Algebra worksheet — GCSE Foundation

1.The point B has coordinates (−2, −2). In which quadrant is B?

2.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.

3.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

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

5.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.

6.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?

7.n = 3. Work out the value of (2n)².

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

9.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

10.Make m the subject of the formula w = m − 8.

11.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.

12.Solve 3x − 5 = 4.

13.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

14.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

15.Which of these equations describes a vertical line?