Algebra worksheet — GCSE Higher

1.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

2.The curve y = x² − 1 and the line y = 3x − 3 meet at two points. Work out the x-coordinates of those two points.

3.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

4.Work out the integer values of x that satisfy x² − 2x − 8 ≤ 0.

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

6.The graph of y = sin x is reflected in the x-axis to give the graph of y = g(x). Work out the value of g(90), where x is measured in degrees.

7.The nth term of a sequence is 3n² + 2n − 1. Work out the 10th term.

8.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?

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.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.

11.How many turning points does the graph of y = x² − 7x + 10 have?

12.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

13.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

14.Solve 3(2x − 1) = 27

15.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.