Algebra worksheet — GCSE Foundation

1.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

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

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

4.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

5.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

6.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

7.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

8.Factorise fully 5x + 5y − 5

9.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.

11.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

12.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

13.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

14.A square tile has an area of 144 cm². Work out the side length of the tile.

15.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.