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Math 3 Flashcards

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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 everyday I will announce ahead ... – PowerPoint PPT presentation

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Title: Math 3 Flashcards


1
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.

2
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?

3
Quadratic Equations
  • Pink Card

4
Vertex Formula
  • What is it good for?

1
5
  • Tells us the x-coordinate of the maximum point
  • Axis of symmetry

1
6
Quadratic Formula
  • What is it good for?

2
7
  • Tells us the roots
  • (x-intercepts).

2
8
Define Inverse Variation
Give a real life example
  • 3

9
  • 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
10
State the General Form of an inverse variation
equation.
  • Draw an example of a typical inverse variation
    and name the graph.

4
11
xy k or .
HYPERBOLA (ROTATED)
4
12
  • General Form of a Circle

5
13
5
14
Identify an Ellipse?
6
15
Unequal Coefficients Plus sign 2 squared terms
6
16
Graph an Ellipse?
7
17
Set equation 1 (h,k) center a horizontal
radius b vertical radius
7
18
Also on back of 7
19
Identify Hyperbola Sketch Hyperbola
8
20
Minus Sign 2 Squared Terms
8
21
FUNCTIONS
  • BLUE CARD

22
Define Domain Define Range
9
23
  • DOMAIN - List of all possible x-values
  • (aka List of what x is allowed to be).
  • RANGE List of all possible y-values.

9
24
  • Test whether a relation (any random equation) is
    a FUNCTION or not?

10
25
Vertical Line Test
  • Each member of the DOMAIN is paired with one and
    only one member of the RANGE.

10
26
Define 1 to 1 Function How do you test for
one?
11
27
1-to-1 Function A function whose inverse is also
a function.
  • Horizontal Line Test

11
28
How do you find an INVERSE Function
ALGEBRAICALLY? GRAPHICALLY?
12
29
Algebraically Switch x and y solve for
y. Graphically Reflect over the line yx
12
30
What notation do we use for Inverse?
  • If point (a,b) lies on f(x)

13
31
Notation
  • then point (b,a) lies on

13
32
  • TRANSFORMATIONS
  • GREEN CARD

33
Define ISOMETRY
  • 14

34
  • A transformation that preserves distance
  • A DILATION is NOT an isometry

14
35
Direct Isometry
  • List all examples

15
36
  • Preserves orientation (the order you read the
    vertices)
  • Translation, rotation

15
37
Opposite Isometry
  • List all examples

16
38
  • Does not preserve orientation
  • Reflections

16
39
f(-x)
  • Identify the action
  • Identify the result

17
40
  • Action Negating x
  • Result Reflection over the y-axis

17
41
-f(x)
  • Identify the action
  • Identify the result

18
42
  • Action negating y
  • Result Reflection over the x-axis

18
43
Instead of memorizing mappings such as
(x,y)?(-y,-x)
19
44
  • 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
45
COMPLEX NUMBERS
  • YELLOW CARD

46
  • Explain how to simplify powers of i

20
47
Divide the exponent by 4. Remainder becomes the
new exponent.
20
48
Describe How to Graph Complex Numbers
21
49
  • x-axis represents real numbers
  • y-axis represents imaginary numbers
  • Plot point and draw vector from origin.

21
50
How do you identify the NATURE OF THE ROOTS?
22
51
DISCRIMINANT
22
52
POSITIVE, PERFECT SQUARE?
23
53
ROOTS Real, Rational, Unequal
  • Graph crosses the x-axis twice.

23
54
  • POSITIVE,
  • NON-PERFECT SQUARE

24
55
ROOTS Real, Irrational, Unequal
  • Graph still crosses x-axis twice

24
56
  • ZERO

25
57
ROOTS Real, Rational, Equal
  • GRAPH IS TANGENT TO THE X-AXIS.

25
58
  • NEGATIVE

26
59
ROOTS IMAGINARY
  • GRAPH NEVER CROSSES THE
  • X-AXIS.

