Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = x/2 − 5.

2.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

3.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

4.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

5.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

6.Which expression is equivalent to 5x − (x + 3)?

7.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

8.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

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

10.Work out the value of 2x² when x = −3

11.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

12.Solve 2(x + 3) = 10

13.Solve 7x − 5 = 3x + 11

14.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

15.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.