Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as (x + 7) ÷ 4.

2.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

3.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

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

5.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

6.Solve 5x + 2 = 17.

7.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

8.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

9.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

10.Expand and simplify (x − 3)²

11.Which expression means 'y squared, multiplied by 3'?

12.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

13.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

14.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

15.Solve the inequality 4x + 1 > 2x + 9.