mycbasehandout

C-BASE Math Review

T. Murphy

Numbers:

Integers: are positive and negative whole numbers, and zero.

Rational: a number is rational if it can be written as a fraction.

Irrational: any real number that is not rational (it is a non-repeating, non-terminating decimal).

Real: Rational and Irrational numbers, (a real number is a number that is on your number line).

Imaginary: imaginary part of a complex number, a + bi; i=

Prime: the only integer factors are itself and one.

Properties of Real Numbers:

Cummutative Property: a+b=b+a (for addition) and ab=ba (for Multiplication)

Associative Property: a+(b+c)=(a+b)+c (for addition) and a(bc)=(ab)c (for Multiplication)

Distributive Property: a(b+c)=ab+ac

Additive Identity Property of 0: 0+a=a

Multiplicative Identity Property of 1: 1a=a

Additive Inverse Property of Addition/Subtraction: a-a=a+(-a)=0

Multiplicative Inverse Property of Multiplication/Division: a/a=a(1/a)=1

Transitive Property: If a=b and b=c, then a=c

Order of Operations:

Please Excuse My Dear Aunt Sally
Parentheses (innermost first);
Exponentiation (Left to right as they occur) ;
Multiplication/Division (Left to right as they occur);
Addition/Subtraction (Left to right as they occur)

Solving

Linear Equations

Linear Equation: Ax + B = 0 (highest exponent is 1 no x times y A, B are real numbers and a not equal to 0)

numerical coefficient

The number factor of a term (in front of the letter).

variable

The letters that are chosen to be place holders for numbers.

Like Terms: have the same variables raised to the same exponent, (the numerical coefficient does not matter)

Steps for Solving Linear Equations

1. Eliminate Fractions (multiply every term by LCM)

2. Eliminate Parentheses (apply distributive Property)

3. Get Variables on one side Constants on the other side-- using properties of linear equations, collect all terms that contain variables on one side of the equation, and all constant terms on the other side of the equation.

4. Simplify Like Terms

Linear Inequalities

Quadratic Equation:

Quadratic Formula

Set Theory

Set: A set is a collection of elements. Notation-- when you list the members of a set, use the brackets { } the elements are contained within the brackets. If set S contained the elements 1,2,3 then S = {1,2,3}.

Finite: A set with a limited number of elements, you can count the elements. ( The empty set is also considered as a finite set). for ex. {1,2,3}

Infinite: A set with an infinite (unlimited) number of elements, you cannot just count the elements. EX. real numbers, whole numbers, real and complex numbers, ...

Intersection: The intersection of two sets is the set containing the elements that are common to the two sets and is denoted by the symbol