Algebra worksheet — GCSE Foundation

1.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

2.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

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

4.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

5.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.

6.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

7.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

8.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

9.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.

10.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

11.Factorise x² − 64.

12.Write down the expression that means the same as 3 × y × y.

13.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

14.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

15.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.