Algebra worksheet — GCSE Foundation

1.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

2.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

3.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

4.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

5.A straight line has equation y = 5x. Work out the value of y when x = 3.

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

7.Solve 2x + 1 = 9

8.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

9.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

10.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

11.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.

12.A square has sides of length y cm. Write down an expression for the perimeter of the square.

13.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

14.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

15.x = 5. Work out the value of 3x² − 4.