Algebra worksheet — GCSE Foundation

1.Simplify 2b − 1 + 2b − 4 + 2b

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

3.Which of these statements is an equation with exactly one solution?

4.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

5.Expand 2(x − 13)

6.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

7.Write down the number of terms in the expression 4x² − 7x + 3.

8.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.

9.Solve the inequality 6x ≥ 18.

10.Write down the gradient of the line with equation y = −x + 3.

11.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

12.Solve the inequality 3x + 6 ≤ 0.

13.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

14.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

15.Solve x² − 6x = 0.