Algebra worksheet — GCSE Higher

1.The graph of y = sin x is transformed onto the graph of y = sin x + 1. Which statement correctly describes the transformation and the new range of the graph?

2.Solve 3(2x − 1) = 27

3.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

4.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

5.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

6.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

7.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?

8.Solve (2x + 1)/3 = 5

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

10.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

11.Which expression means 'add 3 to n, then multiply the result by 4'?

12.A candidate solves the inequality x² > 9 and writes: "x² > 9, so x > 3." Which of these is a correct comment on the candidate's work?

13.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

14.Which of these rules generates the sequence 6, 11, 16, 21, …?

15.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.