Practice Discrete vs Continuous in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The distinction between quantities that take separate, distinct values (discrete, like number of students) and quantities that can take any value in a range (continuous, like height or temperature).

People come in whole numbers (discrete). Height can be any value (continuous).

Example 1

easy
Classify each quantity as discrete or continuous, and explain: (a) number of students in a class, (b) the height of a student, (c) the number of text messages sent, (d) the temperature in a room.

Example 2

medium
A discrete model counts bacteria in a culture as B(t) = 2^t (where t is in hours, integer values). A continuous model uses B(t) = e^{0.693t}. Compare the models at t = 0, 1, 2, 3 and explain when each is appropriate.

Example 3

easy
Which type of graph is appropriate for each: (a) the number of cars sold each month (bar chart or line graph with any real y-values?), (b) the speed of a car over a journey?

Example 4

medium
Shoe sizes in the UK come in steps of \frac{1}{2} (e.g., 6, 6.5, 7, 7.5, \ldots). Is shoe size discrete or continuous? What about actual foot length in centimetres?
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