Algebra worksheet — GCSE Foundation

1.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

2.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

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

4.A vertical line passes through the point (4, 7). Write down the equation of this line.

5.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

6.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

7.Solve x − 4 = −9

8.Make b the subject of the formula a = 5b.

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

10.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.

11.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

12.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

13.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.

14.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

15.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.