Algebra worksheet — GCSE Foundation

1.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

2.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.

3.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.

4.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

5.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

6.Solve 2x + 7 = x + 13

7.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

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

9.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

10.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

11.Which expression is equivalent to 0.5(4x + 6) − x?

12.Solve x/4 + 1 = 3

13.Solve 2(x + 3) = 10

14.Write down the gradient of the line with equation y = 6 + 4x.

15.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.