Algebra worksheet — GCSE Foundation

1.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

2.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

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

4.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.

5.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

6.Which of these is an inequality?

7.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

8.Work out the value of 2x² when x = −3

9.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

10.Write down the first four terms of the sequence with nth term 6n − 5.

11.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.

12.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

13.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

14.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

15.Make a the subject of the formula b = 20 − a.