Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

2.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

3.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

4.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

5.y = 3x − 2. Work out the value of y when x = 4.

6.Solve 5x² − 15x = 0.

7.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

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

9.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

10.Make x the subject of the formula y = 5x + 3.

11.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

12.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

13.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

14.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

15.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.