1. Algebra II TRIG Flashcards
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.

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 (Axis of Symmetry)
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. Describe the Steps for “Completing the Square”
How does it compare to the quadratic formula? #3

9. 1. ) Leading Coeff = 1 (Divide if necessary) 2. ) Move ‘c’ over 3
1.) Leading Coeff = 1 (Divide if necessary) 2.) Move ‘c’ over 3.) 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

10. General Form for DIRECT VARIATION Characteristics & Sketch#4

11. General Form: y = kx Characteristics: y –int = 0 (always
General Form: y = kx Characteristics: y –int = 0 (always!) Sketch: (any linear passing through the origin) #4

12. Define Inverse Variation
Give a real life example #5

13. 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

14. State the General Form of an inverse variation equation.
Draw an example of a typical inverse variation and name the graph. #6

15. xy = k or
HYPERBOLA (ROTATED) #6

16. General Form of a Circle#7

17. #7

18. FUNCTIONS
BLUE CARD

19. Define Domain Define Range#8

20. DOMAIN - List of all possible x-values
(aka – List of what x is allowed to be).
RANGE – List of all possible y-values. #8

21. Test whether a relation (any random equation) is a FUNCTION or not?#9

22. Vertical Line Test
Each member of the DOMAIN is paired with one and only one member of the RANGE. #9

23. Define 1 – to – 1 Function How do you test for one?
#10

24. 1-to-1 Function: A function whose inverse is also a function.
Horizontal Line Test
#10

25. How do you find an INVERSE Function… ALGEBRAICALLY? GRAPHICALLY?
#11

26. Algebraically:. Switch x and y…. …solve for y. Graphically:
Algebraically: Switch x and y… …solve for y. Graphically: Reflect over the line y=x (look at your table and switch x & y values)
#11

27. 1. )What notation do we use for. Inverse. 2. ) Functions f and g are
1.)What 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

28. 2.) f(g(x)) = x and g(f(x)) = x 3.) …then point (b,a) lies on
1.) Notation:
2.) f(g(x)) = x and g(f(x)) = x
3.) …then point (b,a) lies on
#12

29. Describe the shift performed to f(x) f(x) + a f(x) – a f(x+a) f(x-a)
SHIFTS Let f(x) = x2
Describe the shift performed to f(x)
f(x) + a
f(x) – a
f(x+a)
f(x-a)
#13

30. f(x) + a = shift ‘a’ units upward
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

31. COMPLEX NUMBERS
YELLOW CARD

32. Explain how to simplify
powers of i
#14

33. Divide the exponent by 4. Remainder becomes the new exponent.
#14

34. Describe How to Graph Complex Numbers
#15

35. #15 x-axis represents real numbers y-axis represents imaginary numbers
Plot point and draw vector from origin.
#15

36. How do you evaluate the ABSOLUTE VALUE (Magnitude) of a complex number?
|a + bi| |2 – 5i|
#16

37. Pythagorean Theorem
|a + bi| = a2 + b2 = c2
|5 – 12i| = 13
#16

38. How do you identify the NATURE OF THE ROOTS?
#17

39. DISCRIMINANT…
#17

40. POSITIVE,
PERFECT SQUARE?
#18

41. ROOTS = Real, Rational, Unequal
Graph crosses the x-axis twice.
#18

42. POSITIVE,
NON-PERFECT SQUARE
#19

43. ROOTS = Real, Irrational, Unequal
Graph still crosses x-axis twice
#19

44. ZERO
#20

45. ROOTS = Real, Rational, Equal
GRAPH IS TANGENT TO THE X-AXIS.
#20

46. NEGATIVE
#21

47. GRAPH NEVER CROSSES THE
ROOTS = IMAGINARY
GRAPH NEVER CROSSES THE
X-AXIS.
#21

48. What is the SUM of the roots? What is the PRODUCT of the roots?
#22

49. SUM =
PRODUCT =
#22

50. How do you write a quadratic equation given the roots?
#23

51. Find the SUM of the roots Find the PRODUCT of the roots
#23

52. Multiplicative Inverse
#24

53. #24 One over what ever is given. Don’t forget to RATIONALIZE
Ex. Multiplicative inverse of 3 + i
#24

54. Additive Inverse
#25

55. What you add to, to get 0.
Additive inverse of i is
3 – 4i
#25

56. Inequalities and Absolute Value
Green card

57. Solve Absolute Value …
#26

58. Split into 2 branches
Only negate what is inside the absolute value on negative branch.
CHECK!!!!!
#26

59. Quadratic Inequalities…
#27

60. Factor and find the roots like normal
Make sign chart
Graph solution on a number line (shade where +)
#27

61. Solve Radical Equations …
#28

62. Isolate the radical
Square both sides
Solve
CHECK!!!!!!!!!
#28

63. Rational Expressions pink card

64. Multiplying & Dividing Rational Expressions
#29

65. #29 Change Division to Multiplication flip the second fraction Factor
Cancel (one on top with one on the bottom)
#29

66. Adding & Subtracting Rational Expressions
#30

67. #30 FIRST change subtraction to addition Find a common denominator
Simplify
KEEP THE DENOMINATOR!!!!!!
#30

68. Rational Equations
#31

69. #31 First find the common denominator
Multiply every term by the common denominator
“KILL THE FRACTION”
Solve
Check your answers
#31

70. Complex Fractions
#32

71. Multiply every term by the common denominator
Factor if necessary
Simplify
#32

72. Irrational Expressions

73. Conjugate
#33

74. Change only the sign of the second term
Ex i
conjugate 4 – 3i
#33

75. Rationalize the denominator
#34

76. Multiply the numerator and denominator by the CONJUGATE
Simplify
#34

77. Multiplying & Dividing Radicals
#35

78. #35 Multiply/divide the numbers outside the radical together
Multiply/divide the numbers in side the radical together
#35

79. Adding & Subtracting Radicals
#36

80. #36 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
#36

81. Exponents

82. When you multiply…
the base and
the exponents
#37

83. KEEP (the base)
ADD (the exponents)
#37

84. When dividing… the base & the exponents.
#38

85. Keep (the base)
SUBTRACT (the exponents)
#38

86. Power to a power…
#39

87. MULTIPLY the exponents
#39

88. Negative Exponents…
#40

89. Reciprocate the base
#40