Algebra worksheet — GCSE Foundation

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

2.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

3.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

4.a = 2 and b = 5. Work out the value of a²b.

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

6.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

7.A straight line has equation y = 5x. Work out the value of y when x = 3.

8.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.

9.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

10.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

11.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

12.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

13.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.

14.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

15.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.