(final exam review topics)
ABOUT THE FINAL_______________
PLACE: SH 121 (smith hall 121)
TIME: 12:00pm – 1:50 PM, December 5th (Monday)
Below is a list of all the stuff we’ve talked about this term. Here are a couple things to note about our
final exam
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The final is cumulative, and will have stuff from each chapter on it.
It is worth 20% of your overall grade (same as your other exams)
If you score higher on the final than either one of your previous exams, I will replace your lowest
exam score with whatever you get on the final
You may use a 3x5 notecard, front and back
(chapter 5) - Functions
(5.2) – functions (page 252)
o Understand the definition of a function.
o Know how to determine if a given relation is a function (input vs. output, vertical line test)
o Know how to find domain and range of a function (via graph, equation, blob diagram, table)
(5.3) – function notation (page 262)
o Know how to evaluate a function at a specific point.
o Know how to find the output when given the input (and vice versa)
(5.4) – finding linear equations (page 269)
o Know how to find the equation of a line given
o slope and a point
o two points
o a point and a parallel or perpendicular line
(chapter 7) – Polynomials Functions and Properties of Exponents
(7.1) – adding and subtracting polynomials (page 388)
o know how to combine like terms
o Sum and difference functions
o Know the standard form of a quadratic equation
(7.2 & 7.3) – multiplying polynomials & powers of polynomials / difference of squares (page 400 & 409)
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Know how to multiply polynomials
o Binomial times binomial, trinomial times binomial, etc…
o Review the box method for multiplying polynomials!
o Multiplying binomial conjugates (a-b)(a+b) (yielding difference of squares)
o Squaring binomials
(7.4) – properties of exponents (page 416)
o Know the properties of exponents
o Quotient and product properties of exponents
o Raising power to a power
o Raising quotient to a power
o Raising product to a power
o Simplifying power expressions
o Using properties to simplify power expressions
(chapter 10)
(10.1) – integer exponents (page 597)
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Be able to simplify power expressions with negative exponents
Know how to convert between standard decimal notation and scientific notation
(10.2) – rational exponents (page 610)
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Be able to simplify power expressions with fractional exponents
(10.3) – exponential functions (page 616)
o Graphing exponential functions
o Know how to easily locate y-intercept
o Know where the horizontal asymptote is
o Finding equations of exponential functions.
(chapter 8) – Factoring and Solving Polynomials
(8.1) – factoring 𝑥 2 + 𝑏𝑥 + 𝑐 (page 441)
o Know how to factor 𝑥 2 + 𝑏𝑥 + 𝑐
o Know how to factor a difference of squares
(8.2) – factoring out the GFC and factoring by grouping (page 449)
o Know how to factor out GCF
o Know how to factor by grouping
o Example: 12𝑥 3 + 3𝑥 2 + 8𝑥 + 2
(8.3) – Factoring 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 with 𝑎 ≠ 1 (page 456)
o Know the trial and error method and also grouping method
(8.5) – solving polynomial equations by factoring (page 468)
o Using zero factor property to find the “zeros” of a quadratic equation
o Finding the x-intercepts of quadratic functions (basically same thing as finding zeros)
(chapter 9) – Quadratic Functions
(9.1) – graphing quadratic functions in vertex form (page 495)
o Know the steps needed to take to graph 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘 where 𝑎 = 0
o Know how to easily find the vertex given a function in vertex form
o Find two point on same side of axis of symmetry and reflect them
o Graph of parabola is always “U” shape (up or down) – never a “V” shape.
(9.2) – graphing quadratic functions in standard form (page 506)
o Know the steps needed to take to graph 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 where 𝑎 = 0
o Know how to locate the y-intercept
o Know the vertex formula (page 492)
o Know how to find symmetric points
o Note: graphing quadratics in standard form requires two points (pair of symmetric
points – one of the points is the y-intercept) and a vertex.
o Know how to find the min/max of a quadratic equation (find the vertex)
(9.3) – Simplifying radical (square root) expressions (page 518)
o Know the product and quotient properties for square roots
o Know how to simplify a radical (factor tree stuff)
o Know how to rationalize a denominator
(9.4) – Using square roots to solve quadratic equations (page 527)
o Know that the square root of a number yields a positive and negative result
o by factoring
o know what a complex number is and know the definition of 𝑖 = √−1
(9.5) – completing the square (page 538)
o Know how to use completing the square
(9.6) – The Quad. Form. (page 545)
o Know the quadratic formula (put it on your page of notes!)
o Know how to find the # and type of solutions to an equation by using the discriminant
(chapter 12) – Rational Functions
(12.1) – Finding the domains of rational functions and simplifying rational expressions (page 728)
o Know how to find the domain of a rational functions (this is really the same as finding the
excluded values of a rational function)
o Understand how to properly simplify a rational expression
o Know how to find the quotient function (page 703)
o Know how to locate vertical asymptotes
(12.2) – multiplying and dividing rational expressions (page 741)
o Know how to multiply and divide two (or more) rational expressions (and then simplify your
result)
(12.3) – adding and subtracting rational expressions (page 751)
o know how to find common denominator to add or subtract rational expressions (instructions on
page 726)
(12.5) – solving rational equations (page 773)
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know to multiply through by the least common denominator to turn your equation into
something easier to solve (instructions on page 745)
(chapter 13) – Radical Functions
(13.1) – simplifying radical expressions (page 827)
o know how to simplify nth roots in a similar way that we simplify square roots
(13.4) – Radical Function Transformations
o know how to graph radical functions using the base function 𝑓(𝑥) = √𝑥
o Know the order of transformations
(13.5) – solving radical equations (page 854)
o Know how to use the squaring property of equality
o Know how to check for extraneous solutions
o Know steps needed to take in order to solve radical equations (steps on page 833)
(Additional Thoughts)
I would review for the final by looking over the following:
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ii.
iii.
iv.
Homework
Past exams
Quizzes
Lecture notes
I would also create a practice exam for yourself. Our final is an hour and 50 minutes, and I don’t think
you should create something that will take you that long, but maybe if you pick our 5 or 6 challenging
questions, sit down with just your notecard and pencil/paper and see if you can do those problems in 40
minutes. The idea is to be comfortable with a time constraint by the time you take your final.
ありがとうございました。