Algebra worksheet — GCSE Foundation

1.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

2.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

3.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.

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

5.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

6.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

7.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

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

9.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

10.Work out the value of 3n − 2 when n = 1

11.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

12.Write down the gradient of the line with equation y = 6 + 4x.

13.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

14.Solve the inequality 2(x − 1) ≤ 8.

15.Solve x² − 5x + 6 = 0 by factorising.