This document is a pre-calculus power point flash drill developed by Susan Cantey and Elizabeth Albert at Walnut Hills H.S. in 2006. It contains over 50 questions testing knowledge of pre-calculus concepts like functions, graphs, trigonometry, logarithms, and algebra to prepare students for success in calculus. The questions cover defining functions, graphing, trig identities, logarithmic properties, and the binomial theorem.

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

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. )()( xfxf =−
Note: It is NOT enough to
know the graph is
symmetric with respect to
the y-axis.

5. Define an
Odd Function

6. )()( xfxf −=−
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. lyrespective
xxf
and
xxf
=
=
)(
)( 2

9. How about these?

10. lyrespective
xxf
and
xxf
3
3
)(
)(
=
=

11. What about this one?
2
π
2
π−

12. xxf 1
tan)( −
=
Did you know it?
You are a tiger!

13. How about these?

14. x
xf
1
)( =
and
222
ryx =+
respectively

15. and finally:

16. lyrespective
xxf
and
exf x
ln)(
)(
=
=

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. x
1

24. ?2/1
=x

25. x

26. ?2
=−
x

27. 2
1
x

28. ?=n m
x

29. n
m
x
Think “flower” & “root”

30. ?ln =n
x

31. xnln

32. ?ln =xy

33. yx lnln +

34. ?ln =
y
x

35. yx lnln −

36. ?
?
log =xb

37. b
x
ln
ln

38. ?
1
ln =





x

39. xln−

40. ?1ln =

41. 0

42. ?ln
=x
e

43. x

44. ?ln =x
e

45. x

46. OK…enough of the logs
already!

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

48. 12
12
xx
yy
x
y
−
−
=
∆
∆

49. Point slope
equation of a
line ?

50. )( 11 xxmyy −=−

51. Midpoint Formula = ?

52. 




 ++
2
,
2
2121 yyxx

53. Distance Formula=?

54. 2
12
2
12 )()( xxyy −+−

55. xDefine:

56. {|x|
x for x 0≥
-x for x<0

57. [ ][ ] ?98.2 =

58. 2(Greatest integer < 2.98)

59. [ ][ ] ?17.2 =−

60. 3−
You always round
down the number line!

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

62. ?0sin =

63. 0

64. ?0cos =

65. 1

66. ?
6
sin =
π

67. 2
1

68. ?
4
sin =
π

69. 2
2
2
1
or

70. ?
3
sin =
π

71. 2
3

72. ?
2
sin =
π

73. 1

74. ?
2
cos =
π

75. 0

76. ?
3
cos =
π

77. 2
1

78. ?
4
cos =
π

79. 2
2
2
1
or

80. ?
6
cos =
π

81. 2
3

82. ?cos =π

83. 1−

84. ?0tan =

85. 0

86. ?
4
tan =
π

87. 1
4
sin
4
cos
ππ
=because:

88. ?
2
tan =
π

89. ∞(or undefined)

90. ?
3
tan =
π

91. 3

92. ?
6
tan =
π

93. 3
1
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. [ ]






−






−
2
,
2
2
,
2
,0
ππ
ππ
π for cosine
for sine
for tangent
(Different texts assign different principle
domains to the other three trig
functions, so we won’t bother with
them.)

96. ?
2
1
sin 1
=−

97. 6
π

98. ?
2
1
cos 1
=




 −−

99. 4
3π

100. ?
2
3
sin 1
=−

101. 3
π

102. ?1tan 1
=−

103. sine and cosine
have to be equal!
4
π

104. ( ) ?3tan 1
=−−

105. 3
1
3
1
0
3
1−
1−
3−
Answer:
3
π−
∞
∞−

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

107. ?cossin 22
=+ xx

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

109. ?sin2
=x

110. x2
cos1−
OK, that’s really the same one!

111. ?sin2
=x
What’s the one with the ½’s in it?

112. x2cos2
1
2
1
−
That one is harder, but you will
need it in calculus!

113. ?cos2
=x
Do you know both of them?

114. x
and
x
2cos
sin1
2
1
2
1
2
+
−
You rock!!!

115. ?tan1 2
=+ x

116. x2
sec
Did ya get the ol’
“stamp of approval”
on that one?

117. ?1sec2
=−x

118. x2
tan
They’re laughing
because this is
really the same
one again!

119. ?sincos 22
=− xx
Ho Ho Ho!!

120. x2cos
I don’t know why Santa thought
this was funny!

121. ?2sin =x

122. xxcossin2
This one is very important!!

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

124. ?22
=−ba

125. ( )( )baba −+

126. ?33
=−ba

127. ( )( )22
bababa ++−
Notice there is NO “2”

128. ?33
=+ ba

129. ( )( )22
bababa +−+
Still no 2!!!

130. ?)( 2
=+ ba
(almost finished!!!)

131. 22
2 baba ++
There’s that two you wanted before!!

132. Last one!!!!
( )3
ba +

133. 3223
33 babbaa +++
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!