Algebra worksheet — GCSE Higher

1.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

2.Factorise 6x² − 7x − 3.

3.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

4.Make x the subject of the formula y = 2x − 9.

5.(2x + 3)(x + a) ≡ 2x² + 11x + 12 is an identity. Work out the value of a.

6.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

7.The line y = 2x + 7 and the circle x² + y² = 4 are given. By finding the discriminant of the resulting quadratic, without solving it fully, work out how many points the line and the circle intersect at.

8.Which expression is equivalent to 7x − 3(2x − 6)?

9.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

10.The first five terms of a quadratic sequence are −1, 4, 13, 26, 43. Work out an expression, in terms of n, for the nth term.

11.The graph of y = f(x) has x-intercepts at x = −2 and x = 6 and crosses the y-axis at (0, −12). Work out the x-intercepts and the y-intercept of y = −f(x).

12.Which expression means 'y squared, multiplied by 3'?

13.A circle has centre (0, 0) and equation x² + y² = 8. Work out the radius of the circle, giving your answer as a surd in its simplest form.

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

15.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.