Download presentation
Presentation is loading. Please wait.
Published byBrice Wheeler Modified over 9 years ago
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 everyday…I 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 #3 Give a real life example
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
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 y=x #12
30
What notation do we use for Inverse? If point (a,b) lies on f(x)… #13
31
…then point (b,a) lies on Notation: #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
#23 POSITIVE, PERFECT SQUARE?
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. Don’t 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… #34 At least 4 out of 6 At most 2 out of 6
77
At least 4 out of 6 4or5or6 At most 2 2or1 or0 #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
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 > 1 Growth b < 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(a+b) #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. logx m #57
127
m log x #57
128
Convert exponential to log form 2 3 = 8 #58
130
Convert log form to exponential form log 2 8 = 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
148
sin 60 or sin #67
150
sin 45 or sin #68
152
sin 0 #69
153 0
154
sin 90 or sin #70
155
1
156
sin 180 or sin #71
157 0
158
sin 270 or sin #72
159
#72
160
sin 360 or sin #73
161 0
162
cos 30 or cos #74
164
cos 60 or cos #75
166
cos 45 or cos #76
168
cos 0 #77
169
1
170
cos 90 or cos #78
171 0
172
cos 180 or cos #79
173
#79
174
cos 270 or cos #80
175 0
176
cos 360 or cos #81
177
1
178
tan 30 or tan #82
180
tan 60 or tan #83
182
tan 45 or tan #84
183
1
184
tan 0 #85
185 0
186
tan 90 or tan #86
187
D.N.E. or Undefined #86
188
tan 180 or tan #87
189 0
190
tan 270 or tan #88
191
D.N.E. Or Undefined #88
192
tan 360 or tan #89
193 0
194
Trigonometry Identities
195
Reciprocal Identity sec = #90
197
Reciprocal Identity csc = #91
199
cot = Reciprocal Identity #92
201
Quotient Identity #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
B) asymptotes are odd multiples of Draw in ghost sketch #101
220
y=cotx A) graph B) location of asymptotes #102
221
B) multiplies of Always decreasing #102
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.