Algebra worksheet — GCSE Foundation

1.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

2.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

3.Which expression is equivalent to 3(2x − 5) + 4x?

4.Write down the gradient of the line with equation y = −x + 3.

5.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

6.Work out the value of 2x² when x = −3

7.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

8.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

9.Make c the subject of the formula k = 6c.

10.y = 5x − 1. Work out the value of y when x = 3.

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

12.Solve 4x − (2x − 6) = 18

13.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

14.Solve 3(2x − 1) = 27

15.Which expression is equivalent to 7x − 3(2x − 6)?