Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

2.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.

3.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

4.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.

5.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.

6.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

7.A number machine adds 5 to its input. Work out the output when the input is 0.

8.Solve 4(x − 3) = 2x + 6.

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

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

11.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

12.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

13.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

14.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

15.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.