Algebra worksheet — GCSE Foundation

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

2.Solve x² − 2x − 24 = 0.

3.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

4.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

5.Solve the inequality 3x + 6 ≤ 0.

6.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

7.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

8.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.

9.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

10.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

11.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

12.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

13.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

14.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

15.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.