Algebra worksheet — GCSE Foundation

1.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

2.Which of these rules generates the sequence 6, 11, 16, 21, …?

3.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

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

5.Solve the inequality 9 − 2x ≥ 1.

6.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.

7.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

8.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

9.Solve x/4 + 1 = 3

10.Solve x² = 81.

11.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

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

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

14.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

15.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).