Algebra worksheet — GCSE Foundation

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

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

3.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

4.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.

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

6.Write down the gradient of the line with equation y = 6 + 4x.

7.x = 5. Work out the value of 3x² − 4.

8.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

9.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

10.Solve x² − 2x − 24 = 0.

11.Work out the value of 5y + 9 when y = 0

12.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

13.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

14.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.

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