Algebra worksheet — GCSE Foundation

1.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

2.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

3.Make x the subject of the formula y = (x − 4)/5.

4.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

5.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.

6.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

7.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

9.Work out the gradient of the straight line with equation 3y = 12 − 6x.

10.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

11.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

12.Expand 4(2x − 3).

13.Work out the value of 5m² + 3m when m = −2.4

14.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

15.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.