Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

2.Solve (2x + 1)/3 = 5

3.Expand 2(x − 13)

4.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

5.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

6.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

7.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.

8.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

9.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

10.Solve 5x − 9 = 16

11.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

12.Solve 3x − 5 = 4.

13.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.

14.Factorise x² − 64.

15.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.