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.Work out the value of m² + 3m when m = −2
(a)−10
(b)10
(c)−14
(d)−2
2.A market stall's cost of hiring n tables is modelled by two formulas: Formula A: C = 3(2n + 5); Formula B: C = 6n + 15, where C is in pounds. A stallholder says the two formulas always give the same cost. Work out the cost given by each formula when n = 4, and use your results to decide whether the stallholder is correct.
(a)Formula A gives £39 and Formula B gives £39, but the stallholder is wrong because the two formulas use a different number of terms.
(b)Formula A gives £29 and Formula B gives £39, so the stallholder is wrong.
(c)Formula A gives £39 and Formula B gives £39, but this is only true when n = 4, so the stallholder is wrong.
(d)Formula A gives £39 and Formula B gives £39, and since 3(2n + 5) expands to 6n + 15 for every value of n, the stallholder is correct.
3.A circle has centre (0, 0) and equation x² + y² = 25. Work out the x-coordinates of the two points where the circle crosses the line y = 3.
(a)x = 3 and x = −3
(b)x = 4
(c)x = 5 and x = −5
(d)x = 4 and x = −4
4.A bacteria colony doubles every 4 hours and its size is recorded only every 4 hours. The recorded population 20 hours after the start is 9,600. After how many hours did the recorded population first exceed 1,000?
(a)0
(b)12
(c)20
(d)8
5.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.
(a)(2, −5)
(b)(−2, 5)
(c)(2, 5)
(d)(−2, −5)
6.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)
7.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
8.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.
(a)720
(b)184
(c)176
(d)45
9.Make x the subject of the formula y = 4x − 3.
y = 4x − 3
(a)x = 4(y + 3)
(b)x = y/4 + 3
(c)x = (y − 3)/4
(d)x = (y + 3)/4
10.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.
(a)x = 14, y = −4
(b)x = 7, y = 3
(c)x = 5, y = 5
(d)x = 7, y = 4
11.A distance-time graph is a straight line from (0, 0) to (4, 100), where time is in hours and distance is in kilometres. Work out the gradient of the line.
(a)25
(b)400
(c)0.04
(d)100
12.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.
(a)y = −2x + 7
(b)y = −2x − 5
(c)y = 2x + 7
(d)y = −2x + 1
13.Which of these rules generates the sequence 6, 11, 16, 21, …?
(a)6n
(b)5n − 1
(c)5n + 1
(d)n + 5
14.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?
(a)A formula, relating two quantities
(b)An identity, true for all values of x
(c)An expression, with x terms and numbers
(d)An equation, true for one value of x
15.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.
(a)£50
(b)£120
(c)£60
(d)£40

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