Algebra worksheet — GCSE Foundation

1.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

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

3.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

4.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

5.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

6.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

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

8.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

9.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

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

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

12.Work out the value of 5y + 9 when y = 0

13.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

14.Work out the value of 3n − 2 when n = 1

15.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.