Algebra worksheet — GCSE Foundation

1.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

2.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

3.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

4.Solve x² + 7x = 0.

5.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

6.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

7.Which expression is equivalent to 7x − 3(2x − 6)?

8.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.

9.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

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

11.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

12.Make x the subject of the formula y = 4x − 3.

13.Write down 0.2x with its coefficient written as a fraction in its simplest form.

14.Which of these is an identity?

15.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.