Algebra worksheet — GCSE Higher

1.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

2.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

3.Find the common ratio of the geometric sequence 5, 5√2, 10, 10√2, ... Give your answer in surd form.

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

5.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

6.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

7.The nth term of a sequence is 3n² + 2n − 1. Work out the 10th term.

8.Solve the inequality 3x + 6 ≤ 0.

9.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

10.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.

11.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

12.Simplify 5a/6 − a/3

13.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.

14.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

15.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.