Algebra worksheet — GCSE Foundation

1.Work out the value of m² + 3m when m = −2

2.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.

3.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

4.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.

5.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

6.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

7.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

8.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.

9.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

10.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

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

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

13.A straight line has equation y = 5x. Work out the value of y when x = 3.

14.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

15.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.