Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as w ÷ 6.

2.Solve the inequality 2(x − 1) ≤ 8.

3.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

4.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

5.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

6.Work out the value of 2(x + 2) when x = −5

7.Which of these is a factor of 15x + 20?

8.Write down the expression that means the same as p + p + p + q.

9.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

10.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?

11.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

12.A number machine multiplies its input by 5. Work out the output when the input is −1.

13.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

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

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