Algebra worksheet — GCSE Foundation

1.Solve x² + 7x = 0.

2.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.

3.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

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

5.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

6.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.

7.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.

8.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

9.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

10.Factorise fully 5x + 5y − 5

11.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

12.Which of these statements is an equation with exactly one solution?

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

14.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

15.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.