Algebra worksheet — GCSE Higher

1.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

2.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

3.f(x) = 2x − 1. Work out ff(x).

4.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

5.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

6.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

7.Which of these pairs of lines are perpendicular to each other?

8.Solve x² + 3x − 10 = 0.

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

10.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

11.Work out the gradient of the straight line with equation 3y = 12 − 6x.

12.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

13.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).

14.Points A(8, 15) and B(−8, 15) both lie on the circle x² + y² = 289, which has centre (0, 0). Work out the length of the chord AB.

15.n = 3. Work out the value of (2n)².