Algebra worksheet — GCSE Foundation

1.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

2.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

3.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

4.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.

5.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

6.Which expression is equivalent to 6x − (2x − 5)?

7.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

8.Factorise x² − 64.

9.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

10.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

11.Which expression is equivalent to 3(2x − 5) + 4x?

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

13.Write down the expression that means the same as 3 × y × y.

14.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

15.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.