Algebra worksheet — GCSE Higher

1.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.

2.A student attempts to prove that the product of two consecutive integers is always even: (i) Let the two consecutive integers be n and n + 1. (ii) Since n(n + 1) is even, one of n and n + 1 must be an even number. (iii) Therefore, n(n + 1) is even. At which statement does the proof first assume the very fact it is trying to prove?

3.Make x the subject of the formula y = x/2 − 5.

4.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.

5.A curve has equation y = x² − 9. Which statement about its graph is correct?

6.The graph of y = f(x) has a minimum turning point at (3, −5), crosses the x-axis at x = 1, and crosses the y-axis at (0, −2). Exactly one of these statements about the graph of y = −f(x + 2) is true. Which statement is true?

7.Solve 4x² − 9 = 0.

8.f(x) = 3x − 2. Find f⁻¹(x).

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

10.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?

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

12.Which of these statements is an equation with exactly one solution?

13.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

14.Work out the gradient of the straight line with equation 3y = 12 − 6x.

15.Solve the inequality x² − 5x + 6 < 0.