Algebra worksheet — GCSE Foundation

1.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.

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.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

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

5.Solve x² − 6x = 0.

6.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

7.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

8.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

9.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

10.Write down the gradient of the line with equation y = −x + 3.

11.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

12.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

13.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.

14.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

15.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.