Algebra worksheet — GCSE Foundation

1.Work out the gradient of the straight line with equation y = (2x/5) − 3.

2.Work out the value of 5m² + 3m when m = −2.4

3.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?

4.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.

5.Which expression means the same as 3 × a × b?

6.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

7.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

8.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.

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

10.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

11.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.

12.Write down the first four terms of the sequence with nth term 6n − 5.

13.Solve 2x − 2 = 2

14.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

15.Factorise x² − 3x − 10.