1. 
prerequisites: language of mathematics essentials

2. 
prerequisites: function review; difference quotients

3. 
solving linear inequalities in one variable

4. 
solving nonlinear inequalities in one variable (introduction)

5. 
the test point method for sentences like ‘$f(x) \gt 0$’

6. 
the test point method for sentences like ‘$f(x) \gt g(x)$’

7. 
the test point method ‘in a nutshell’ and additional practice

8. 
absolute value as distance from zero

9. 
absolute value as distance between two numbers

10. 
circles and the ‘completing the square’ technique

11. 
review of lines and slopes of lines

12. 
distance between points; the midpoint formula

13. 
sketching regions in the coordinate plane

14. 
testing equations for symmetry

15. 
more on difference quotients

16. 
finding the domain and range of a function

17. 
working with linear functions: finding a new point, given a point and a slope

18. 
increasing and decreasing functions

19. 
reading information from the graph of a function

20. 
basic function models you must know

21. 
piecewisedefined functions

22. 
direct and inverse variation

23. 
proportionality problems

24. 
What is the graph of $\,y = f(x)\,$?

25. 
shifting graphs up/down/left/right

26. 
horizontal and vertical stretching/shrinking

27. 
reflecting about axes, and the absolute value transformation

28. 
multistep practice with all the graphical transformations

29. 
even and odd functions

30. 
extreme values of functions (max/min)

31. 
review of quadratic functions: vertex form, max/min, intercepts, more

32. 
max/min problems resulting in quadratic functions

33. 
combining functions to get new functions

34. 
composition of functions

35. 
writing a function as a composition

36. 
using a function box ‘backwards’

37. 
onetoone functions

38. 
‘undoing’ a onetoone function; inverse functions

39. 
properties of inverse functions

40. 
finding inverse functions (when there's only one $x$ in the formula)

41. 
finding inverse functions (switch input/output names method)

42. 
the graph of an inverse function

43. 
introduction to polynomials

44. 
relationship between the zeros (roots) and factors of polynomials

45. 
end behavior of polynomials

46. 
turning points of polynomials

47. 
long division of polynomials

48. 
the division algorithm

49. 
synthetic division

50. 
the remainder theorem

51. 
‘trapping’ the roots of a polynomial;
an interval guaranteed to contain all real roots

52. 
introduction to complex numbers

53. 
arithmetic with complex numbers

54. 
the square root of a negative number

55. 
the complex conjugate

56. 
the quadratic formula revisited; the discriminant

57. 
multiplicity of zeros and graphical consequences

58. 
discussion: graphing polynomials with technology (optional; no exercises)

59. 
Solve an equation? Find a zero? Your choice!

60. 
the fundamental theorem of algebra

61. 
polynomials with real number coefficients

62. 
solving polynomial equations

63. 
introduction to rational functions

64. 
introduction to asymptotes

65. 
introduction to puncture points (holes)

66. 
finding vertical asymptotes

67. 
finding ‘puncture points’ of graphs

68. 
finding horizontal asymptotes

69. 
finding slant asymptotes

70. 
exponential functions: review and additional properties

71. 
linear versus exponential functions

72. 
recognizing linear and exponential behavior from tables of data

73. 
the natural exponential function

74. 
introduction to average rate of change

75. 
introduction to instantaneous rate of change and tangent lines

76. 
a special property of the natural exponential function

77. 
(optional)
a surprising appearance of the irrational number e ; diluting a toxic liquid

78. 
simple versus compound interest

79. 
continuous compounding

80. 
logarithmic functions: review and additional properties

81. 
logarithm summary: properties, formulas, laws

82. 
exponential growth and decay: introduction

83. 
exponential growth and decay: relative growth rate

84. 
solving exponential equations

85. 
solving logarithmic equations

86. 
solving exponential growth and decay problems

87. 
doubling time, halflife

88. 
introduction to trigonometry

89. 
the right triangle approach to trigonometry

90. 
the unit circle approach to trigonometry

91. 
compatibility of the right triangle and unit circle approaches

92. 
special triangles and common trigonometric values

93. 
reference angles

94. 
radian measure: associating real numbers with points on the unit circle

95. 
the trigonometric functions

96. 
signs of all the trigonometric functions

97. 
trigonometric values of special angles

98. 
fundamental trigonometric identities

99. 
periodic functions

100. 
the period of a periodic function

101. 
graphs of sine and cosine

102. 
graphing generalized sine and cosines, like $y = a\sin k(x\pm b)$ and $y = a\cos (kx\pm B)$

103. 
amplitude, period, and phase shift

104. 
given amplitude, period, and phase shift, write an equation

105. 
graph of the tangent function

106. 
graph of the secant function

107. 
review of circles (and related concepts)

108. 
length of a circular arc (and related concepts)

109. 
(optional) the angle subtended by a geometric object at an external point

110. 
area of a circular sector

111. 
sine and cosine as scaling factors of hypotenuse

112. 
area of a triangle

113. 
law of sines

114. 
Given two sides and a nonincluded angle, how many triangles?

115. 
law of cosines

116. 
(optional) revisiting ‘equal’ versus ‘approximately equal’

117. 
using the Law of Cosines in the SSS case (& introduction to the arccosine function)

118. 
summary: solving triangles (all types)

119. 
verifying trigonometric identities

120. 
addition and subtraction formulas for sine and cosine

121. 
doubleangle formulas for sine and cosine

122. 
trying to ‘undo’ trigonometric functions

123. 
inverse trigonometric function: arcsine

124. 
inverse trigonometric function: arccosine

125. 
inverse trigonometric function: arctangent

126. 
inverse trigonometric function problems: all mixed up

127. 
solving simple trigonometric equations

128. 
solving pseudoquadratic equations

129. 
introduction to vectors

130. 
working with the arrow representation for vectors

131. 
working with the analytic representation for vectors

132. 
unit vectors

133. 
formula for the length of a vector

134. 
vectors: from direction/magnitude to horizontal/vertical components

135. 
vectors: from horizontal/vertical components to direction/magnitude

136. 
vector application: finding true speed and direction

137. 
vector application: forces acting an an object in equilibrium

138. 
introduction to partial fraction expansion/decomposition (PFE)

139. 
PFE: linear factors

140. 
PFE: irreducible quadratic factors

141. 
introduction to conic sections

142. 
identifying conics by the discriminant

143. 
(optional)
intersecting an infinite double cone and a plane: looking at the equations

144. 
(optional)
How is it that the conic discriminant tells us the type of conic?

145. 
parabolas: definition, reflectors/collectors, derivation of equations

146. 
finding the equation of a parabola

147. 
definition of an ellipse

148. 
reflecting property of an ellipse

149. 
equations of ellipses in standard form: foci on the $\,x$axis

150. 
(optional) getting an ellipse by stretching/shrinking a circle

151. 
(optional) two useful transforms: reflection about the line $\,y = x\,$ and counterclockwise rotation by $\,90^\circ$

152. 
equations of ellipses in standard form: foci on the $\,y$axis

153. 
summary: equations of ellipses in standard form

154. 
definition of a hyperbola

155. 
equations of hyperbolas in standard form

156. 
graphing hyperbolas

157. 
reflecting property of a hyperbola

158. 
shifting conics (shifting any equation in two variables)

159. 
polar coordinates
