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.Solve the inequality 9 − 2x ≥ 1.
(a)x ≤ 5
(b)x ≥ 4
(c)x ≤ 4
(d)x ≤ −4
2.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.
(a)28
(b)35
(c)37
(d)39
3.Expand and simplify (x + 1)(x + 2)(x + 3).
(a)x³ + 6x² + 11x + 5
(b)x³ + 6x² + 6x + 6
(c)x³ + 5x² + 11x + 6
(d)x³ + 6x² + 11x + 6
4.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.
(a)10
(b)−6
(c)4
(d)−2
5.A circle has centre (0, 0) and equation x² + y² = 50. Work out the radius of the circle, giving your answer as a surd in its simplest form.
(a)50
(b)25
(c)25√2
(d)5√2
6.Work out the gradient of the straight line with equation 3y = 12 − 6x.
(a)2
(b)4
(c)−2
(d)−6
7.A circle has centre (0, 0) and equation x² + y² = 36. Work out the coordinates of the two points where the circle crosses the y-axis.
(a)(0, 36) and (0, −36)
(b)(0, 6) and (0, −6)
(c)(0, 18) and (0, −18)
(d)(6, 0) and (−6, 0)
8.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
9.A cyclist's velocity increases from 3 m/s to 11 m/s over 5 seconds, at a constant rate. Work out the cyclist's acceleration, in m/s².
(a)0.625 m/s²
(b)1.6 m/s²
(c)8 m/s²
(d)2.2 m/s²
10.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
11.A company's weekly profit, in £, is modelled by y = f(x), where x is the number of weeks since launch. The graph of y = f(x) has a maximum at (10, 45000). A rival company uses the same marketing strategy but starts trading 6 weeks later and has fixed costs £8000 higher every week, so its profit is modelled by y = f(x − 6) − 8000. In which week does the rival's maximum weekly profit occur, and what is it?
(a)Week 16, £53,000
(b)Week 4, £37,000
(c)Week 16, £37,000
(d)Week 4, £53,000
12.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.
(a)7
(b)8
(c)6
(d)9
13.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?
y = 2x − 5
(a)Yes, but step 2 should give x = 2(y + 5)
(b)No; it should be x = (y − 5)/2
(c)Yes; x = (y + 5)/2 is right
(d)No; it should be x = y/2 + 5
14.Work out the value of a² − 2b when a = −3 and b = 4.
(a)1
(b)−17
(c)−11
(d)17
15.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
(a)2
(b)−18
(c)−6
(d)−2

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