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.x = 5. Work out the value of 3x² − 4.

3.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

4.p = 4. Work out the value of 2p³.

5.Which of these equations gives a straight-line graph when plotted?

6.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

7.A square tile has an area of 144 cm². Work out the side length of the tile.

8.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

9.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

10.Solve the inequality 3x − 1 ≤ 11.

11.Work out the gradient of the straight line with equation 3y = 12 − 6x.

12.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

13.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

14.Work out the distance of the point (−6, 4) from the x-axis.

15.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.