Algebra worksheet — GCSE Foundation

1.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

2.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

3.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

4.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

5.Which of these is an inequality?

6.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

7.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

8.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

9.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

10.Solve the inequality 2(x − 1) ≤ 8.

11.Which of these equations gives a straight-line graph when plotted?

12.Which of these is a formula?

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

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

15.Solve 2(x + 3) = 10