Algebra worksheet — GCSE Foundation

1.Work out the value of a² − 2b when a = −3 and b = 4.

2.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

3.Write down the expression that means 5 more than half of n.

4.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.

5.Work out the value of 5a + 2 when a = 3

6.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

7.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

8.Make x the subject of the formula y = x/2 − 5.

9.A number machine multiplies its input by 5. Work out the output when the input is −1.

10.Solve 4x + 3 = 19

11.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

12.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.

13.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

14.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

15.A graph has equation y = −2x² + 5. Which statement about its shape is correct?