Algebra worksheet — GCSE Foundation

1.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

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

3.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

4.Solve the inequality 6x ≥ 18.

5.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

6.Solve 5(x + 3) = 40

7.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

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

9.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

10.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.

11.Solve 4x² − 9 = 0.

12.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

13.A number machine multiplies its input by 3. The output is 15. Work out the input.

14.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

15.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).