Algebra worksheet — GCSE Higher

1.Which of these quadratic graphs does NOT cross the x-axis at all?

2.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

3.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

4.Work out the value of 2x² when x = −3

5.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

6.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.

7.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

8.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

9.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.

10.A tap's flow rate, in litres per minute, is plotted against time, in minutes, on a graph. What are the units of the area under this graph?

11.Solve 4(x − 3) = 2x + 6.

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

13.Solve 3(2x − 1) = 27

14.f(x) = 2x − 1. Work out ff(x).

15.A student claims: 'For every positive integer n, n² + n + 1 is a prime number.' Which value of n shows that this claim is false?