Learning Resources
Outcomes
By the end of this lesson you will be able to answer questions like the ones in the pre-test below.
If you prefer, you can proceed directly to the first page of the lesson without doing the pre-test. To do this simply click on the Lesson button above.
Alternately you can first answer the questions on the pre-test below in your Math 3103 binder. Then refer only to the pages of the lesson that contain instruction on the questions for which you get an incorrect answer or for which you would like some further explanation.
Pre-test
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Identify the set of numbers that would be used in each situation below:
(a) The number of pop tins that a person returns for recycling.
(b) The length of the hypotenuse in a right triangle.
(c) The temperature showing on a digital thermometer that can only record temperatures with a precision to the nearest degree.
(d) The ratio of wins to games played for a hockey team. -
A digital switch turns on the heating system in a house when the temperature falls below 20 °C. If the switch has a precision that can only sense a temperature change to the nearest degree, write both a sentence and a mathematical inequality to describe:
(a) The restriction on the temperature when the heating system is turned off.
(b) The restriction on the temperature when the heating system is turned on. -
Whenever she has any free time from school work, Bonnie works at a sewing shop where she cuts the material for making dresses. She is paid $10.00 for each dress she cuts, but if she only cuts the material for part of a dress she gets paid based on the proportion cut, e.g. if she cuts out 40% of a dress , then she gets paid 40% of $10.00 or $4.00.
(a) The possible number of dresses she can cut is described fully by which number system?
(b) Although the time Bonnie has for work varies greatly, the maximum number of hours that she can work on any given day is 5 and it takes her 40 minutes to cut one complete dress. If x represents the number of dresses cut, write both a sentence and a mathematical inequality to describe the possible number of dresses she can cut in any given day.
(c) If y represents the amount of money Bonnie can earn, use the conditions of part (b) to write a sentence and a mathematical inequality to show the amount of money she can earn in any given day. - Examine the two graphs below and then answer (a) to (d) for both:
Graph 1 Graph 2
By the end of this section you should be able to:
- Identify a given number as belonging to the various subsets of the real numbers.
- Recognize situations in which the various subsets of the real numbers can be applied.
- Write either a sentence or an inequality to describe domain and range for various problem situations.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- The numbers that constitute the real number system and its various subsets.