Algebra worksheet — GCSE Foundation

1.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

2.The point B has coordinates (−2, −2). In which quadrant is B?

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

4.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

5.Work out the value of 3a − 2b when a = 5 and b = 4

6.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

7.Expand 4(2x − 3).

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

9.a = 2 and b = 5. Work out the value of a²b.

10.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

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

12.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

13.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

14.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.

15.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.