Algebra worksheet — GCSE Foundation

1.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

2.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

3.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

4.Which of these is a formula, rather than an expression, an equation, or an identity?

5.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

6.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

7.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

8.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

9.A number machine adds 6 to its input. Work out the output when the input is −4.

10.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

11.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

12.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

13.Work out the value of 3a − 2b when a = 5 and b = 4

14.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

15.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.