Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

2.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

3.The diagram shows the graph of a function. Which equation could it represent?

4.Write down the expression that means the same as m × m × m × n.

5.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

6.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

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

8.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?

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

10.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

11.p = 4. Work out the value of 2p³.

12.Solve 6x + 4 = 28

13.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.

14.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

15.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.