Algebra worksheet — GCSE Higher

1.Work out the value of 2x² when x = −3

2.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

3.A circle has centre (0, 0) and equation x² + y² = 8. Work out the radius of the circle, giving your answer as a surd in its simplest form.

4.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

5.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

6.Solve 3(2x − 1) = 27

7.Work out the value of (x − 4)/2 + 3 when x = 10

8.A car's journey is represented by a velocity-time graph. The total distance travelled, found from the area under the graph, is 350 metres, and the total time for the journey is 25 seconds. Work out the car's average speed for the whole journey, in m/s.

9.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

10.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

11.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

12.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

13.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.

14.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

15.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.