Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 3(2x − 5) + 4x?

2.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

3.Work out the coordinates of the reflection of (6, −3) in the y-axis.

4.Solve x² − 2x − 24 = 0.

5.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

6.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.

7.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

8.Solve x² = 81.

9.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

10.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.

11.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?

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

13.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

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

15.Solve x² − 6x = 0.