Algebra worksheet — GCSE Foundation

1.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

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.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

4.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

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

6.Write down the first four terms of the sequence with nth term 6n − 5.

7.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

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

9.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

10.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

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

12.Solve x² + 7x = 0.

13.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

14.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

15.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.