Algebra worksheet — GCSE Foundation

1.How many turning points does the graph of y = x² − 7x + 10 have?

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

3.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

4.Solve 3x − 1 = 8

5.Which expression means the same as 3 × a × b?

6.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.

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

8.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

9.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

10.Solve (2x + 1)/3 = 5

11.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

12.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

13.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

14.Which of these is a factor of 15x + 20?

15.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.