Algebra worksheet — GCSE Foundation

1.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?

2.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

3.Which expression is equivalent to 5x − (x + 3)?

4.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

5.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

6.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

7.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

8.The point B has coordinates (−2, −2). In which quadrant is B?

9.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

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

11.Work out the value of 2(x + 2) when x = −5

12.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

13.Write down the gradient of the line with equation y = 6 + 4x.

14.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.

15.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.