Algebra worksheet — GCSE Higher

1.The graph of y = f(x) crosses the x-axis at x = −3 and x = 7, and crosses the y-axis at (0, 21). A second graph crosses the x-axis at x = −7 and x = 3, and crosses the y-axis at the same point, (0, 21). The second graph is y = g(x). Which of these could be the equation of g(x)?

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

3.p = 4. Work out the value of 2p³.

4.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.

5.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

6.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.

7.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

8.Solve x² − 2x − 24 = 0.

9.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

10.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

11.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

12.Solve x² − 5x + 6 = 0 by factorising.

13.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).

14.Solve 7x − 5 = 3x + 11

15.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.