Algebra worksheet — GCSE Foundation

1.Solve x − 4 = −9

2.Solve 5x² − 15x = 0.

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

4.Which of these equations gives a straight-line graph when plotted?

5.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

6.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

7.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

8.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

9.Solve the inequality x − 10 < −3.

10.Write down the gradient of the line with equation y = 7x − 2.

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

12.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

13.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

14.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

15.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.