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.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.
(a)233 minutes
(b)158 minutes
(c)308 minutes
(d)218 minutes
2.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.
(a)8 m
(b)24 m
(c)16 m
(d)12 m
3.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)
4.The equation x² = 5x − 3 is to be solved using iteration. Work out which of these iterative formulas comes from a correct rearrangement of the equation.
(a)xₙ₊₁ = 5(xₙ² + 3)
(b)xₙ₊₁ = (xₙ² + 3) ÷ 5
(c)xₙ₊₁ = (xₙ + 3) ÷ 5
(d)xₙ₊₁ = (xₙ² − 3) ÷ 5
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.Solve x² + 7x = 0.
(a)x = 0 or x = 7
(b)x = 0 or x = −14
(c)x = 0 or x = −7
(d)x = −7
7.The trapezium rule is used to estimate the area under a curve between x = 2 and x = 6. The curve is concave up (it curves upwards, like the inside of a bowl) throughout this interval. Which statement about the estimate is correct?
(a)Overestimates — trapezium edges lie above the curve.
(b)Underestimates — trapezium edges lie below the curve.
(c)Exact — straight lines model any curve with no error.
(d)Overestimates, because more strips always increase it.
8.Solve the inequality 5 − x ≤ 2.
(a)x ≤ −3
(b)x ≥ −3
(c)x ≥ 3
(d)x ≤ 3
9.Which expression is equivalent to 3(2x − 5) + 4x?
(a)10x + 15
(b)6x − 15
(c)10x − 15
(d)10x − 5
10.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².
(a)2 m/s²
(b)22 m/s²
(c)12 m/s²
(d)72 m/s²
11.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.
(a)22.33
(b)20.67
(c)19
(d)11.8
12.Describe a sequence of two transformations that maps the graph of y = cos x onto the graph of y = cos(x + 90°) − 2.
y = cos(x)
(a)Translate −90° in x, then translate +2 in y.
(b)Translate −90° in x, then translate −2 in y.
(c)Reflect in the x-axis, then translate −90° in x.
(d)Translate +90° in x, then translate −2 in y.
13.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.
(a)An identity, because it is true for every value of x
(b)An identity, because the brackets can be expanded
(c)An equation, because solving it gives x = 3
(d)A formula, because it works out 4x + 12 from x
14.Solve x² + 3x − 10 = 0.
(a)x = 2 or x = 5
(b)x = −2 or x = 5
(c)x = −5 or x = −2
(d)x = 2 or x = −5
15.A train's distance-time graph shows it travelling 100 km at a steady speed in the first 1.5 hours, waiting at a signal for 0.25 hours, then travelling a further 47 km in 0.75 hours. Work out the average speed for the whole journey, correct to 1 decimal place.
(a)65.3 km/h
(b)58.8 km/h
(c)66.7 km/h
(d)64.7 km/h

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