Algebra worksheet — GCSE Foundation

1.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

2.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

3.Expand and simplify (x − 3)²

4.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

5.Write down the expression that means the same as m² × m × 3.

6.Simplify 5a/6 − a/3

7.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.

8.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

9.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

10.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

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

12.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?

13.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

14.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

15.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.