Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

2.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

3.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

4.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

5.Solve the inequality 5 − x ≤ 2.

6.Solve (3x + 2)/5 = (x + 4)/3

7.A number machine multiplies its input by 3. The output is 15. Work out the input.

8.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

9.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

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

11.Solve x² − 2x − 24 = 0.

12.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.

13.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

14.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

15.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?