Algebra worksheet — GCSE Foundation

1.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

2.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

3.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

4.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

5.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

6.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

7.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

8.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.

9.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

10.Expand 2(x + 12)

11.Which of these is an inequality?

12.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

13.Solve 5x + 2 = 17.

14.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

15.y = 3x − 2. Work out the value of y when x = 4.