Algebra worksheet — GCSE Higher

1.Solve 4(x − 3) = 2x + 6.

2.The numbers x and y satisfy x + y = 10 and xy = 21. Work out the pair of values.

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

4.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

5.A car's velocity–time graph is a straight line from (0 s, 4 m/s) rising to (6 s, V m/s), followed by a straight line falling from (6 s, V m/s) to (9 s, 0 m/s). The gradient of the second line is −8 m/s². Work out the total distance travelled between t = 0 and t = 9 seconds.

6.Write down the expression that means the same as m² × m × 3.

7.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

8.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

9.A market trader builds a display of oranges in a rectangular block. The block is n oranges wide and 4 oranges longer than it is wide. The number of oranges needed is 5 when n = 1, 12 when n = 2, 21 when n = 3, 32 when n = 4, and 45 when n = 5. Work out an expression, in terms of n, for the number of oranges needed for a display of width n.

10.Work out the gradient of the straight line with equation 3y = 12 − 6x.

11.The 2nd term of a geometric sequence is 6 and the 4th term is 24. Given that all the terms of the sequence are positive, work out the common ratio.

12.A circle has centre (0, 0) and passes through the point (12, 35). Work out the equation of the circle.

13.Which of these is a formula, rather than an expression, an equation, or an identity?

14.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

15.Solve 3x + 14 = 8x − 6