Algebra worksheet — GCSE Foundation

1.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

2.Make x the subject of the formula y = x + 7.

3.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

4.Solve the inequality 3x − 1 ≤ 11.

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

6.A number machine multiplies its input by 3. The output is 15. Work out the input.

7.Which expression is equivalent to 0.5(4x + 6) − x?

8.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

9.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

10.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.

11.Solve the inequality 9 − 2x ≥ 1.

12.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

13.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

14.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

15.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.