Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

2.Which of these is a formula?

3.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.

4.Simplify p + p + p.

5.Solve x² − x − 12 = 0.

6.Solve 2x² − 32 = 0.

7.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

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

9.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

10.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

11.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.

12.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

13.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

14.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

15.Solve x² + 3x − 10 = 0.