Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

2.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

3.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.

4.x = 5. Work out the value of 3x² − 4.

5.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

6.Which expression is equivalent to 5x − (x + 3)?

7.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

8.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

9.a = 3 and b = 5. Work out the value of a²b.

10.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

11.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

12.Work out the value of 3n − 2 when n = 1

13.Solve 4x + 3 = 19

14.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

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