Algebra worksheet — GCSE Foundation

1.Work out the value of 2(x + 2) when x = −5

2.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

3.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

4.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.

5.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

6.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

7.Factorise x² − 3x − 10.

8.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

9.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

10.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

11.Solve the inequality 6x ≥ 18.

12.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

13.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

14.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

15.Simplify 5a/6 − a/3