Algebra worksheet — GCSE Foundation

1.Solve 2x + 7 = x + 13

2.Solve 2(x + 3) = 10

3.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

4.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

5.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

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

7.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

8.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

9.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

10.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

11.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.

12.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

13.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

14.Simplify k + k + k + k + k.

15.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.