Algebra worksheet — GCSE Foundation

1.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

2.Solve the inequality 2(x − 1) ≤ 8.

3.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

4.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

5.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

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

7.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

8.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

9.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

10.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

11.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

12.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

13.Work out the value of m² + 3m when m = −2

14.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

15.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.