Printable · GCSE Foundation · ages 14-16

Algebra worksheet — GCSE Foundation

Fifteen questions across the algebra statements at Foundation 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 Foundation

Maths · GCSE Foundation · Algebra · 15 questions

MathsUKwww.geekhero.co.uk

1.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.
(a)88 km/h
(b)180 km/h
(c)45 km/h
(d)92 km/h
2.Work out the gradient of the straight line with equation 3y = 12 − 6x.
(a)2
(b)4
(c)−2
(d)−6
3.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.
(a)8
(b)32
(c)5
(d)13
4.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.
(a)2
(b)5
(c)9
(d)−5
5.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
6.a = 2 and b = 5. Work out the value of ab².
(a)50
(b)10
(c)20
(d)100
7.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
8.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.
(a)3
(b)40
(c)−3
(d)13
9.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.
(a)4
(b)26
(c)6
(d)2
10.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.
(a)£165
(b)£105
(c)£75
(d)£90
11.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.
(a)5p + 7q
(b)5p + 6q
(c)2p + 7q
(d)12pq
12.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.
(a)27
(b)22.5
(c)18
(d)36
13.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?
(a)Isla is wrong, because 5 − 1 = 4
(b)Isla is wrong, because 5 × 1 = 5
(c)Isla is right, because the machine adds 1 to its output
(d)Isla is right, because 5 + 1 = 6
14.Simplify x + x + 4
(a)x² + 4
(b)6x
(c)x + 4
(d)2x + 4
15.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.
(a)6n + 4
(b)4n + 6
(c)4n − 2
(d)4n + 2

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