Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

2.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

3.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

4.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

5.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

6.Which of these statements is an equation with exactly one solution?

7.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

8.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

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

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

11.Which of these points lies in the first quadrant?

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

13.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

14.Work out the value of 2x² when x = −3

15.Write down the first four terms of the sequence with nth term 6n − 5.