Algebra worksheet — GCSE Foundation

1.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

2.A straight line has equation y = 4 − 3x. Work out the gradient of the 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.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

5.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

6.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

7.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

8.Solve 5(x + 3) = 40

9.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

10.Work out the value of n² − n when n = −3

11.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

12.Which expression is equivalent to 0.5(4x + 6) − x?

13.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.

14.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

15.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.