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Algebra II TRIG FlashcardsPowerPoint Presentation

Algebra II TRIG Flashcards

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### Algebra II TRIG Flashcards

### FUNCTIONS (constant

### How do you find an INVERSE or not?Function… ALGEBRAICALLY?GRAPHICALLY?

### COMPLEX NUMBERS or not?

### Describe How to Graph Complex Numbers or not?

As the year goes on we will add more and more flashcards to our collection.

Bring your cards every TUESDAY for eliminator practice!

Your flashcards will be collected on every test day! At the end of the quarter the grade received will be equivalent in value to a test grade. Essentially, if you lose your flashcards it will be impossible to pass the quarter.

What will my flashcards be graded on?

- Completeness – Is every card filled out front and back completely?
- Accuracy – This goes without saying. Any inaccuracies will be severely penalized.
- Neatness – If your cards are battered and hard to read you will get very little out of them.
- Order - Is your card #37 the same as my card #37?

Quadratic Equations

- Pink Card

1.) Leading Coeff = 1 (Divide if necessary)2.) Move ‘c’ over3.) Half ‘b’ and square (add to both sides)4.) Factor and Simplify left side.5.) Square root both sides (don’t forget +/-)6.) Solve for x.*Same answer as Quadratic Formula.

#3

General Form for DIRECT VARIATIONCharacteristics & Sketch

#4

General Form: y = kxCharacteristics: y –int = 0 (always!)Sketch: (any linear passing through the origin)

#4

- The PRODUCT of two variables will always be the same (constant).
xy=c

- Example:
- The speed, s, you drive and the time, t, it takes for you to get to Rochester.

#5

State the General Form of an inverse variation equation. (constant

Draw an example of a typical inverse variation and name the graph.

#6

General Form of a Circle (constant

#7

#7 (constant

BLUE CARD

Define Domain (constantDefine Range

#8

- DOMAIN - List of all possible x-values (constant
(aka – List of what x is allowed to be).

- RANGE – List of all possible y-values.

#8

Vertical Line Test or not?

- Each member of the DOMAIN is paired with one and only one member of the RANGE.

#9

Define 1 – to – 1 Function or not?How do you test for one?

#10

#11

Algebraically: or not?Switch x and y……solve for y.Graphically:Reflect over the line y=x (look at your table and switch x & y values)

#11

1.)What or not?notation do we use for Inverse?2.) Functions f and g are inverses of each other if _______ and ________!3.) If point (a,b) lies on f(x)…

#12

SHIFTS or not?Let f(x) = x2

Describe the shift performed to f(x)

- f(x) + a
- f(x) – a
- f(x+a)
- f(x-a)

#13

- f(x) + a = shift ‘a’ units upward or not?
- f(x) – a = shift ‘a’ units down.
- f(x+a) = shift ‘a’ units to the left.
- f(x-a) = shift ‘a’ units to the right.

#13

YELLOW CARD

Divide the exponent by 4. or not?Remainder becomes the new exponent.

#14

#15

- x-axis represents real numbers or not?
- y-axis represents imaginary numbers
- Plot point and draw vector from origin.

#15

How do you identify the NATURE OF THE ROOTS? complex number?

#17

DISCRIMINANT… complex number?

#17

ZERO complex number?

#20

NEGATIVE complex number?

#21

What is the SUM of the roots? complex number?What is the PRODUCT of the roots?

#22

- SUM = complex number?
- PRODUCT =

#22

How do you write a quadratic equation given the roots? complex number?

#23

- Find the SUM of the roots complex number?
- Find the PRODUCT of the roots

#23

Multiplicative Inverse complex number?

#24

- One over what ever is given. complex number?
- Don’t forget to RATIONALIZE
- Ex. Multiplicative inverse of 3 + i

#24

Additive Inverse complex number?

#25

- What you add to, to get 0. complex number?
- Additive inverse of -3 + 4i is
3 – 4i

#25

Inequalities and Absolute Value complex number?

Green card

Solve Absolute Value … complex number?

#26

- Split into 2 branches complex number?
- Only negate what is inside the absolute value on negative branch.
- CHECK!!!!!

#26

Quadratic Inequalities… complex number?

#27

- Factor and find the roots like normal complex number?
- Make sign chart
- Graph solution on a number line (shade where +)

#27

Solve Radical Equations … complex number?

#28

- Isolate the radical complex number?
- Square both sides
- Solve
- CHECK!!!!!!!!!

#28

Rational Expressions complex number?pink card

Multiplying complex number?&Dividing Rational Expressions

#29

- Change Division to Multiplication flip the second fraction complex number?
- Factor
- Cancel (one on top with one on the bottom)

#29

Adding complex number?&Subtracting Rational Expressions

#30

- FIRST change subtraction to addition complex number?
- Find a common denominator
- Simplify
- KEEP THE DENOMINATOR!!!!!!

#30

Rational Equations complex number?

#31

- First find the common denominator complex number?
- Multiply every term by the common denominator
- “KILL THE FRACTION”
- Solve
- Check your answers

#31

Complex Fractions complex number?

#32

- Multiply every term by the common denominator complex number?
- Factor if necessary
- Simplify

#32

Irrational Expressions complex number?

Conjugate complex number?

#33

- Change only the sign of the second term complex number?
- Ex. 4 + 3i
conjugate 4 – 3i

#33

Rationalize the denominator complex number?

