Algebra worksheet — GCSE Higher

1.The iterative formula xₙ₊₁ = 12 ÷ (xₙ + 2) is used repeatedly, starting from x₀ = 1. Work out the value that xₙ approaches, correct to 2 decimal places.

2.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

3.When a number is added to its square the result is 30. Work out the possible values of the number.

4.The point (20, 21) lies on the circle x² + y² = 841, which has centre O(0, 0). The tangent to the circle at (20, 21) crosses the x-axis at P and the y-axis at Q. Work out the area of triangle OPQ, correct to 1 decimal place.

5.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

6.Which expression means 'triple c, then add double d'?

7.Solve 2x² − 32 = 0.

8.The nth term of a sequence is n² − 2n + 5. Work out the 10th term.

9.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

10.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

11.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?

12.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

13.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

14.A distance-time graph is a straight line from (0, 0) to (4, 100), where time is in hours and distance is in kilometres. Work out the gradient of the line.

15.Solve the inequality x² − 5x + 6 < 0.