Algebra worksheet — GCSE Foundation

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

2.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

3.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

4.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

5.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

6.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

7.Make a the subject of the formula b = 20 − a.

8.Solve x² − 100 = 0.

9.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

10.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

11.Work out the value of 3b − 4 when b = 6

12.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

13.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

14.Work out the distance of the point (−6, 4) from the x-axis.

15.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.