Algebra worksheet — GCSE Foundation

1.Solve x² − 2x − 24 = 0.

2.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

3.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

4.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

5.Work out the value of 3a − 2b when a = 5 and b = 4

6.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

7.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

8.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.

9.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

10.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

11.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

12.Make a the subject of the formula b = 20 − a.

13.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

14.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

15.A point lies on the y-axis. What can be said about the x-coordinate of that point?