Algebra worksheet — GCSE Foundation

1.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

2.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

3.Write down the gradient of the line with equation y = 6 + 4x.

4.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.

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

6.Work out the gradient of the straight line with equation y = (2x/5) − 3.

7.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

8.Which of these is an expression?

9.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

10.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

11.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

12.Make b the subject of the formula a = 5b.

13.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

15.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.