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Math 3 Flashcards

- As the year goes on we will add more and more

flashcards to our collection. You do not need to

bring them to class everydayI will announce

ahead of time when you need to bring them. - Your flashcards will be collected at the end of

the third and fourth quarters for a grade. 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

Vertex Formula

- What is it good for?

1

- Tells us the x-coordinate of the maximum point
- Axis of symmetry

1

Quadratic Formula

- What is it good for?

2

- Tells us the roots
- (x-intercepts).

2

Define Inverse Variation

Give a real life example

- 3

- The PRODUCT of two variables will always be the

same (constant). - Example
- The speed, s, you drive and the time, t, it takes

for you to get to Rochester.

3

State the General Form of an inverse variation

equation.

- Draw an example of a typical inverse variation

and name the graph.

4

xy k or .

HYPERBOLA (ROTATED)

4

- General Form of a Circle

5

5

Identify an Ellipse?

6

Unequal Coefficients Plus sign 2 squared terms

6

Graph an Ellipse?

7

Set equation 1 (h,k) center a horizontal

radius b vertical radius

7

Also on back of 7

Identify Hyperbola Sketch Hyperbola

8

Minus Sign 2 Squared Terms

8

FUNCTIONS

- BLUE CARD

Define Domain Define Range

9

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

9

- Test whether a relation (any random equation) is

a FUNCTION or not?

10

Vertical Line Test

- Each member of the DOMAIN is paired with one and

only one member of the RANGE.

10

Define 1 to 1 Function How do you test for

one?

11

1-to-1 Function A function whose inverse is also

a function.

- Horizontal Line Test

11

How do you find an INVERSE Function

ALGEBRAICALLY? GRAPHICALLY?

12

Algebraically Switch x and y solve for

y. Graphically Reflect over the line yx

12

What notation do we use for Inverse?

- If point (a,b) lies on f(x)

13

Notation

- then point (b,a) lies on

13

- TRANSFORMATIONS
- GREEN CARD

Define ISOMETRY

- 14

- A transformation that preserves distance
- A DILATION is NOT an isometry

14

Direct Isometry

- List all examples

15

- Preserves orientation (the order you read the

vertices) - Translation, rotation

15

Opposite Isometry

- List all examples

16

- Does not preserve orientation
- Reflections

16

f(-x)

- Identify the action
- Identify the result

17

- Action Negating x
- Result Reflection over the y-axis

17

-f(x)

- Identify the action
- Identify the result

18

- Action negating y
- Result Reflection over the x-axis

18

Instead of memorizing mappings such as

(x,y)?(-y,-x)

19

- Just plug the point (4,1) into the mapping and

plot the points to identify the transformation - (x,y)?(-y,-x)
- (4,1) ?(-1,-4)

19

COMPLEX NUMBERS

- YELLOW CARD

- Explain how to simplify powers of i

20

Divide the exponent by 4. Remainder becomes the

new exponent.

20

Describe How to Graph Complex Numbers

21

- x-axis represents real numbers
- y-axis represents imaginary numbers
- Plot point and draw vector from origin.

21

How do you identify the NATURE OF THE ROOTS?

22

DISCRIMINANT

22

POSITIVE, PERFECT SQUARE?

23

ROOTS Real, Rational, Unequal

- Graph crosses the x-axis twice.

23

- POSITIVE,
- NON-PERFECT SQUARE

24

ROOTS Real, Irrational, Unequal

- Graph still crosses x-axis twice

24

- ZERO

25

ROOTS Real, Rational, Equal

- GRAPH IS TANGENT TO THE X-AXIS.

25

- NEGATIVE

26

ROOTS IMAGINARY

- GRAPH NEVER CROSSES THE
- X-AXIS.

26

What is the SUM of the roots? What is the

PRODUCT of the roots?

27

- SUM
- PRODUCT

27

- How do you write a quadratic equation given the

roots?

28

- Find the SUM of the roots
- Find the PRODUCT of the roots

28

Multiplicative Inverse

29

- One over what ever is given.
- Dont forget to RATIONALIZE
- Ex. Multiplicative inverse of 3 i

29

Additive Inverse

30

- What you add to, to get 0.
- Additive inverse of -3 4i is
- 3 4i

30

- Inequalities and Absolute Value
- Pink card

- Solve Absolute Value

31

- Split into 2 branches
- Only negate what is inside the absolute value on

negative branch. - CHECK!!!!!

31

- Quadratic Inequalities

32

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

32

- Solve Radical Equations

33

- Isolate the radical
- Square both sides
- Solve
- CHECK!!!!!!!!!

33

Probability and Statistics

- blue card

Probability Formula

At least 4 out of 6 At most 2 out of 6

34

At least 4 out of 6 4 or 5 or 6 At most

2 2 or 1 or 0

34

Binomial Theorem

35

Watch your SIGNS!!

