Math 102/Review: Difference between revisions
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=overview= | |||
Review Chapter | Review Chapter | ||
* Real numbers | * Real numbers | ||
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* Rational Expressions | * Rational Expressions | ||
* Radicals, nth roots, and Rational Exponents | * Radicals, nth roots, and Rational Exponents | ||
==Section R1: real numbers== | |||
Raster notation, sets and set-building | |||
Intersection and union of sets | |||
Complement of set | |||
Number classification (integer, rational, irrational, real) | |||
Approximation | |||
Value of expression | |||
Commutative property | |||
Associative property | |||
Distributive property | |||
Identity property | |||
Additive inverse | |||
Reciprocal | |||
Differences and quotients (definition) | |||
Rules of signs | |||
Zero product property | |||
Add/subtract/multiply/divide quotients (fractions) | |||
Least common multiple for adding fractions | |||
==Section R2: algebra essentials== | |||
Real number line | |||
Positive and negative numbers | |||
Inequality symbols | |||
Absolute value | |||
Distance on a number line | |||
Algebraic expressions | |||
Finding domain of variable | |||
Circumference of circle | |||
Laws of exponents | |||
Negative exponents | |||
Evaluating square roots | |||
Using graphing calculator to do exponents | |||
Scientific to decimal notation | |||
==Section R3: geometry review== | |||
Pythagorean Theorem | |||
Right/isosceles/scalene triangles | |||
Using geometry formulas | |||
Similar triangles | |||
==Section R4: polynomials== | |||
Monomials: definition | |||
Polynomials: definition | |||
Addition and subtraction of polynomials | |||
Multiplication of polynomials and distributive properties | |||
Special product formulas | |||
* Difference of 2 squares x2 - a2 | |||
* Perfect square binomials (x+a)2 or (x-a)2 | |||
* Sum and difference of 2 cubes x3 + a3 = (x+a)(x2 - ax + a2), x3 - a3 = (x-a)(x2 + ax + a2) | |||
Dividing polynomials using long division | |||
Polynomials in 2 variables | |||
==Section R5: Factoring== | |||
Factor the difference of 2 squares | |||
Factor the sum and difference of 2 cubes | |||
Factor perfect squares | |||
Factor trinomials x2 + bx + c | |||
Factor by grouping | |||
Factor 2nd degree polynomials ax2 + bx + c | |||
Complete the square | |||
Summary: Type of polynomial/method/example | |||
==Section R6: synthetic division== | |||
Syntehtic division method | |||
==Section R7: Rational Expressions== | |||
Reducing rational expressions to lowest terms | |||
Multiplying and dividing rational expressions | |||
Adding and subtracting rational expressions | |||
Using LCM method | |||
Simplifying complex rational expressions | |||
==Section R8: Rational Exponents, nth Roots== | |||
Working with nth roots, properties of radicals | |||
Simplifying radical expressions | |||
Rationalizing denominators | |||
Simplifying rational exponent expressions | |||
Revision as of 05:16, 19 September 2016
overview
Review Chapter
- Real numbers
- Algebra essentials
- Geometry essentials
- Polynomials
- Factoring polynomials
- Synthetic division
- Rational Expressions
- Radicals, nth roots, and Rational Exponents
Section R1: real numbers
Raster notation, sets and set-building
Intersection and union of sets
Complement of set
Number classification (integer, rational, irrational, real)
Approximation
Value of expression
Commutative property
Associative property
Distributive property
Identity property
Additive inverse
Reciprocal
Differences and quotients (definition)
Rules of signs
Zero product property
Add/subtract/multiply/divide quotients (fractions)
Least common multiple for adding fractions
Section R2: algebra essentials
Real number line
Positive and negative numbers
Inequality symbols
Absolute value
Distance on a number line
Algebraic expressions
Finding domain of variable
Circumference of circle
Laws of exponents
Negative exponents
Evaluating square roots
Using graphing calculator to do exponents
Scientific to decimal notation
Section R3: geometry review
Pythagorean Theorem
Right/isosceles/scalene triangles
Using geometry formulas
Similar triangles
Section R4: polynomials
Monomials: definition
Polynomials: definition
Addition and subtraction of polynomials
Multiplication of polynomials and distributive properties
Special product formulas
- Difference of 2 squares x2 - a2
- Perfect square binomials (x+a)2 or (x-a)2
- Sum and difference of 2 cubes x3 + a3 = (x+a)(x2 - ax + a2), x3 - a3 = (x-a)(x2 + ax + a2)
Dividing polynomials using long division
Polynomials in 2 variables
Section R5: Factoring
Factor the difference of 2 squares
Factor the sum and difference of 2 cubes
Factor perfect squares
Factor trinomials x2 + bx + c
Factor by grouping
Factor 2nd degree polynomials ax2 + bx + c
Complete the square
Summary: Type of polynomial/method/example
Section R6: synthetic division
Syntehtic division method
Section R7: Rational Expressions
Reducing rational expressions to lowest terms
Multiplying and dividing rational expressions
Adding and subtracting rational expressions
Using LCM method
Simplifying complex rational expressions
Section R8: Rational Exponents, nth Roots
Working with nth roots, properties of radicals
Simplifying radical expressions
Rationalizing denominators
Simplifying rational exponent expressions