#34

- Multiply the numerator and denominator by the CONJUGATE complex number?
- Simplify

#34

Multiplying complex number?&Dividing Radicals

#35

- Multiply/divide the numbers outside the radical together complex number?
- Multiply/divide the numbers in side the radical together

#35

Adding complex number?& Subtracting Radicals

#36

- Only add and subtract “LIKE RADICALS” complex number?
- The numbers under the radical must be the same.
- ADD/SUBTRACT the numbers outside the radical. Keep the radical

#36

Exponents complex number?

- KEEP complex number? (the base)
- ADD (the exponents)

#37

When dividing… complex number? the base& the exponents.

#38

- Keep complex number? (the base)
- SUBTRACT (the exponents)

#38

Power to a power… complex number?

#39

- MULTIPLY complex number? the exponents

#39

Negative Exponents… complex number?

#40

- Reciprocate the base complex number?

#40

Ground Hog Rule complex number?

#41

#41 complex number?

Exponential Equations complex number?y = a(b)xIdentify the meaning of a & b

#42

- Exponential equations occur when the exponent contains a variable
- a = initial amount
- b = growth factor
b > 1 Growth

b < 1 Decay

#42

Name 2 ways to solve an Exponential Equation variable

#43

1. Get a variablecommon base, set the exponents equal2. Take the log of both sides

#43

A typical variableEXPONENTIAL GRAPH looks like…

#44

Horizontal asymptote y = 0 variable

#44

Solving Equations with Fractional Exponents variable

#45

Logarithms variable

Expand variable1) Log (ab) 2) Log(a+b)

#46

1. log(a) + log (b) variable2. Done!

#46

Expand variable1. log (a/b)2. log (a-b)

#47

1. log(a) – log(b) variable2. DONE!!

#47

Expand variable1. logxm

#48

m log x variable

#48

Convert exponential to log form variable23 = 8

#49

#49 variable

Convert log form to exponential form variablelog28 = 3

#50

Follow the arrows. variable

#50

Log Equations variable1. every term has a log2. not all terms have a log

#51

1. Apply log properties and knock out all the logs variable2. Apply log properties condense log equationconvert to exponential and solve

#51

What does a typical logarithmic graph look like? variable

#52

Vertical asymptote at x = 0 variable

#52

Change of Base Formula variableWhat is it used for?

#53

Used to graph logs variable

#53

Probability and Statistics variable

Binomial Theorem variable

#55

Watch your SIGNS!! variable

#55

Summation variable

#56

- "The summation from 1 to 4 of 3 variablen":

#56

Normal Distribution variable

- What percentage lies within 1 S.D.?
- What percentage lies within 2 S.D.?
- What percentage lies within 3 S.D.?

#57

- What percentage lies within 1 S.D.? variable
68%

- What percentage lies within 2 S.D.?
95%

- What percentage lies within 3 S.D.?
99%

#57

Permutation variableor combination

#58

Permutation – order is important variableex: position, placementCombination: order is not importantex: teams,

#58

Mean variable&Standard deviation

#59

Varience variable

#60

Standard deviation squared variable

#60

EXACT TRIG VALUES variable

sin 30 variableorsin

#61

# variable61

sin 60 variableorsin

#62

# variable62

sin 45 variableorsin

#63

# variable63

sin 0 variable

#64

0 variable

#64

sin 90 variableor sin

#65

1 variable

#65

sin 180 variableorsin

#66

0 variable

#66

sin 270 variableor sin

#67

-1 variable

#67

sin 360 variableor sin

#68

0 variable

#68

cos 30 variableor cos

#69

#69 variable

cos 60 variableorcos

#70

# variable70

cos 45 variableor cos

#71

# variable71

cos 0 variable

#72

1 variable

#72

cos 90 variableor cos

#73

0 variable

#73

cos 180 variableor cos

#74

-1 variable

#74

cos 270 variableor cos

#75

0 variable

#75

cos 360 variableor cos

#76

1 variable

#76

tan 30 variableor tan

#77

#77 variable

tan 60 variableor tan

#78

#78 variable

tan 45 variableor tan

#79

1 variable

#79

tan 0 variable

#80

0 variable

#80

tan 90 variableor tan

#81

D.N.E. variableorUndefined

#81

tan 180 variableor tan

#82

0 variable

#82

tan 360 variableor tan

#84

0 variable

#84

Trig Graphs variable

Amplitude variable

#85

Height from the midline variabley = asin(fx)y = -2sinxamp = 2

#85

Frequency variable

#86

How many complete cycles between 0 variableand

#86

Period variable

#87

How long it takes to complete one full cycle variableFormula:

#87

y = sinx variablea) graph b) amplitudec) frequencyd) periode) domain f) range

#88

a) variableb) 1c) 1d)e) all real numbersf)

#88

y = cosx variablea) graph b) amplitudec) frequencyd) periode) domain f) range

#89

a) variableb) 1c) 1d)e) all real numbersf)

#89

y = tan x variablea) graphb) amplitudec) asymptotes at…

#90

- B) multiplies of variable
- Always decreasing

#93

Vertical Shifts variablef(x) = asin(fx) + c

#94

* Identify the vertical shift. variableDraw a ghost sketch of the midline.

amplitude

Freq = 1

1 cycle till 2pi

midline

#94

Horizontal variable Shift f(x) = asin(fx+b) + c

#95

• Horizontal Shifts go in the variableopposite directionSTEPS: Ignore the shift, make a ghost sketch then apply the shift!

Graph y = cos(x-pi) + 3

Now shift your graph over pi and redraw! y = cos(x-pi) + 3

1st graph y = cosx + 3

#95

Trigonometry Identities variable

# variable99

#100 variable

#101 variable

Quotient Identity variable

#102

#102 variable