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 · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.
(a)9.5
(b)8
(c)17.5
(d)4.75
2.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.
(a)40
(b)11
(c)20
(d)80
3.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.
(a)x = −8
(b)x = 5
(c)x = 5 or x = −8
(d)x = 4
4.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
5.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.
(a)x < 2 or x > 6
(b)2 < x < 6
(c)−6 < x < −2
(d)2 ≤ x ≤ 6
6.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
7.The graph of y = 60 × (0.5)ˣ is sketched for x ≥ 0. Which statement correctly describes what happens to the curve as x increases?
(a)It gets closer to zero but never actually reaches it.
(b)It decreases steadily and reaches zero when x = 60.
(c)It levels off at y = 0.5 as x increases.
(d)It decreases at first, then becomes negative for large x.
8.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?
(a)Yes — the t² coefficient is negative, giving an n-shape.
(b)No — it is U-shaped, since height starts by increasing.
(c)No — the shape comes from the story, not the coefficient.
(d)Yes, but only because the rocket eventually lands.
9.A circular pond has equation x² + y² = 20, with lengths in metres from the centre of the garden. A straight path runs along the line y = 2x, entering the pond and leaving it again. Work out the coordinates of the two points where the path meets the edge of the pond.
y = 2x
(a)(2, 4)
(b)(2, 4) and (−2, −4)
(c)(2, 1) and (−2, −1)
(d)(2, −4) and (−2, 4)
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.By completing the square, find the turning point of the curve y = 3x² + 12x + 7.
y = 3x² + 12x + 7
(a)x = −2, y = 5
(b)x = −4, y = −41
(c)x = 2, y = −5
(d)x = −2, y = −5
12.A tap fills a tank at a varying rate. A graph shows the rate of flow, in litres per minute, against time, in minutes. What does the area under this graph represent?
(a)The rate at which the flow rate changes, in litres/min².
(b)The total volume of water, in litres, that has flowed in.
(c)The average rate of flow, in litres per minute.
(d)The total time taken to fill the tank, in minutes.
13.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.
(a)12 km/h
(b)8 km/h
(c)6 km/h
(d)4 km/h
14.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.
(a)s = t / d
(b)s = d / t
(c)s = d − t
(d)s = dt
15.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.
(a)£13.20
(b)£15.50
(c)£34.20
(d)£16.70

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