26
60
What is the SUM of the roots? What is the
PRODUCT of the roots?
27
61
  • SUM
  • PRODUCT

27
62
  • How do you write a quadratic equation given the
    roots?

28
63
  • Find the SUM of the roots
  • Find the PRODUCT of the roots

28
64
Multiplicative Inverse
29
65
  • One over what ever is given.
  • Dont forget to RATIONALIZE
  • Ex. Multiplicative inverse of 3 i

29
66
Additive Inverse
30
67
  • What you add to, to get 0.
  • Additive inverse of -3 4i is
  • 3 4i

30
68
  • Inequalities and Absolute Value
  • Pink card

69
  • Solve Absolute Value

31
70
  • Split into 2 branches
  • Only negate what is inside the absolute value on
    negative branch.
  • CHECK!!!!!

31
71
  • Quadratic Inequalities

32
72
  • Factor and find the roots like normal
  • Make sign chart
  • Graph solution on a number line (shade where )

32
73
  • Solve Radical Equations

33
74
  • Isolate the radical
  • Square both sides
  • Solve
  • CHECK!!!!!!!!!

33
75
Probability and Statistics
  • blue card

76
Probability Formula
At least 4 out of 6 At most 2 out of 6
34
77
At least 4 out of 6 4 or 5 or 6 At most
2 2 or 1 or 0
34
78
Binomial Theorem
35
79
Watch your SIGNS!!
35
80
Summation
36
81
  • "The summation from 1 to 4 of 3n"  

36
82
Normal Distribution
  • What percentage lies within 1 S.D.?
  • What percentage lies within 2 S.D.?
  • What percentage lies within 3 S.D.?

37
83
  • 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
84
Rational Expressions green card
85
Multiplying Dividing Rational Expressions
38
86
  • Change Division to Multiplication flip the
    second fraction
  • Factor
  • Cancel (one on top with one on the bottom)

38
87
Adding Subtracting Rational Expressions
39
88
  • FIRST change subtraction to addition
  • Find a common denominator
  • Simplify
  • KEEP THE DENOMINATOR!!!!!!

39
89
Rational Equations
40
90
  • First find the common denominator
  • Multiply every term by the common denominator
  • KILL THE FRACTION
  • Solve
  • Check your answers

40
91
Complex Fractions
41
92
  • Multiply every term by the common denominator
  • Factor if necessary
  • Simplify

41
93
Irrational Expressions
94
Conjugate
42
95
  • Change only the sign of the second term
  • Ex. 4 3i
  • conjugate 4 3i

42
96
Rationalize the denominator
43
97
  • Multiply the numerator and denominator by the
    CONJUGATE
  • Simplify

43
98
Multiplying Dividing Radicals
44
99
  • Multiply/divide the numbers outside the radical
    together
  • Multiply/divide the numbers in side the radical
    together

44
100
Adding Subtracting Radicals
45
101
  • 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
102
Exponents
103
  • When you multiply
  • the base and
  • the exponents

46
104
  • KEEP (the base)
  • ADD (the exponents)

46
105
When dividing the base the exponents.
47
106
  • Keep (the base)
  • SUBTRACT (the exponents)

47
107
Power to a power
48
108
  • MULTIPLY the exponents

48
109
Negative Exponents
49
110
  • Reciprocate the base

49
111
Ground Hog Rule
50
112
50
113
Exponential Equations y a(b)x Identify the
meaning of a b
51
114
  • Exponential equations occur when the exponent
    contains a variable
  • a initial amount
  • b growth factor
  • b gt 1 Growth
  • b lt 1 Decay

51
115
Name 2 ways to solve an Exponential Equation
52
116
1. Get a common base, set the exponents
equal 2. Take the log of both sides
52
117
A typical EXPONENTIAL GRAPH looks like
53
118
Horizontal asymptote y 0
53
119
Solving Equations with Fractional Exponents
54
120
  • Get x by itself.
  • Raise both sides to the reciprocal.

