Algebra worksheet — GCSE Foundation

1.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

2.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

3.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.

4.Make x the subject of the formula y = 4x − 3.

5.A square tile has an area of 144 cm². Work out the side length of the tile.

6.Which expression is equivalent to 4(x − 2) + 10?

7.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

8.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

9.Expand 7(a + 8)

10.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

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

13.Which of these statements is an identity?

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

15.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.