HPC
Final Exam Expectations
MATH FINAL
Thursday, December 19, 2013
10:20-11:50
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Chapter 1: Functions and Their Graphs
Sec. 1.1: Write linear equations given points on lines and their slopes. Use slopeintercept forms of linear equations to sketch lines. Use slope to identify parallel and
perpendicular lines.
Sec. 1.2: se function notation and evaluate functions. Find the domains of functions.
Use functions to model and solve real-life problems. Evaluate difference quotients.
Sec. 1.3: Find the domains and ranges of functions and use the Vertical Line Test for
functions. Determine intervals on which functions are increasing, decreasing, or
constant. Determine relative maximum and relative minimum values of functions.
Identify and graph step functions and other piecewise-defined functions. Identify
even and odd functions.
Sec. 1.4: Recognize graphs of parent functions. Use vertical and horizontal shifts and
reflections to graph functions. Use nonrigid transformations to graph functions.
Sec. 1.5: Add, subtract, multiply, and divide functions. Find compositions of one
function with another function. Use combinations of functions to model and solve
real-life problems.
Sec. 1.6: Find inverse functions informally and verify that two functions are inverse
functions of each other. Use graphs of functions to decide whether functions have
inverse functions. Determine if functions are one-to-one. Find inverse functions
algebraically.
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.
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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.
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Chapter 8: Sequences, Series and Probability
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. 8.4 Use mathematical induction to prove a conjecture. Find the sums of powers
of integers.