Algebra worksheet — GCSE Foundation

1.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

2.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.

3.Work out the gradient of the straight line with equation 2x + y = 8.

4.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

5.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

6.Write down the expression that means the same as w ÷ 6.

7.A number machine adds 6 to its input. Work out the output when the input is −4.

8.Work out the value of 2(x + 2) when x = −5

9.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

10.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

11.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

12.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

13.Work out the y-intercept of the graph of y = x² + 3x − 10.

14.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

15.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.