Algebra worksheet — GCSE Foundation

1.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

2.Make x the subject of the formula y = 3(x + 2).

3.a = 2 and b = 5. Work out the value of a²b.

4.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

5.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

6.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

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

8.Factorise fully 5x + 5y − 5

9.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

10.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

11.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

12.Solve 2x − 2 = 2

13.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

14.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

15.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.