Algebra worksheet — GCSE Higher

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

2.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.

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

4.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

6.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

7.Work out the period of the graph of y = cos x, in degrees.

8.The equation x² − 4x + k = 0 has two different real solutions. Work out the range of values of k.

9.The tangent to a curve at the point where x = 4 passes through the points (2, 5) and (6, 21). Use these two points to estimate the gradient of the curve at x = 4.

10.Work out the value of n² − n when n = −3

11.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

12.A cyclist's speed-time graph is described as follows: speed increases steadily from 0 m/s to 8 m/s over the first 4 seconds, stays constant at 8 m/s for the next 6 seconds, then decreases steadily to 0 m/s over the final 2 seconds. Work out the total distance travelled.

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

14.Solve x² + 7x = 0.

15.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.