Algebra worksheet — GCSE Foundation

1.Which expression means 'add 3 to n, then multiply the result by 4'?

2.Which expression is equivalent to 0.5(4x + 6) − x?

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 number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

5.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

6.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

7.A number machine adds 5 to its input. Work out the output when the input is 0.

8.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

9.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

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

11.a = 2 and b = 5. Work out the value of ab².

12.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

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

14.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.

15.Write down the gradient of the line with equation y = −x + 3.