Algebra worksheet — GCSE Higher

1.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.

2.Solve the inequality 2(3x − 1) ≥ 4x + 8.

3.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

4.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

6.A geometric sequence has first term 4 and common ratio √2. Work out the sum of the first three terms of the sequence, giving your answer in the form a + b√2.

7.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

8.A Fibonacci-type sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₁ = 5 and a₃ = 17, work out a₂.

9.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

10.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

11.n = 3. Work out the value of (2n)².

12.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

13.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

14.Solve 2x² − 32 = 0.

15.Solve the simultaneous equations y = 2x − 1 and y = x² − x − 1, giving both pairs of solutions.