Algebra worksheet — GCSE Foundation

1.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

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

3.Simplify p + p + p.

4.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

5.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

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

7.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

8.Which expression is equivalent to 4(x − 2) + 10?

9.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

10.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

11.Expand and simplify (x − 3)²

12.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

13.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

14.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

15.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.