Algebra worksheet — GCSE Foundation

1.Which of these rules generates the sequence 6, 11, 16, 21, …?

2.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

3.Which of these is a term, rather than a whole expression, an equation, or a formula?

4.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

5.Solve 2x + 1 = 9

6.Solve the inequality x + 5 < 12.

7.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

8.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

9.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

10.Solve 5x + 2 = 17.

11.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?

12.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

13.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

14.The point B has coordinates (−2, −2). In which quadrant is B?

15.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.