35

Summation

36

- "The summation from 1 to 4 of 3n"

36

Normal Distribution

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

37

- What percentage lies within 1 S.D.?
- 68
- What percentage lies within 2 S.D.?
- 95
- What percentage lies within 3 S.D.?
- 99

37

Rational Expressions green card

Multiplying Dividing Rational Expressions

38

- Change Division to Multiplication flip the

second fraction - Factor
- Cancel (one on top with one on the bottom)

38

Adding Subtracting Rational Expressions

39

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

39

Rational Equations

40

- First find the common denominator
- Multiply every term by the common denominator
- KILL THE FRACTION
- Solve
- Check your answers

40

Complex Fractions

41

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

41

Irrational Expressions

Conjugate

42

- Change only the sign of the second term
- Ex. 4 3i
- conjugate 4 3i

42

Rationalize the denominator

43

- Multiply the numerator and denominator by the

CONJUGATE - Simplify

43

Multiplying Dividing Radicals

44

- Multiply/divide the numbers outside the radical

together - Multiply/divide the numbers in side the radical

together

44

Adding Subtracting Radicals

45

- Only add and subtract LIKE RADICALS
- The numbers under the radical must be the same.
- ADD/SUBTRACT the numbers outside the radical.

Keep the radical

45

Exponents

- When you multiply
- the base and
- the exponents

46

- KEEP (the base)
- ADD (the exponents)

46

When dividing the base the exponents.

47

- Keep (the base)
- SUBTRACT (the exponents)

47

Power to a power

48

- MULTIPLY the exponents

48

Negative Exponents

49

- Reciprocate the base

49

Ground Hog Rule

50

50

Exponential Equations y a(b)x Identify the

meaning of a b

51

- Exponential equations occur when the exponent

contains a variable - a initial amount
- b growth factor
- b gt 1 Growth
- b lt 1 Decay

51

Name 2 ways to solve an Exponential Equation

52

1. Get a common base, set the exponents

equal 2. Take the log of both sides

52

A typical EXPONENTIAL GRAPH looks like

53

Horizontal asymptote y 0

53

Solving Equations with Fractional Exponents

54

- Get x by itself.
- Raise both sides to the reciprocal.

Example

54

Logarithms

Expand 1) Log (ab) 2) Log(ab)

55

1. log(a) log (b) 2. Done!

55

Expand 1. log (a/b) 2. log (a-b)

56

1. log(a) log(b) 2. DONE!!

56

Expand 1. logxm

57

m log x

57

Convert exponential to log form 23 8

58

58

Convert log form to exponential form log28 3

59

Follow the arrows.

59

Log Equations 1. every term has a log 2. not

all terms have a log

60

1. Apply log properties and knock out all the

logs 2. Apply log properties condense log

equation convert to exponential and solve

60

What does a typical logarithmic graph look like?

61

Vertical asymptote at x 0

61

Change of Base Formula What is it used for?

62

Used to graph logs

62

Coordinate Geometry

Slope formula What is it? When do you use it?

63

- Used to show lines are PARALLEL (SAME SLOPE)
- Used to show lines are PERPENDICULAR (Slope are

opposite reciprocal)

63

Distance Formula What is it? What is it used

for?

64

Used to show two lines have the same length

64

Midpoint Formula What is it? What is it used

for?

65

Used to show diagonals bisect each other (THE

MIDDLE)

65

EXACT TRIG VALUES

sin 30 or sin

66

66

sin 60 or sin

67

67

sin 45 or sin

68

68

sin 0

69

0

69

sin 90 or sin

70

1

70

sin 180 or sin

71

0

71

sin 270 or sin

72

-1

72

sin 360 or sin

73

0

73

cos 30 or cos

74

74

cos 60 or cos

75

75

cos 45 or cos

76

76

cos 0

77

1

77

cos 90 or cos

78

0

78

cos 180 or cos

79

-1

79

cos 270 or cos

80

0

80

cos 360 or cos

81

1

81

tan 30 or tan

82

82

tan 60 or tan

83

83

tan 45 or tan

84

- 1

84

tan 0

85

- 0

85

- tan 90 or tan

86

D.N.E. or Undefined

86

- tan 180 or tan

87

- 0

87

- tan 270 or
- tan

88

- D.N.E.
- Or
- Undefined

88

- tan 360 or tan

89

- 0

89

- Trigonometry Identities

Reciprocal Identity

- sec

90

90

Reciprocal Identity

- csc

91

91

Reciprocal Identity

- cot

92

92

Quotient Identity

93

93

Trig Graphs

Amplitude

94

Height from the midline y asin(fx) y

-2sinx amp 2

94

Frequency

95

How many complete cycles between 0 and

95

Period

96

How long it takes to complete one full

cycle Formula

96

y sinx a) graph b) amplitude c) frequency d)

period e) domain f) range

97

a) b) 1 c) 1 d) e) all real numbers f)

97

y cosx a) graph b) amplitude c) frequency d)

period e) domain f) range

98

a) b) 1 c) 1 d) e) all real numbers f)

98

y tan x a) graph b) amplitude c) asymptotes at

99

a) b) No amplitude c) Asymptotes are at odd

multiplies of

Graph is always increasing

99

y csc x

- A) graph
- B) location of the asymptotes

100

b) Asymptotes are multiples of

Draw in ghost sketch

100

y secx

- A) graph
- B) location of the asymptotes

101

Draw in ghost sketch

- B) asymptotes are odd multiples of

101

ycotx

- A) graph
- B) location of asymptotes

102

- B) multiplies of
- Always decreasing

102