SEQUENCE & SERIES

EXAMPLES

Arithmetic- SUBTRACT to find d (common difference) Geometric- DIVIDE to find r (common ratio)

Summation Notation

sum(seq(1/(2^x), x, 3, 6, 1)= 15

64

REAL/COMPLEX NUMBERS

EXAMPLES

-PUT in a +bi MODE to add, subtract, etc.

-Convert radicals (sq. roots) to decimals!

Complex Conjugates (a + bi) (a - bi)

QUADRATICS/ POLYNOMIALS

EXAMPLES

-Ways to solve a quadratic/polynomial- Factoring, Graphing, Quadratic Formula,

Square Roots & Completing the Square

-It is possible to have real and/or complex solutions

The number of roots a polynomial has is the same as its degree -

-The solutions- are called “zeros” or “roots”

The Discriminant

TWO real roots

ONE real root

NO REAL roots- Complex Roots

EQUATIONS / INEQUALITIES

Absolute Value Equations Absolute Value Inequalities

Quadratic Inequalities- GRAPH IN THE CALCULATOR **remember how to shade up or down***

http://mathbits.com/MathBits/TISection/Algebra2/absolutevalue.htm

Your calculator will solve an equation or inequality using the

INTERSECTION function

Exponential Equations Examples

Logarithmic Equations Examples

Radical Equations Example

Systems of Equations

To solve a 2 x2 or 3 x 3 system of equations plug the coefficients it into your calculator as a matrix and use rref [A]

Examples

Systems of Inequalities

GRAPH IN THE CALCULATOR **remember how to shade up or down***

The area where they are BOTH shaded is the answer.

The calculator WILL NOT show SOLID or DASHED lines!!

Examples

MORE POLYNOMIALS

Adding/Subtracting Examples

Multiplying Examples

Dividing

Long Division

Synthetic Division

RATIONAL EXPRESSIONS

SIMPLIFYING

MULTIPLYING

EXAMPLES

DIVIDING

EXPONENTS

ADDING / SUBTRACTING RATIONAL AND COMPLEX FRACTIONS

FUNCTIONS

Examples

ADD,SUBTRACT,MULTIPLY,DIVIDE

Examples

-A relation is a function IF every ‘x’ value has ONE ‘y’ value (meaning it passes the vertical test)

- Domain- x coordinates Range- y -coordinates

- In analyzing a function (the equation) you are really looking for restrictions in the domain

and range (i.e. no zeros in the bottom of a fraction, no negative numbers underneath a

radical)

COMPOSITION

Examples

INVERSE FUNCTIONS f -1

(x) Solve algebraically: Solving for an inverse algebraically is a three step process:

1. Set the function = y 2. Swap the x and y variables 3. Solve for y

*** REMEMBER- all inverses are not functions!!! They must pass the vertical line test!!!****

Examples

Composition Tips

http://mathbits.com/MathBits/TISection/Algebra2/composition.htm

The notation used for composition is: and is read "f composed with g of x" or "f of g of x".

TRANSFORMATION OF FUNCTIONS

Reflection Translation Stretch/ Compression

Examples

STATISTICS

Mean, Median, Mode, Standard Deviation, Variance

Examples

or - Mean

- Variance

Calculator Method

****Mode and Range WILL NOT be listed in the calculator!!****

*** If all the data were multiplied by a number the MEAN and RANGE will not be effected ***

-IQR (Interquartile Range)**Has to be calculated**--- (Q3 –Q1)

http://mathbits.com/MathBits/TISection/Statistics1/BasicCommands.htm

REGRESSION MODELS

Regression Models are used to make predictions given a certain set of data.

The CORRELATION COEFFICIENT (r) indicates how well a model (regression equation) fits a particular set of data.

Designated by r, it falls into the range -1 < r < 1. If r is close to 1 (or -1), the model is considered a "good fit (strong correlation)". If r is close to 0, the model is "not a good fit (weak correlation)".

Examples

Exponential

y = abx

Quadratic

y = ax2 + bx + c

Linear

y = a + bx

Cubic

y = ax3 + bx2+ cx + d

Sinusoidal

y = a sin(bx + c) + d

Logarithmic

y = a + blnx

http://www.regentsprep.org/Regents/math/algtrig/ATS4/RegressionLesson.htm

(Y1 comes from VARS

→ YVARS, #Function,

ZOOM #9

ZoomStat to see

the scatterplot

To turn see

Corr. Coeff.

Press 2nd

CATALOG

TRIGONOMETRY

Examples

Unit Circle

GRAPHS OF TRIG FUNCTIONS

Period=

Period=

BINOMIAL EXPANSION/ PROBABILITY

Examples

Binomial Theorem Tips

http://mathbits.com/MathBits/TISection/Algebra2/binomialtheorem.htm

To find a row of

Pascal’s Triangle

(x+y)5

**Remember to Highlight L2**

Type “ 5 nCr L1”

Coefficients in the 5th

row of

Pascal’s Triangle

CONIC SECTIONS

Examples