Algebra worksheet — GCSE Foundation

1.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

2.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

3.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

4.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

5.Make m the subject of the formula w = m − 8.

6.Make x the subject of the formula y = x/2 − 5.

7.Solve (3x + 2)/5 = (x + 4)/3

8.Which of these is an equation, rather than an expression, a formula or an identity?

9.Solve x² − x − 12 = 0.

10.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

11.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

12.Which expression means the same as a × a × a?

13.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

14.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

15.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.