Algebra worksheet — GCSE Foundation

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

2.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

3.Solve (2x + 1)/3 = 5

4.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

5.Work out the value of 3n − 2 when n = 1

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

7.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

8.Work out the value of m² + 3m when m = −2

9.A square has sides of length y cm. Write down an expression for the perimeter of the square.

10.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.

11.Simplify 2b − 1 + 2b − 4 + 2b

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

13.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

14.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

15.Solve x/4 + 1 = 3