Algebra worksheet — GCSE Higher

1.Which of these is an identity?

2.The graph of y = f(x) crosses the x-axis at x = −3 and x = 7, and crosses the y-axis at (0, 21). A second graph crosses the x-axis at x = −7 and x = 3, and crosses the y-axis at the same point, (0, 21). The second graph is y = g(x). Which of these could be the equation of g(x)?

3.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

4.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

5.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

6.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.

7.A car's velocity–time graph is a straight line from (0 s, 4 m/s) rising to (6 s, V m/s), followed by a straight line falling from (6 s, V m/s) to (9 s, 0 m/s). The gradient of the second line is −8 m/s². Work out the total distance travelled between t = 0 and t = 9 seconds.

8.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

9.Work out the maximum value of y = sin x, and the smallest positive value of x, in degrees, at which it occurs.

10.Expand and simplify 2(a + 6) − 2(a − 7)

11.Which of these equations is equivalent to 5x − 2 = 3x + 8?

12.The nth term of a sequence is 3n² + 2n − 1. Work out the 10th term.

13.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

14.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.

15.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.