Algebra worksheet — GCSE Foundation

1.A number machine adds 5 to its input. Work out the output when the input is 0.

2.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.

3.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.

4.Which of these statements is an equation with exactly one solution?

5.Which expression is equivalent to 2(x + 6)?

6.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

7.Solve the inequality 6x ≥ 18.

8.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

9.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

10.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

11.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

12.Simplify 2a + 3b − a + 2b − b

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

14.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

15.Factorise fully 56x − 24