Show Menu
Cheatography
  1. Home >
  2. Education >

Midterm Math BMMA 1st Term Cheat Sheet (DRAFT) by

BMMA 1st Term Midterm Exam Cheat Sheet

This is a draft cheat sheet. It is a work in progress and is not finished yet.

What is Inductive Reasoning

It is the process of reaching a general conclusion by examining specific examples.
Conjecture is the conclusion brought upon this reasoning. This conclusion may be right or wrong

Uses of Inductive Reasoning

Use Inductive Reasoning to Predict a Number
Using inductive reasoning to predict the next number
Use Inductive Reasoning to Make a Conjecture
Using inductive reasoning to make a conjecture about the relati­onship between the size of the resulting number and the size of the original number
Use Inductive Reasoning to Solve an Applic­ation
Scientists often use inductive reasoning.

What is Deductive Reasoning?

It is the process of reaching a conclusion by applying general assump­tions, proced­ures, or princi­ples.
 
Uses of Deductive Reasoning
Using Deductive Reasoning to Establish a Conjecture
 
Logic Puzzles
These can be solved by using deductive reasoning and a chart that enables us to display the given inform­ation in a visual manner.
 

Problem Solving with Patterns

Term of a Sequence
An ordered list of numbers such as 5,14,2­7,44,65 … is called a sequence.
 
The numbers in a sequence that are separated by commas are the terms of the sequence.
 
. It is customary to use the subscript notation to designate the nth term of a sequence.
 
 
The “nth” term is a formula with “n” in it which enables you to find any term of a sequence without having to go up from one term to the next.
a1 represents the 1st term of a sequence.
“n” stands for the term number, so to find the 50th term, we would just substitute 50 in the formula in place of “n”.
a2 represents the 2nd term of a sequence.
 
a3 represents the 3rd term of a sequence..
 
aN represents the nth term of a sequence.
 
 
Difference Table
The difference table shows the differ­ences between successive terms of the sequence
 

Polya’s Four-Step Problem Solving Strategy

Understand the Problem
Can you restate the problem in your own words?
This part of Polya’s four-step strategy is often overlo­oked. You must have a clear unders­tanding of the problem.
Can you determine what is known about these types of problems?
 
Is there a missing inform­ation that, if known, would allow you to solve the problem?
 
Is there an extraneous inform­ation that is not needed to solve the problem?
 
What is the goal?
 
Devise A Plan
Make a list of the known inform­ation. • Make a list of inform­ation that is needed.
. Successful problem solvers use a variety of techniques when they attempt to solve a problem.
Draw a diagram. • Make an organized list that shows all the possib­ili­ties.
 
Make a table or a chart. • Work backwards.
 
Try to solve a similar but simpler problem. • Look for a pattern.
 
Write an equation. If necessary, define what each variable repres­ents. • Perform an experi­ment.
 
Guess at a solution, then check your result.
 
Carry out the Plan
Once you have devised a plan, you must carry it out.
Work carefully. • Keep an accurate and neat record of all your attempts.
 
Realize that some of your initial plans will not work and that you may have to devise another plan or modify your existing plan.
 
Review the Solution
Ensure that the solution is consistent with the facts of the problem. • Interpret the solution in the context of the problem.
 
Ask yourself if there are genera­liz­ations of the solution that could apply to other problems.