Algebra worksheet — GCSE Foundation

1.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

2.y = x + 4. Work out the value of y when x = 3.

3.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.

4.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

5.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

6.Solve 7x − 5 = 3x + 11

7.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

8.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

9.Make p the subject of the formula n = p/3.

10.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

11.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

12.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

13.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

14.The point B has coordinates (−2, −2). In which quadrant is B?

15.Work out the value of 4p² − 3 when p = 2.5