Algebra worksheet — GCSE Foundation

1.Solve 3(2x − 1) = 27

2.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.

3.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

4.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

5.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

6.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

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

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

9.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

10.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

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 sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

13.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

14.In which quadrant does the point (−3, 0.5) lie?

15.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.