Algebra worksheet — GCSE Higher

1.Expand and simplify (x + 1)(x + 2)(x + 3).

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

3.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.

4.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.

5.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

6.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

7.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

8.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

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

10.The nth term of a geometric sequence is given by aₙ = 3 × 2ⁿ⁻¹. Work out the position of the first term that is greater than 1,000.

11.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

12.A van's value depreciates by 18% each year. After 2 years it is worth £5,379.20. Work out its value when it was new, correct to the nearest pound.

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

14.How many turning points does the graph of y = x² − 7x + 10 have?

15.Work out the value of 5m² + 3m when m = −2.4