Algebra worksheet — GCSE Foundation

1.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

2.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

3.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

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

5.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

6.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

7.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.

8.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

9.Which of these is a factor of 15x + 20?

10.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.

11.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

12.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

13.Write down 0.2x with its coefficient written as a fraction in its simplest form.

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

15.Which of these numbers is a cube number?