)f/s
(d)s − f
12.A circle has centre (0, 0) and equation x² + y² = 100. A straight line is drawn from the origin through the point P(8, 9). Work out whether P lies inside, on, or outside the circle.
(a)P lies inside the circle
(b)P lies on the circle
(c)Cannot be determined from this information
(d)P lies outside the circle
13.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?
(a)11
(b)48
(c)15.5
(d)12
14.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.
(a)500 m
(b)300 m
(c)200 m
(d)400 m
15.Work out the coordinates of the reflection of (6, −3) in the y-axis.
(a)(−6, −3)
(b)(6, −3)
(c)(−6, 3)
(d)(6, 3)

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