Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

2.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.

3.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

4.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

5.Solve x − 4 = −9

6.Which of these equations gives a straight-line graph when plotted?

7.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

8.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

9.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.

10.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

11.Work out the value of 5y + 9 when y = 0

12.Work out the value of (x − 4)/2 + 3 when x = 10

13.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

14.A number machine multiplies its input by 3. The output is 15. Work out the input.

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