Algebra worksheet — GCSE Foundation

1.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

2.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

3.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

4.Make x the subject of the formula y = (x − 4)/5.

5.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

6.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

7.Which expression is equivalent to 4(x − 2) + 10?

8.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.

9.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

10.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

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

12.In which quadrant does the point (−3, 0.5) lie?

13.Solve x² = 81.

14.p = 4. Work out the value of 2p³.

15.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.