Algebra worksheet — GCSE Foundation

1.Solve the inequality 5 − x ≤ 2.

2.Solve x² − x − 12 = 0.

3.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

4.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

5.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

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

7.Solve x − 4 = −9

8.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

9.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.

10.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

11.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

12.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

13.Work out the value of 2x² when x = −3

14.Work out the value of 4p² − 3 when p = 2.5

15.Write down the expression that means the same as w ÷ 6.