This document is a powerpoint presentation that serves as a pre-calculus review quiz covering topics like: - Definitions of even and odd functions - Identifying graphs of simple functions like f(x)=x^2 - Logarithmic and trigonometric identities and properties - Trigonometric function values for common angles - Algebraic identities for expanding expressions like (a+b)^3 The presentation is interactive, asking questions and providing feedback on slides to test the user's knowledge of important pre-calculus concepts needed for success in calculus. It concludes by stating if the user knows this material, they are prepared to begin studying calculus.

1. Welcome to the
Pre-Calculus
Power Point
Flash Drill!
Developed by Susan Cantey
and student Elizabeth Albert
at Walnut Hills H.S.
2006

2. I’m going to ask you a lot of questions about math.
These are facts that you should know extremely
well. You also need to be able to recall them
quickly if you want to succeed in Calculus.
When you think you know the answer,
(or if you give up ) click to get to the
next slide to see if you were correct.
Ready?

3. Define an
Even Function

4. f ( x) f ( x)
Note: It is NOT enough to
know the graph is
symmetric with respect to
the y-axis.

5. Define an
Odd Function

6. f ( x) f ( x)
Again, please note that it
is NOT enough to know
that the graph has origin
symmetry.

7. See if you can identify the
function that probably goes
with each of these simple
graphs….

8. 2
f ( x) x
and
f ( x) x
respectively

9. How about these?

10. 3
f ( x) x
and
3
f ( x) x
respectively

11. What about this one?
2
2

12. 1
f ( x) tan x
Did you know it?
You are a tiger!

13. How about these?

14. 1
f ( x)
x
and
2 2 2
x y r
respectively

15. and finally:

16. x
f ( x) e
and
f ( x ) ln x
respectively

17. The graph
of x = a
is…

18. … a vertical line.

19. The graph
of y = a
is…

20. … a horizontal line.

21. OK…that’s enough about
graphs!
Let’s move on…

22. 1
x ?

23. 1
x

24. 1/ 2
x ?

25. x

26. 2
x ?

27. 1
2
x

28. n m
x ?

29. m
x n
Think “flower” & “root”

30. n
ln x ?

31. n ln x

32. ln xy ?

33. ln x ln y

34. x
ln ?
y

35. ln x ln y

36. ?
log b x
?

37. ln x
ln b

38. 1
ln ?
x

39. ln x

40. ln 1 ?

41. 0

42. ln x
e ?

43. x

44. x
ln e ?

45. x

46. OK…enough of the logs
already!

47. The formula for
the slope of a
line is
m=?

48. y y2 y1
x x2 x1

49. Point slope
equation of a
line ?

50. y y1 m( x x1 )

51. Midpoint Formula = ?

52. x1 x2 y1 y2
,
2 2

53. Distance Formula=?

54. 2 2
( y2 y1 ) ( x2 x1 )

55. Define: x

56. x for x 0
|x|
-x for x<0

57. 2.98 ?

58. 2
(Greatest integer < 2.98)

59. 2.17 ?

60. 3
You always round
down the number line!

61. Here comes your favorite
thing!
Yeah! Trigonometry!

62. sin 0 ?

63. 0

64. cos0 ?

65. 1

66. sin ?
6

67. 1
2

68. sin ?
4

69. 1 2
or
2 2

70. sin ?
3

71. 3
2

72. sin ?
2

73. 1

74. cos ?
2

75. 0

76. cos ?
3

77. 1
2

78. cos ?
4

79. 1 2
or
2 2

80. cos ?
6

81. 3
2

82. cos ?

83. 1

84. tan 0 ?

85. 0

86. tan ?
4

87. 1
because: cos sin
4 4

88. tan ?
2

89. (or undefined)

90. tan ?
3

91. 3

92. tan ?
6

93. 1 3
or
3 3

94. What are the Principle
domains of the 6 trig
functions?
That is, what quadrants are the
angles in which can be used to
answer inverse trig function
problems?

95. 0, for cosine
, for sine
2 2
, for tangent
2 2
(Different texts assign different principle
domains to the other three trig functions,
so we won’t bother with them.)

96. 1 1
sin ?
2

97. 6

98. 1 1
cos ?
2

99. 3
4

100. 1 3
sin ?
2

101. 3

102. 1
tan 1 ?

103. sine and cosine
have to be equal!
4

104. 1
tan 3 ?

105. 3
11
3
0
1
3
1
3
Answer:
3

106. OK…now let’s see if you know your
identities!

107. 2 2
sin x cos x ?

108. 1
I hope you knew that one!!!

109. 2
sin x ?

110. 2
1 cos x
OK, that’s really the same one!

111. What’s the one with the ½’s in it?
2
sin x ?

112. 1 1
2 2 cos 2 x
That one is harder, but you will
need it in calculus!

113. 2
cos x ?
Do you know both of them?

114. 2
1 sin x
and
You rock!!!
1 1
2 2 cos 2 x

115. 2
1 tan x ?

116. 2
sec x
Did ya get the ol’
“stamp of approval”
on that one?

117. 2
sec x 1 ?

118. 2
tan x
They’re laughing
because this is
really the same
one again!

119. 2 2
cos x sin x ?
Ho Ho Ho!!

120. cos2x
I don’t know why Santa thought
this was funny!

121. sin 2x ?

122. 2 sin xcos x
This one is very important!!

123. Now for a little algebra and you’ll be done!!

124. 2 2
a b ?

125. a b a b

126. 3 3
a b ?

127. 2 2
a b a ab b
Notice there is NO “2”

128. 3 3
a b ?

129. 2 2
a b a ab b
Still no 2!!!

130. 2
( a b) ?
(almost finished!!!)

131. 2 2
a 2ab b
There’s that two you wanted before!!

132. Last one!!!!
3
a b

133. 3 2 2 3
a 3a b 3ab b
Don’t be foiled!
Use the
binomial
Theorem.

134. If you know all this material,
then you are prepared to begin
calculus… All you need now is a
sharp mind, a sharp pencil and
a really big eraser!

135. GOODBYE!!!!
ADIOS!
AUFWIEDESEHEN!
CHOW!