Algebra worksheet — GCSE Foundation

1.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

2.Write down the coefficient of p in the expression 7 − 4p + 9q.

3.Expand 2(x + 12)

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

5.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

6.Which expression means 'y squared, multiplied by 3'?

7.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

8.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

9.Make x the subject of the formula y = 5x + 3.

10.Which expression is equivalent to 2(x + 6)?

11.Solve 5x² − 15x = 0.

12.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

13.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

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

15.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.