Algebra worksheet — GCSE Foundation

1.A square has sides of length y cm. Write down an expression for the perimeter of the square.

2.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

3.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

4.Simplify 2b − 1 + 2b − 4 + 2b

5.Write down the coefficient of p in the expression 7 − 4p + 9q.

6.Write down the expression that means 5 more than half of n.

7.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.

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

9.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

10.Which expression means 'triple c, then add double d'?

11.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

12.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

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

14.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

15.Solve 5(x + 3) = 40