Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

2.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.

3.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.

4.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

5.Work out the value of 3b − 4 when b = 6

6.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

7.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

8.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

9.Solve 2x + 7 = x + 13

10.Which of these values of x is a solution of x² + 2x − 15 = 0?

11.Which of these is an expression?

12.Write down the first four terms of the sequence with nth term 6n − 5.

13.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

14.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.

15.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.