Algebra worksheet — GCSE Foundation

1.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

2.Work out the value of 3a − 2b when a = 5 and b = 4

3.Make x the subject of the formula y = 2x − 9.

4.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?

5.The diagram shows the graph of a quadratic function. Which equation could it represent?

6.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

7.Which of these equations describes a vertical line?

8.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

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.

10.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

11.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

12.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

13.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

14.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

15.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.