Algebra worksheet — GCSE Foundation

1.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.

2.Which expression means 'y squared, multiplied by 3'?

3.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

4.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

5.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.

6.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

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

8.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

9.Which of these is a term, rather than a whole expression, an equation, or a formula?

10.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

11.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

12.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

13.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

14.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

15.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.