Algebra worksheet — GCSE Higher

1.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

2.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

3.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.

4.The diagram shows the graph of a function. Which equation could it represent?

5.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

6.The curve y = 2x² − 12x + 7 has a minimum point. By completing the square, find the value of x at which the minimum occurs.

7.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

8.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

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

10.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

11.Work out the period of the graph of y = cos x, in degrees.

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

13.Using the table of values of f(x) (x = 0, 1, 2, 3 gives f(x) = 5, 8, 4, 1), work out the value of −f(x) when x = 1.

14.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

15.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.