Algebra worksheet — GCSE Foundation

1.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

2.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

3.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

4.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

5.Make b the subject of the formula a = 5b.

6.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

7.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

8.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

9.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

10.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

11.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

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

14.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

15.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?