Algebra worksheet — GCSE Foundation

1.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

2.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

3.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

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

5.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

6.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

7.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

8.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

9.Solve 3x − 1 = 8

10.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

11.Work out the gradient of the straight line with equation 3y = 12 − 6x.

12.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

13.Solve 2(x + 3) = 10

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

15.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.