Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

2.Solve the inequality x − 10 < −3.

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

4.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

5.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

6.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

7.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

8.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

9.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

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

11.Simplify 5a/6 − a/3

12.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

13.Solve the inequality 3x + 6 ≤ 0.

14.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

15.Solve 2(x + 3) = 10