Algebra worksheet — GCSE Foundation

1.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

2.Solve the inequality 6x ≥ 18.

3.A number machine multiplies its input by 5. Work out the output when the input is −1.

4.A number machine adds 5 to its input. Work out the output when the input is 0.

5.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

6.Which of these is a formula, rather than an expression, an equation, or an identity?

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

8.The point A is at (5, −3). In which quadrant does A lie?

9.Simplify x + x + 4

10.Solve the inequality 5 − x ≤ 2.

11.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

12.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

13.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

14.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

15.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.