HPC
Final Exam Expectations
MATH FINAL
Thursday, December 17, 2015
8:15 – 9:45
Chapter 2: Polynomial and Rational Functions
 Sec. 2.1 Analyze graphs of quadratic functions.
 Sec. 2.2 Analyze graphs of polynomial functions. Use information about end
behavior, the leading coefficient test, zeros and their multiplicities to graph without a
calculator. Determine the equation of a cubic function given its zeros.
 Sec. 2.3 Determine rational zeros of polynomials functions. Use long and/or synthetic
division to determine the zeros of a function.
 Sec. 2.4 Perform operations with complex numbers and plot complex numbers.
 Sec. 2.5 Determine real and complex zeros of polynomials by graphing, factoring,
quadratic formula, rational zero test, and synthetic division
 Sec. 2.6 Determine domains and asymptotes of rational functions. Write equations
for horizontal, vertical, and slant asymptotes. Write coordinates for holes, x- and yintercepts.
Chapter 3: Exponential and Logarithmic Functions
 Sec. 3.1 Graph exponential functions and their transformations. Use exponential
functions to model and solve real-life problems. Apply compound interest formulas.
 Sec. 3.2 Graph logarithmic functions and their transformations. Use logarithmic
functions to model and solve real-life problems. Evaluate logarithmic expressions
using properties of logarithms including natural logarithms.
 Sec. 3.3 Rewrite logarithms with different bases. Use logarithmic properties to
evaluate, rewrite, expand, and condense logarithmic expressions. These properties
include: change of base, quotient, power, and product properties.
 Sec. 3.4 Use exponential and logarithmic equations to model and solve real-world
problems.
 Sec. 3.5 Recognize and apply the five most common types of equations using
exponential and logarithmic functions.
Chapter 4: Trigonometric Functions
 Sec. 4-1: Given an angle of any measure (including radians, degrees, minutes,
seconds), draw a picture of that angle and its coterminal angles. Solve problems
involving linear and angular speed.
 Sec. 4-2: Evaluate trigonometric functions using the Unit Circle.
 Sec. 4-3: State the six reciprocal, two quotient, and three Pythagorean Identities and
verify trigonometric identities using these identities. Geometrically determine the
Pythagorean Identity sin 2   cos2   1 .
 Sec. 4-4: Find the sine and cosine of angles that share the same reference angle. Sketch
a sinusoidal function without a calculator.
 Sec. 4-5: Learn the meanings of amplitude, period or frequency, phase displacement,
and cycle of a sinusoidal graph. Describe transformations such as vertical and
horizontal dilation, vertical and horizontal displacement, and reflection over the
sinusoidal axis. Given information about a sinusoidal function, write the equation
and/or graph the function. Write the equation of a harmonic motion graph as a sum
or product of two sinusoids.
 Sec. 4-6: Graph the six trigonometric functions, including discontinuities on the graph.
Generalize transformations in equation form. Be able to apply the Quotient properties
for tangent and cotangent.
 Sec. 4-7: Plot graphs of inverse trigonometric functions and relations. Find exact
values of functions of inverse trigonometric functions.
 Sec. 4-8: Solve real life problems involving right triangle, directional bearings and
harmonic motion.
Chapter 5: Analytic Trigonometry
 Sec. 5-1: Use fundamental trigonometric identities to simplify trigonometric
expressions.
 Sec. 5-2: Use fundamental trigonometric identities to verify trigonometric identities.
 Sec. 5-3: Use standard algebraic techniques and trigonometric inverses to solve
trigonometric equations. Solve trigonometric equations involving quadratics and
multiple angles.
 Sec. 5-4: Use sum and difference formulas to evaluate and solve trigonometric
equations and to verify identities.
 Sec. 5-5: Use multiple-angle, power-reducing, half-angle, product-to-sum and sumto-product formulas to evaluate trigonometric functions.
 Derive properties for cos 2A, sin2A, and tan 2A in terms of functions of A. Derive
properties for cos 1/2A, sin 1/2A, and tan 1/2A in terms of functions of A. Derive
sum and difference properties.
Chapter 6: Additional Topics in Trigonometry
 Sec. 6-1: Use the Law of Cosines to solve oblique triangles (AAS, ASA, or SSA) and
real world problems. Find the Area of triangles.
 Sec. 6-2: Use the Law of Cosines to solve oblique triangles (SSS or SAS) and real world
problems. Use Heron’s Formula to find the area of triangles.
 Sec. 6-3: Write vectors as the sum of components and as linear combinations of unit
vectors. Perform basic vector operations to model and solve real world problems.
 Sec. 6-4: Use vector properties and the dot product to find the work done by a force.
Find angles between two vectors to determine whether two vectors are orthogonal.
 Sec. 6-5: Write the trigonometric form and find the absolute value of complex
numbers. Perform basic operations such as multiplication, division, roots, and powers
of complex numbers.
Chapter 8 Test Expectations

Sec. 8-1: Given a few terms in a sequence or series of numbers, find more terms. Given a
series, find the sum of a specified number of terms. Represent sequences explicitly and
recursively. Given information about a sequence, find a term given its term number, and
find the term number of a given term. Use factorial notation. Use sequence mode or the
calculator recursion feature to solve situations that are defined recursively.

Sec. 8-2: Given an arithmetic series, find the sum of a specified number of terms. Given a
series, find a specified partial sum, or find the number of terms if the partial sum is
given. Use sigma notation to write partial sums.

Sec. 8-3: Given a geometric series, find a specified partial or infinite sum, or find the
number of terms if the partial sum is given. Use sigma notation to write partial and
infinite sums. Use sigma notation to write partial sums.

Use the ratio and/or comparison test to determine if a series converges or diverges.

Sec. 8.5 Use the binomial theorem to expand binomials, calculate terms in the expansion,
and use Pascal’s triangle to calculate coefficients.
You will need to memorize make meaning of  the following formulas:
Law of Cosines
Law of Sines
Hero’s Area Formula
1
Area Property AV  ab sin C
2
If b sin A  a  b , then 2 triangles exist.
Logarithmic:
exponential to logarithmic form
properties of logarithms (power, product, and quotient)
Change-of-base
Trigonometric Identities
Six reciprocal, two quotient, and three Pythagorean Identities
sum and difference properties for sine and cosine
double and half-angle formulas for sine and cosine
Cofuntions and odd-even properties
Radians to degrees and vice versa
Arccosine, arctangent, arcsine
Arithmetic and Geometric
Recursive Formulas
Explicit Formulas
Summation Formulas
Complex Trigonometric Form
Product Property
Quotient Property
Power Property
a + bi form
Dot Product of Vectors
Vector and Scalar Projection