sum(seq(1/(2^x), x, 3, 6, 1)= 15 64

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SEQUENCE & SERIES Summation Notation sum(seq(1/(2^x), x, 3, 6, 1)= 15 64 Arithmetic-

1 SEQUENCE & SERIES Summation Notation sum(seq(1/(2^x), x, 3, 6, 1)= Arithmetic- SUBTRACT to find d (common difference) Geometric- DIVIDE to find r (common ratio) EXAMPLES

2 REAL/COMPLEX NUMBERS Complex Conjugates (a + bi) (a - bi) -PUT in a +bi MODE to add, subtract, etc. -Convert radicals (sq. roots) to decimals! EXAMPLES

QUADRATICS/ POLYNOMIALS -The solutions- are

quadratic/polynomial- Factoring, Graphing,

the Square -It is possible to have real and/or

roots ONE real root NO REAL roots- Complex

3 QUADRATICS/ POLYNOMIALS -The solutions- are called zeros or roots -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 Discriminant TWO real roots ONE real root NO REAL roots- Complex Roots The number of roots a polynomial has is the same as its degree - EXAMPLES

4 EQUATIONS / INEQUALITIES Your calculator will solve an equation or inequality using the INTERSECTION function Absolute Value Equations Absolute Value Inequalities Quadratic Inequalities- GRAPH IN THE CALCULATOR **remember how to shade up or down***

5 Exponential Equations Logarithmic Equations Radical Equations Example

6 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]

7 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!!

8 MORE POLYNOMIALS Adding/Subtracting Multiplying Dividing Long Division Synthetic Division

9 RATIONAL EXPRESSIONS SIMPLIFYING EXAMPLES MULTIPLYING

10 DIVIDING EXPONENTS

11 ADDING / SUBTRACTING RATIONAL AND COMPLEX FRACTIONS

12 FUNCTIONS -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) ADD,SUBTRACT,MULTIPLY,DIVIDE

13 COMPOSITION Composition Tips The notation used for composition is: and is read "f composed with g of x" or "f of g of x". 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!!!****

14 TRANSFORMATION OF FUNCTIONS Reflection Translation Stretch/ Compression

15 STATISTICS Mean, Median, Mode, Standard Deviation, Variance or - Mean - Variance ****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**--- (Q 3 Q 1 ) Calculator Method

17 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)". To turn see Corr. Coeff. Press 2nd CATALOG ZOOM #9 ZoomStat to see the scatterplot (Y 1 comes from VARS YVARS, #Function, Linear y = a + bx Exponential y = ab x Quadratic y = ax 2 + bx + c Logarithmic y = a + blnx Cubic y = ax 3 + bx 2 + cx + d Sinusoidal y = a sin(bx + c) + d

20 TRIGONOMETRY Unit Circle

22 GRAPHS OF TRIG FUNCTIONS Period= Period=

htm To find a row of Pascal s Triangle (x+y) 5 **Remember to

24 BINOMIAL EXPANSION/ PROBABILITY Binomial Theorem Tips To find a row of Pascal s Triangle (x+y) 5 **Remember to Highlight L 2 ** Type 5 n C r L 1 Coefficients in the 5 th row of Pascal s Triangle

26 CONIC SECTIONS

NFC ACADEMY COURSE OVERVIEW

NFC ACADEMY COURSE OVERVIEW Algebra II Honors is a full-year, high school math course intended for the student who has successfully completed the prerequisite course Algebra I. This course focuses on algebraic