Algebra worksheet — GCSE Foundation

1.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

2.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

3.Write down the gradient of the line with equation y = 6 + 4x.

4.Write down the coefficient of p in the expression 7 − 4p + 9q.

5.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

6.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

7.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

8.Solve 7x − 5 = 3x + 11

10.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

11.Which of these equations is equivalent to 5x − 2 = 3x + 8?

12.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.

13.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

14.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?

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