Algebra worksheet — GCSE Foundation

1.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

2.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

3.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

4.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

5.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

6.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

7.Solve the inequality x + 5 < 12.

8.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

9.Which of these numbers is a cube number?

10.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

11.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

12.a = 3 and b = 5. Work out the value of a²b.

13.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.

14.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

15.Which of these equations describes a vertical line?