Algebra worksheet — GCSE Foundation

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

2.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

3.Work out the value of m² + 3m when m = −2

4.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

5.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

6.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

7.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

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

9.Which of these is a factor of 15x + 20?

10.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

11.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

12.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

13.Make x the subject of the formula y = 4(x − 6).

14.n = 3. Work out the value of (2n)².

15.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.