Algebra worksheet — GCSE Foundation

1.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

2.Work out the gradient of the straight line with equation 2x + y = 8.

3.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

4.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.

5.Write down the gradient of the line with equation y = 7x − 2.

6.Work out the value of 2x² when x = −3

7.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

8.Which of these numbers is a cube number?

9.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

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

11.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

12.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

13.Factorise fully 12x² + 18x.

14.Make x the subject of the formula y = 5x + 3.

15.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.