Download eoc review (1).

SEQUENCE & SERIES
Summation Notation
sum(seq(1/(2^x), x, 3, 6, 1)=
Arithmetic- SUBTRACT to find d (common difference)
EXAMPLES
15
64
Geometric- DIVIDE to find r (common ratio)
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 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
The number of roots a polynomial has is the same as its degree -
EXAMPLES
NO REAL roots- Complex Roots
EQUATIONS / INEQUALITIES
Your calculator will solve an equation or inequality using the
INTERSECTION function
http://mathbits.com/MathBits/TISection/Algebra2/absolutevalue.htm
Absolute Value Equations
Quadratic Inequalities- GRAPH IN THE CALCULATOR
Absolute Value Inequalities
**remember how to shade up or down***
Exponential Equations
Examples
Logarithmic Equations
Radical Equations
Examples
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
Multiplying
Examples
Examples
Dividing
Long Division
Synthetic Division
RATIONAL EXPRESSIONS
SIMPLIFYING
MULTIPLYING
EXAMPLES
DIVIDING
EXPONENTS
ADDING / SUBTRACTING RATIONAL AND COMPLEX FRACTIONS
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)
Examples
ADD,SUBTRACT,MULTIPLY,DIVIDE
Examples
COMPOSITION
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".
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
TRANSFORMATION OF FUNCTIONS
Reflection
Examples
Translation
Stretch/ Compression
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**--- (Q3 –Q1)
http://mathbits.com/MathBits/TISection/Statistics1/BasicCommands.htm
Calculator Method
Examples
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)".
http://www.regentsprep.org/Regents/math/algtrig/ATS4/RegressionLesson.htm
To turn see
Corr. Coeff.
Press 2nd
CATALOG
ZOOM #9
ZoomStat to see
the scatterplot
(Y1 comes from VARS
→ YVARS, #Function,
Linear
y = a + bx
Examples
Exponential
x
y = ab
Quadratic
y = ax2 + bx + c
Logarithmic
y = a + blnx
Cubic
y = ax3 + bx2+ cx + d
Sinusoidal
y = a sin(bx + c) + d
TRIGONOMETRY
Unit Circle
Examples
GRAPHS OF TRIG FUNCTIONS
Period=
Period=
BINOMIAL EXPANSION/ PROBABILITY
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
Examples
CONIC SECTIONS
Examples