Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

2.Solve x − 4 = −9

3.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

4.Which of these is a term, rather than a whole expression, an equation, or a formula?

5.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

6.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

7.Solve 3x − 5 = 4.

8.Work out the distance of the point (−6, 4) from the x-axis.

9.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

10.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

11.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.

12.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

13.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

14.Solve the inequality 3x + 6 ≤ 0.

15.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.