Algebra worksheet — GCSE Foundation

1.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

2.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

3.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

4.Write down the number of terms in the expression 4x² − 7x + 3.

5.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

6.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

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

8.Solve the inequality 9 − 2x ≥ 1.

9.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

10.Work out the coordinates of the reflection of (6, −3) in the y-axis.

11.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

12.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

13.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

14.Which expression is equivalent to 4(x − 2) + 10?

15.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.