Algebra worksheet — GCSE Foundation

1.Which of these equations describes a vertical line?

2.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

3.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

4.a = 3 and b = 5. Work out the value of a²b.

5.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

6.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.

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

8.Solve the inequality 9 − 2x ≥ 1.

9.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

10.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

11.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

12.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.

13.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

14.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

15.Write down the expression that means the same as 3 × y × y.