Algebra worksheet — GCSE Higher

1.Which expression is equivalent to 0.5(4x + 6) − x?

2.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

3.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

4.Ben is asked to find the inverse of f(x) = 4 − 3x. He writes f⁻¹(x) = (4 − x)/3. Which statement about Ben's answer is correct?

5.A circle has centre O(0, 0) and equation x² + y² = 169. The point Q has coordinates (10, 11). Work out which of these gives the correct position of Q together with correct working.

6.Which of these statements is an identity?

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

8.Which expression is equivalent to 6x − (2x − 5)?

9.Work out the value of 2x² when x = −3

10.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

11.The first five terms of a sequence are 7, 9, 13, 19, 27. By finding the second difference, work out the coefficient of n² in the nth term.

12.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

13.The function f(x) = x² for all real values of x has no inverse function, but g(x) = x² for x ≥ 0 does have one. Which statement correctly explains this?

14.Solve 4(x − 3) = 2x + 6.

15.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.