Algebra worksheet — GCSE Foundation

1.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

2.Simplify 2a + 3b − a + 2b − b

3.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

4.Solve x² − 5x + 6 = 0 by factorising.

5.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

6.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

7.Solve 2x + 7 = x + 13

8.A square has sides of length y cm. Write down an expression for the perimeter of the square.

9.Which expression is equivalent to 4(x − 2) + 10?

10.The point A is at (5, −3). In which quadrant does A lie?

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

12.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.

13.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

14.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.

15.Work out the y-intercept of the graph of y = x² + 3x − 10.