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 knowledge-based
    
• 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! 

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
  
• Re-evaluate 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 “test-able”
• Make a mock-exam
• 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 Free-Response Question:

• Show partial work!
  
• Don’t forget the unit!
  
• Don’t judge length of answer on blank space