Algebra worksheet — GCSE Higher

1.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

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

3.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.

4.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

5.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

6.Solve x² − x − 12 = 0.

7.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

8.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

9.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.

10.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

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

12.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?

13.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.

14.Which of these quadratic graphs does NOT cross the x-axis at all?

15.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.