Algebra worksheet — GCSE Foundation

1.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

2.Which of these is a term, rather than a whole expression, an equation, or a formula?

3.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.

4.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

5.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

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

7.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

8.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

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

10.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

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

12.Which expression means 'y squared, multiplied by 3'?

13.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

14.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

15.Write down the coefficient of p in the expression 7 − 4p + 9q.