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 · Non-calculator · 15 questions

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1.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.
(a)3n − 1
(b)2n + 3
(c)3n − 2
(d)3n + 2
2.Which expression means 'y squared, multiplied by 3'?
(a)3y²
(b)y³
(c)(3y)²
(d)3 + y²
3.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.
(a)4.6
(b)7.4
(c)90
(d)6
4.A number machine adds 6 to its input. Work out the output when the input is −4.
(a)10
(b)−10
(c)2
(d)−24
5.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.
(a)16 km
(b)32 km
(c)23 km
(d)24 km
6.Solve x² − 2x − 24 = 0.
(a)x = 6 or x = −4
(b)x = −6 or x = 4
(c)x = −8 or x = 3
(d)x = −6 or x = −4
7.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?
(a)y = 2x + 1
(b)y = 1/x
(c)y = x²
(d)y = x³
8.The point A is at (5, −3). In which quadrant does A lie?
(a)the first quadrant
(b)the third quadrant
(c)the fourth quadrant
(d)the second quadrant
9.Solve the inequality x − 10 < −3.
(a)x < 13
(b)x > 7
(c)x < −13
(d)x < 7
10.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.
(a)8
(b)64
(c)16
(d)81
11.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.
y = x² − 5x + 6
(a)x = −1 and x = −6
(b)x = 2 and x = −3
(c)x = 2 and x = 3
(d)x = −2 and x = −3
12.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.
(a)y = 200x − 8
(b)y = −8x − 200
(c)y = 200 − 8x
(d)y = 8x + 200
13.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.
(a)4x² + 2x − 20
(b)6x + 6
(c)6x + 14
(d)3x + 3
14.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.
(a)There is not enough information
(b)They are equally steep
(c)Line D
(d)Line C
15.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.
(a)24
(b)18
(c)15
(d)12

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