Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

2.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

3.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

4.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

5.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

6.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

7.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

8.n = 3. Work out the value of (2n)².

9.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

10.Solve 5(x + 3) = 40

11.Write down the expression that means 5 more than half of n.

12.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

13.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.

14.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

15.Work out the value of 3b − 4 when b = 6