Algebra worksheet — GCSE Foundation

1.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

2.Solve x/4 + 1 = 3

3.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

4.Simplify p + p + p.

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

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

7.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

8.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

9.A point lies on the y-axis. What can be said about the x-coordinate of that point?

10.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.

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

12.Expand and simplify 2(a + 6) − 2(a − 7)

13.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

14.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

15.Which expression is equivalent to 2(x + 6)?