Example
54
121
Logarithms
122
Expand 1) Log (ab) 2) Log(ab)
55
123
1. log(a) log (b) 2. Done!
55
124
Expand 1. log (a/b) 2. log (a-b)
56
125
1. log(a) log(b) 2. DONE!!
56
126
Expand 1. logxm
57
127
m log x
57
128
Convert exponential to log form 23 8
58
129
58
130
Convert log form to exponential form log28 3
59
131
Follow the arrows.
59
132
Log Equations 1. every term has a log 2. not
all terms have a log
60
133
1. Apply log properties and knock out all the
logs 2. Apply log properties condense log
equation convert to exponential and solve
60
134
What does a typical logarithmic graph look like?
61
135
Vertical asymptote at x 0
61
136
Change of Base Formula What is it used for?
62
137
Used to graph logs
62
138
Coordinate Geometry
139
Slope formula What is it? When do you use it?
63
140
  • Used to show lines are PARALLEL (SAME SLOPE)
  • Used to show lines are PERPENDICULAR (Slope are
    opposite reciprocal)

63
141
Distance Formula What is it? What is it used
for?
64
142
Used to show two lines have the same length
64
143
Midpoint Formula What is it? What is it used
for?
65
144
Used to show diagonals bisect each other (THE
MIDDLE)
65
145
EXACT TRIG VALUES
146
sin 30 or sin
66
147
66
148
sin 60 or sin
67
149
67
150
sin 45 or sin
68
151
68
152
sin 0
69
153
0
69
154
sin 90 or sin
70
155
1
70
156
sin 180 or sin
71
157
0
71
158
sin 270 or sin
72
159
-1
72
160
sin 360 or sin
73
161
0
73
162
cos 30 or cos
74
163
74
164
cos 60 or cos
75
165
75
166
cos 45 or cos
76
167
76
168
cos 0
77
169
1
77
170
cos 90 or cos
78
171
0
78
172
cos 180 or cos
79
173
-1
79
174
cos 270 or cos
80
175
0
80
176
cos 360 or cos
81
177
1
81
178
tan 30 or tan
82
179
82
180
tan 60 or tan
83
181
83
182
tan 45 or tan
84
183
  • 1

84
184
tan 0
85
185
  • 0

85
186
  • tan 90 or tan

86
187
D.N.E. or Undefined
86
188
  • tan 180 or tan

87
189
  • 0

87
190
  • tan 270 or
  • tan

88
191
  • D.N.E.
  • Or
  • Undefined

88
192
  • tan 360 or tan

89
193
  • 0

89
194
  • Trigonometry Identities

195
Reciprocal Identity
  • sec

90
196
90
197
Reciprocal Identity
  • csc

91
198
91
199
Reciprocal Identity
  • cot

92
200
92
201
Quotient Identity
93
202
93
203
Trig Graphs
204
Amplitude
94
205
Height from the midline y asin(fx) y
-2sinx amp 2
94
206
Frequency
95
207
How many complete cycles between 0 and
95
208
Period
96
209
How long it takes to complete one full
cycle Formula
96
210
y sinx a) graph b) amplitude c) frequency d)
period e) domain f) range
97
211
a) b) 1 c) 1 d) e) all real numbers f)
97
212
y cosx a) graph b) amplitude c) frequency d)
period e) domain f) range
98
213
a) b) 1 c) 1 d) e) all real numbers f)
98
214
y tan x a) graph b) amplitude c) asymptotes at
99
215
a) b) No amplitude c) Asymptotes are at odd
multiplies of
Graph is always increasing
99
216
y csc x
  • A) graph
  • B) location of the asymptotes

100
217
b) Asymptotes are multiples of
Draw in ghost sketch
100
218
y secx
  • A) graph
  • B) location of the asymptotes

101
219
Draw in ghost sketch
  • B) asymptotes are odd multiples of

101
220
ycotx
  • A) graph
  • B) location of asymptotes

102
221
  • B) multiplies of
  • Always decreasing

102
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