Algebra worksheet — GCSE Foundation

1.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

2.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

3.Solve x² − x − 12 = 0.

4.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

5.a = 2 and b = 5. Work out the value of ab².

6.y = 5 − 2x. Work out the value of x when y = 11.

7.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

8.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.

9.Which of these is a formula?

10.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

11.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

12.a = 3 and b = 5. Work out the value of a²b.

13.Which of these values of x is a solution of x² + 2x − 15 = 0?

14.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.

15.A person's body mass index is given by the formula B = m ÷ h², where m is the mass in kg and h is the height in metres. Work out B, to 1 decimal place, when m = 68 and h = 1.6.