Algebra worksheet — GCSE Higher

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

2.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

3.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

4.Describe a sequence of two transformations that maps the graph of y = cos x onto the graph of y = cos(x + 90°) − 2.

5.A geometric sequence has first term 4 and common ratio √2. Work out the sum of the first three terms of the sequence, giving your answer in the form a + b√2.

6.A tram sets off from a stop. Its velocity-time graph rises in a straight line from 0 m/s to 12 m/s over the first 8 seconds, then stays constant at 12 m/s for a further 10 seconds. Work out the total distance the tram travels in these 18 seconds, using the area under the graph.

7.f(x) = (x + 1)/2. Find f⁻¹(x).

8.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

9.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

10.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

11.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

12.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

13.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

14.Which expression means 'add 3 to n, then multiply the result by 4'?

15.Solve the simultaneous equations x + y = 1 and 2x + y = 5.