Algebra worksheet — GCSE Foundation

1.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

2.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

3.Solve the inequality x − 10 < −3.

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.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

6.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

7.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

8.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

9.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.

10.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

11.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

12.Work out the y-intercept of the graph of y = x² + 3x − 10.

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

14.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

15.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.