Algebra worksheet — GCSE Foundation

1.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.

2.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

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

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

5.Solve 4x² − 9 = 0.

6.Solve x² + 7x = 0.

7.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

8.Factorise x² − 3x − 10.

9.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.

10.A number machine multiplies its input by 3. The output is 15. Work out the input.

11.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

12.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?

13.Which of these is a term, rather than a whole expression, an equation, or a formula?

14.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

15.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.