# Math 4C Final Exam Study Guide

Format 12 questions, some multi-part. Questions will be similar to sample
problems in this study guide, homework problems, lecture examples or examples
from the text. The final exam is comprehensive.

Protocol Wednesday, December 10, 3-6 pm in YORK 2622 (tentative). No notes nor
calculators allowed . Bring photo ID. No credit for unsupported work. No makeup
test; however lowest midterm percentage will be automatically replaced by the
final exam percentage if it is higher. Do work on final exam (blue book not
required) or attach scratch paper.

Study Guide Review homework, lecture notes, and notes from reading the textbook.
Work, review sample problems below. Study with one or two other students.
Seek help at office hours; ask specific questions.
Topics, Sample Problems
Supp Expressions and functions 1.3.57, 69, 71, 81; 1.R.3, 5, 9
distinguish between expressions and functions
define polynomial
evaluate polynomials
perform operations on polynomials , e.g., multiplication
factor polynomials over the integers, the rationals, the reals, the complex numbers

Supp Rational expressions, solving equations
evaluate and simplify rational expressions
add, subtract , multiply, and divide rational expressions
determine if a value is a solution to an equation
solve equations by inverse operations

12.7, Partial fractions 12.R.89; 12.T.19

12.8 determine form of partial fraction decomposition (non-repeated linear factors,
repeated linear factors, non-repeated quadratic factors, repeated quadratic
factors)
solve partial fraction decompositions by equating coefficients or choosing
convenient values

12.2 Polynomial division 12.R.1, 5; 12.T.5, 9
divide polynomials using long and synthetic division to find quotients and
remainders

12.3- Roots of polynomial equations 12.R.13, 17, 19, 31, 37, 43, 47, 63, 67; 12.T.1, 2,

12.6 3, 4, 8, 10, 12, 14, 15, 17
use various theorems (Remainder, Factor, Linear Factors, Fundamental Theorem
of Algebra, Location or Intermediate Value, relationship between
coefficients and roots or Vieta's, Rational Roots, Upper and Lower Bound,
Descartes Rule of Signs, Conjugate Roots, Irrational Conjugate Roots) to
solve polynomial equations

5.4 Properties of logarithms 5.R.11, 14, 65
use properties of logarithms to find values of logarithms
use properties of logarithms to simplify or expand logarithmic expressions

5.5 Equations involving exponents and logarithms 5.R.15, 35; 5.T.13
solve exponential and logarithmic equations

5.6 Applications 5.R.103; 5.T.6
solve compound interest problems

5.7 Exponential growth and decay 5.R.3, 78, 83
solve exponential growth problems
solve exponential decay problems

10.1, Systems of linear equations, Gaussian elimination

10.2 recognize when a system of linear equations has one solution, no solutions, or an
infinite number of solutions

3.1 Functions
determine domain, range, independent and dependent variables
3.R.1, 43, 49, 53, 102, 125; 3.T.1, 2
compute values of functions using numbers, using literals
3.R.11, 69, 73, 77, 79, 105, 114, 118; 3.T.10
compute difference quotients 3.R.5, 89, 129; 3.T.5
find slope and average rate of change, use notation 3.R.8, 13
solve application problems 3.T.17

3.2 Graphs of functions
use Vertical Line Test to determine if a graph represents a function
find x- and y-intercepts; positive and negative parts of graph; increasing,
decreasing, and level parts of graph; turning points (local or relative
extrema); global (absolute) extrema; slope, secant lines, and average rate
of change; concavity and (estimate) inflection points; symmetry, odd and
even functions; vertical and horizontal asymptotes; sketch graphs
3.R.10, 101, 103, 104, 107, 108, 109, 110, 111, 116, 117, 123, 124, 127,
128; 3.T.9

3.3 Graphing transformations
relate vertical and horizontal translations (shifts), reflections, and dilations of a
graph to its function 3.R.6, 15, 126
recognize transformations from the function
sketch graphs by applying transformations of a basic graph
3.R.9, 21, 29; 3.T.7, 8, 15

3.4 Combining functions
find sum , difference, product, and quotient of two functions
3.R.4ab, 81, 119; 3.T.3a
find composition of two functions
3.R.2bc, 3, 4c, 85, 86, 87, 120, 121, 122; 3.T.3bc
decompose a function 3.R.63

3.5 Inverse functions
know properties or inverse functions and their graphs (monotonicity, one-to-one,
Horizontal Line Test, compositions of function and its inverse)
find inverse function, if it exists, algebraically 3.R.39, 41, 91, 97, 98; 3.T.6
sketch inverse function from graph of function by reflection through y = x 3.R.7
restrict domain to find inverse function 3.R.112, 113
solve application problems 3.R.16; 3.T.16

4.1 Linear functions
find equations of lines in slope-intercept, point-slope, standard, and
double- intercept forms 4.R.1, 15, 19; 4.T.1
graph linear functions
find equations of lines with graphs that are parallel or perpendicular to a given
linear graph 4.R.17

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