Algebra worksheet — GCSE Foundation

1.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

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

3.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.

4.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.

5.Solve 3x + 14 = 8x − 6

6.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.

7.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

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

9.Work out the value of m² + 3m when m = −2

10.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?

11.Which expression is equivalent to 7x − 3(2x − 6)?

12.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

13.Solve the inequality 3x − 1 ≤ 11.

14.Solve x − 4 = −9

15.Write down the expression that means the same as m² × m × 3.