Algebra worksheet — GCSE Foundation

1.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

2.A straight line has equation y = 5x. Work out the value of y when x = 3.

3.y = 5 − 2x. Work out the value of x when y = 11.

4.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

5.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

6.a = 2 and b = 5. Work out the value of a²b.

7.Work out the value of 3x² − 4x when x = −2.

8.Which of these numbers is a cube number?

9.Solve 3x − 5 = 4.

10.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

11.Expand 2(x + 12)

12.a = 3 and b = 5. Work out the value of a²b.

13.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

14.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

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