Final exam

Math 100. Exploring Mathematics.

Review for the final exam

The final exam will be cumulative. It will consist of 8 problems (some of which may contain multiple parts). Problems may be of any nature: a list of true/false questions that require short explanation; a question that asks you to give an example for a certain concept; some problems will only require short calculations; some will require longer calculation and/or explanations; some will ask you to clearly show the 4 steps of problem solving; some may require you to be creative, some may require you to use common sense and make appropriate assumptions. Review the following topics/problems:

Four steps of problem solving
Strategies of problem solving when devising a plan
Fractions (definition, meaning, representations)
Operations with fractions
Using pattern blocks to illustrate fractions and their operations
Word problems involving operations of fractions (including writing your own problems)
Area model for multiplication
Place value: integers and decimals
Bases other than 10 (convert numbers from one base to another, perform addition/subtraction in another base, word problems)
Divisibility (important terms: divides, divisible by, factor, divisor, multiple)
Prime factorization, GCD (aka GCF), LCM
Number sets (definitions, examples, notations, set inclusions)
Various properties of rational/irrational numbers
Rational numbers as fractions and decimals (convert a fraction into a decimal, convert a finite/periodic decimal into a fraction)
Pattern problems (how many dots/squares/etc. are there in the n-th figure)
Equations; quadratic formula
Word problems that can be solved using equations or other algebraic thinking
Pythagorean theorem
The number pi (definition, properties)
Perimeter, area, surface area, volume (concepts and formulas for some basic shapes)
Similarity (definition, properties, and perimeter, area, surface area, and volume of similar figures/solids)
Proportional reasoning problems