Algebra worksheet — GCSE Higher

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

2.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.

4.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.

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

6.Describe a sequence of two transformations that maps the graph of y = x² onto the graph of y = −(x − 5)².

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

8.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

9.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

10.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

11.Solve x² − 5x + 6 = 0 by factorising.

12.A train's distance-time graph shows it travelling 100 km at a steady speed in the first 1.5 hours, waiting at a signal for 0.25 hours, then travelling a further 47 km in 0.75 hours. Work out the average speed for the whole journey, correct to 1 decimal place.

13.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

14.Factorise 3x² + 10x − 8.

15.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.