Algebra worksheet — GCSE Higher

1.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

2.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

3.Factorise x² − 64.

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

5.f(x) = (x + 1)/2. Find f⁻¹(x).

6.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

7.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

8.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

9.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

10.Simplify (5x² + 3x − 2) − (2x² − x + 5)

11.The solution set of a quadratic inequality is {x : x ≤ −3} ∪ {x : x ≥ 5}. Which of these inequalities has this solution set?

12.A student attempts to prove that the sum of any three consecutive integers is a multiple of 3. Line 1: Let the three consecutive integers be n, n + 1 and n + 2. Line 2: Their sum is n + (n + 1) + (n + 2) = 3n + 2. Line 3: 3n + 2 leaves a remainder of 2 when divided by 3, so it is not a multiple of 3. Line 4: So the sum of three consecutive integers is not always a multiple of 3. Which line contains the FIRST error?

13.f(x) = 3x − 2. Find f⁻¹(x).

14.Solve 5(x + 3) = 40

15.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.