Algebra worksheet — GCSE Foundation

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

2.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

3.Work out the value of 3x² − 4x when x = −2.

4.Make a the subject of the formula b = 20 − a.

5.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

6.Write down 0.2x with its coefficient written as a fraction in its simplest form.

7.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

8.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

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

10.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

11.Solve x² + 7x = 0.

12.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.

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.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.

15.Work out the coordinates of the reflection of (6, −3) in the y-axis.