Home » How to Solve Math Problems
General steps for solving any type of problem in math:
 Identify what is being given
 Clarify what is being asked
 If unclear, try to rephrase it.
 Select a strategy
 Trial & error, search, deductive reasoning, working backwards or knowledgebased
 Solve using selected strategy
 Review
 Check for reasonableness, units
Example:
 What happens to the graph of y=sin x / x as we approach x = 0 (note that it is not asking “at x=0”)?
Step 
Description 
Information 
1 
Identify what’s given 
As x approaches “0”, what is does sin x / x approach? 
2 
Identify what’s being asked 
What does sin x / x approach?

3 
Strategy: Numerical Approach 
Chose x values that approach to “0” – tabulate these values and corresponding sin x / x 
4 
Apply strategy: For x closer to x=0, evaluate f(x)


5 
Review

The limit approaches “1” no matter how we look at it! 
Clue Words:
 Clue Words for Addition: sum, total, in all, perimeter
 Clue Words for Subtraction: difference, how much more, exceed
 Clue Words for Multiplication: product, total, area, times
 Clue Words for Division: share, distribute, quotient, average
Types of Problems:
 The higher the math class, the more types of problems: in earlier classes, problems often required just one step to find a solution.
 Increasingly, you will tackle problems which require several steps to solve them.
 Break these problems down into smaller pieces and solve each piece  divide and conquer!
KUDOS = Problem Solving for Word Problems
K 
nowns 
U 
nknowns 
D 
efinition 
O 
utput 
S 
ubstantiation 
Known: Identify what is known
 Use units to identify information
 Write information symbolically
 Look for implied information
Unknown: Identify what is unknown
 What is the problem seeking?
 Write information symbolically
Definition: Identify the information that is needed
 Choose & rearrange equations
 Look other places for missing info
 Reevaluate your approach if needed
Output: Find the output for your information
 Plug values into equations
 Perform the calculation
Substantiate: Check your results with common sense checks
 Check Validity
 Check Units
Example: Find the distance traveled in 10 seconds by an object moving with a velocity of v(t) = 20 + 7 cos t meters per second.
Step 
Information 
You Write 
K 
Time traveled 
t = 10 sec. 

Velocity function

v(t) = 20 + 7 cos t

U 
What is the distance? 
d = ?

D 
Find the area under the curve v(t) = 20 + 7 cos t

Graph v(t) and divide it into 5 rectangles that are 2 units wide each. The height of each may be calculated using the function. 
O 
Add each of the 5 area’s regions 
2(27.0+17.1+15.4+26.7+19.0)=210m 
S 
Check validity, units

210m is a reasonable answer and “m” is a distance unit 
Preperation Checklist:
 Stay ahead of the game
 Make a cheat sheet
 Know the format & what information is “testable”
 Make a mockexam
 Attend the review session
 Get help early
Day of the Exam Checklist:
 Arrive early and prepared
 Listen & read instructions carefully
 Memory dump first
 Skim the test and make a plan
 Answer questions sequentially
 Apply the guessing rule
Multiple Choice Question Advice:
 Scan all the choices
 Avoid the simplification trap
When Facing a FreeResponse Question:
 Show partial work!
 Don’t forget the unit!
 Don’t judge length of answer on blank space
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Calculus
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