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Precalculus Supplementary Textbook
Functions

Word Problems

Word problems are often difficult for many students, but all good word problem should provide you with information that describe the input and out variables and some clue as to the rules or function types, or model to use to related the input to the output. However, some word problems provide only implicit or indirect clues on all 3 information types. 

A good approach to attempting to solve word problems is to first ask yourself these questions:

1. What is given - variables, attributes descriptions / values ?

2. What is being asked - what output is expected?

3. What model best describes or explains the problem or fit the information given?

One of the first step in solving any word problem is to paraphrase the problems or restate the problems the obtain a clear understanding of the problems to be solved. Often in the rephrasing of the problem the solution jumps out at you.

The next step is to find out what information is given and what solution is requested or asked.

This is obtained by asking the questions above.

The most difficult part and most important part of a problems is the solution strategy: This include finding the best model to solve the problems and deciding on a approach to solving the problem (algebraic or graphical or logical). Though we stress algebraic or graphical approaches to problems, students may find unique ways to solve problems, but must be able to defend solution by the final step below:

Usually one final step after a solution is obtained is often not performed by most students when working out the solution(s) to a problem; that is, checking the consistency of your answers.

Even in checking you may not know for sure if the answer is the correct solution to a problem; however checking validates the following:

1. Corrects application of mathematical model - formula

2. Checks Input with output and output with inputs for consistency

3. Verifies reasonability of solution(s)

4. Corrects computational errors

Since this is a graphics intense text students should use their calculators to verify solutions graphically.

There are various approaches to attacking word problems that will be developed during the lectures associated with this text - strategies for solving problems and making decisions given a set of alternatives. 

The best way to master word problems is to Practice, Practice, Practice! You must work out problems on your own, having the instructor or teacher solve your problem for you is not a substitute for working each problem out on your own.

"I teach you what is mine, what you learn by doing becomes yours", GB

Remember we learn:

10% of what we read

20% of what we hear

30% of what we see

50% of what we see and hear

70% of what we say

90% of what we say and do

The worked out solutions in this text provide amply opportunities for examining some of the strategies for solving word problems.
 

Precalculus: Contemporary Models
by Pin D. Ling

Maintained by professor@pindling.org