Algebra worksheet — GCSE Higher

1.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

2.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

3.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

4.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

5.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

6.The point (3, 4) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the gradient of the tangent to the circle at (3, 4).

7.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

8.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.

9.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

10.f(x) = (x + 1)/2. Find f⁻¹(x).

11.A student uses the iterative formula xₙ₊₁ = √(7xₙ + 3) to find an approximate solution of an equation. Work out which equation this iterative formula solves.

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

13.Which of these equations represents the graph of y = 2ˣ translated by 3 units in the positive y-direction?

14.The graph of y = f(x) has a minimum turning point at (2, −3). The graph of y = −f(x) + a has a maximum turning point at (2, 9). Work out the value of a.

15.The equation x² − 4x + k = 0 has two different real solutions. Work out the range of values of k.