Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

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

3.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

4.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

5.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

6.Solve 4x + 3 = 19

7.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

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

9.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

10.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

11.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.

12.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

13.Expand 2(x + 12)

14.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

15.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.