Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = x + 7.

2.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

3.The point A lies on the x-axis. Which statement about A must be true?

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

5.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.

6.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

7.Expand and simplify (x − 3)²

8.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

9.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

10.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

11.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

12.Write down the expression that means the same as p + p + p + q.

13.Solve 3x − 1 = 8

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

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