Pre-calculus
Final Exam Review
Date:
Thursday December 17, 8 a.m. – 11 a.m., Boyer 308
Format:
35 multiple choice questions (2 points each = 70 points total)
5 free response questions (30 points total)
Unit 1: Functions
Solving Equations/Linear Eq./Erroneous solutions
Functions/Function notation
Transformations
Odd/even
Inverses
Compositions
Minimum/maximum
Intervals Increasing/Decreasing
End Behavior
Piecewise Notation
Absolute Value
*Unit 2*: Polynomials and Rational F(x)s
Graphing Parabolas
Solving Quadratic Equations
Definition of Polynomials/degree
Factor Theorem
Remainder Theorem
Graphs   Equation
Solutions by division(long/synthetic)
Rational Functions
Asymptotes(Vertical, Horizontal, Oblique)
Limits (1-sided, 2-sided, continuity)
Unit 3: Exponential/Logarithmic F(x)s
Equation
Graphs (growth/decay)
y = abx vs. Pert
Solving exponential equations with matching bases
Solving exp. Equations on a calculator
Definition of Logarithms (Number bases)
Combining logarithms using properties
Solving Log. Eq. with matching bases
Solving Exponential Eq. using logs, change of base rule
Graphing logs using change of base rule
Modeling Exponential/Logarithmic F(x)s
*Unit 4*: Trigonometry
Pythagorean Theorem
SOHCAHTOA, definition of 6 trig f(x)s
Law of Sines
Law of Cosines
Degrees   Radians
Arc Length
Area of Sector
Unit circle values
Inverse functions
Graphs of 6 trig f(x)s
Modeling trig functions (SinReg)
Identities
Unit 5: Conic Sections
Parabolas, focus, directrix
Circles
Ellipses, foci, major/minor axis
Hyperbolas, foci, oblique asymptotes
Standard Form/completing the square
Polar Coordinates
Polar Graphing
Unit 6: Sequence and Series
Arithmetic/Geometric
Explicit/Recursive
Sigma Notation
Equations for sequences
Sequence Mode on calculators
Sum formulas
Calculator techniques for summation
Infinite series
Binomial expansion
Tables: Pattern for each type of function
Linear (common difference = slope)
x
y
-2
11
-1
8
0
5
1
2
2
-1
3
-4
4
-7
5
-10
2
15
3
28
4
45
5
66
Quadratic (2nd common difference is equal, changes direction once)
x
y
-2
3
-1
0
0
1
1
6
Polynomial (Degree = which common difference is equal)
x
y
-2
-20
-1
3
0
2
1
1
2
24
3
95
4
238
5
477
0
4
1
8
2
16
3
32
4
64
5
128
1
0
2
3
3
4.755
4
6
5
6.966
2
-1.902
3
-1.902
4
-1.176
5
0
Exponential (Common ratio)
x
y
-2
1
-1
2
Logarithmic (Slow growth, concave down)
x
y
-2
Error
-1
Error
0
Error
Trigonometric (Mainly sine/cosine for modeling-periodic)
x
y
-2
1.902
-1
1.176
0
0
1
-1.176
Without doing a regression, decide if this function is linear, polynomial, exponential, logarithmic or
trigonometric. Answer yes or no on the 1st blank, then verify why it is/is not that particular type.
Width at mid-section 3
Height
4
5
6
7
8
1.688 2.531 3.797 5.695 8.543 12.814
Linear? _____Why?________________________________________________
Polynomial?____Why?__________________________________________________
Exponential?____Why?___________________________________________________
Logarithmic?____Why?___________________________________________________
Trigonometric?____Why?____________________________________________________