Algebra worksheet — GCSE Foundation

1.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

2.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

3.y = x + 4. Work out the value of y when x = 3.

4.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.

5.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

6.Solve the inequality 3x + 6 ≤ 0.

7.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

8.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

9.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

10.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

11.Which expression is equivalent to 7x − 3(2x − 6)?

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.Work out the gradient of the straight line with equation y = (2x/5) − 3.

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.A person's body mass index is given by the formula B = m ÷ h², where m is the mass in kg and h is the height in metres. Work out B, to 1 decimal place, when m = 68 and h = 1.6.