2. Use your graphing calculator to graph each of the functions below over the interval 2, 2

Size: px
Start display at page:

Download "2. Use your graphing calculator to graph each of the functions below over the interval 2, 2"

Transcription

1 MSLC Math 0 Final Eam Review Disclaimer: This should NOT be used as your only guide for what to study. if 0. Use the piece-wise defined function f( ) to answer the following: if a. Compute f(0), f(), f(-), and f(). Plot the points you found above and sketch a complete graph of y = f().. Use your graphing calculator to graph each of the functions below over the interval, and approimate any local etrema. Also, determine the intervals where the functions are increasing and decreasing. Round your answers to three decimal places where appropriate. f a. g c. h d. k. Determine the average rate of change of the functions between the given values of. a. h 7 from to f c. g from to t from 0 to a. Write the equation of the function F transformed in the following ways: a. shifted units to the left, and shifted up units reflected about the -ais, then shifted down units c. shifted unit to the right, and vertically stretched by a factor of d. shifted unit to the left, then reflected about the y-ais. Given f and g find: a. f g g f c. f f d. g g 6. Algebraically find the maima and minima of the functions given. a. f g 7

2 7. Find the inverse of each function, state the domain and range of both the original function and its inverse. f a. g c. k d. h 8. Find all real zeros and the multiplicity of those zeros for the given polynomials, then find their y-intercepts and sketch the graph. p a. p c. p 9. Find all zeros (both real and comple) of the following polynomials. a. P 7 P 6 c. P Factor the polynomials into linear and irreducible quadratic factors with real coefficients. P a. Q. Factor the polynomials into linear factors with comple coefficients. P a. Q. Find a polynomial with integer coefficients having the following properties: a. Degree: Zeros: 0, i Degree: Zeros:, i

3 . Find all intercepts and asymptotes, then sketch the graph of each rational function. a. R R 6 c. R. Solve the following inequalities. Write your answer using interval notation. 9 a. 6 c. 0 d. e. 7 f.. Solve the equation. w w a c. ln( r) ln(r ) d. log ( ) e. f. log e g. 6 log 6 h. i. 6. How much needs to be invested now in order to have $000 in years given a.% interest rate that is compounded: a. daily? continuously? 7. Determine (correct to decimal places) how long it will take for $000 to double if it s invested in an account that gives 6% interest compounded: a) semiannually? b) quarterly? c) monthly? d) daily? e) continuously?

4 8. The frog population in a small pond grows eponentially. The current population is 70 frogs, and the relative growth rate is % per year. a. Find a function that models the population after t years. Use your equation to find the projected population after years. Round your answer to the nearest frog. c. Use your equation to find the number of years required for the frog population to reach 0 frogs. Round your answer to two decimal places. 9. In the circle pictured below, r is the radius of the circle, is the central angle of the sector, A is the area of the sector, and s is the length of the arc subtended by the central angle. Find: a. A and s if r inches, and radians r and s if A. square miles, and 6 c. A and if r meters, and s.7 meters d. r and A if s meters, and radians 0. Use the given information to find the eact value of the si trigonometric functions of the angle in the picture. a) a 8, b b) a, c c) sin 7 d) cot e) cos f) csc. For each part, determine the quadrant lies in and the values of the five remaining trigonometric functions. a) csc 6 and cot 0 b) sec and sin 0 c) tan and cos 0. Find the eact value of each of the following. 99 a. tan sin 0 cos cos

5 . Given triangle ABC with the following properties: b, c 7, B and C is an obtuse angle Find the measure of angle C. Round your answer to decimal places.. A team of surveyors have been hired to measure the distance across a canyon. Using a tree at point T on the opposite site of the canyon as a reference point, they established points A, B, and C and found the following distances: AB =. ft BC = 6. ft AC = ft a. Find the measure of angle ABC. Round your answer to decimal places. Find the distance TC across the canyon to the nearest foot.. Establish the identity: a. sin sec tan sin sec csc sin cos tan cot tan v sin v c. tan v sin v sin v cot cot y d. cot( y) cot cot y e. sin sin f. sin sec csc sin 6. Find the eact solution of: a. sin tan(6 ) 7 c. cos 8 d. tan 7. Given cot and sin 0 find: a. sin cos c. tan

6 8. Find all solutions of: a. cos 0 on the interval 0, cos sin cos 0 on the interval 0,8 c. sin 0 9. Convert to polar coordinates: a. i i 0. Use DeMoivre s Theorem to find a. z i z cos isin z in the standard a bi form:. Given u i j and v i j find: a. u v u v c. u v d. u v e. uv f. the angle (in degrees) between u and v. Round your answer to decimal places.. Find the complete solution for each of the following systems of linear equations. y 0 a. y 8 y z 0 y z 8 y z 7. A boat on a river travels downstream for 0 miles in one hour. The return trip back upstream takes. hours. How fast does the boat travel in still water, and how fast is the current?. A fruit stand sells a bo of Strawberries for $7 and a bo of Kiwi fruit for $0. If they sold a total of boes of fruit and had revenue of $0, how many boes of each fruit did they sell?. From the top of a 0 foot tall lighthouse, the angle of depression to a ship on the water is 7. How far is the ship from the lighthouse? Round your answer to two decimal places.

7 6. Find the equation of the parabola with verte at the origin and a directri of Find the equation of an ellipse with eccentricity of 9 and foci at 0, 8. Find the transverse ais, vertices, foci, and the equations of the asymptotes of the hyperbola described by the equation 9 y Write each of the following sums of a sequence using sigma notation. a Find the sum of the following: a. k k 0 k 0 c. n d. n0 j0 ANSWERS. a) 0 j 7 f ; f ; f f ; b). a. Min: 0,0 ; Increasing: 0, ; Decreasing:,0 Mins:,0 &,0 ; Ma:0, ; Increasing:,0, ; Decreasing:, 0, c. Min: (0,0); Increasing: 0, ; Decreasing:,0 d. Min: 0.78, 0.8 ; Ma: 0.78, 0.8 ; Increasing:, , ; Decreasing: 0.78,0.78. a) b) 6t c) a a a

8 . a) y b) y c) y.a) 0 6 f g 6. a) Min.:, b) Ma.: b)g f 7, 6 6 d) y 7. a) f Domain f, ; Range f, Domain f, ; Range f, b) g Domain g, ; Range g, Domain g, ; Range g, c) f f d) g g c) Domain k,, ; Range k,0 0, k d) h Domain k 8. a) Zeros: (multiplicity:); (multiplicity:); (multiplicity:); y-int: 0, Domain k,0 0, ; Range k,,,,,, k,, ; Range k Domain k,, ; Range b) Zeros: (multiplicity:); (multiplicity:); y-int: 0, c) Zeros: (multiplicity:); (multiplicity:); y-int: 0,9

9 9. a) Zeros: 0; i 7 ; i 7 b) Zeros: ; i ; i c) Zeros: ; i; i; + i ; i 0. a) b). a) i i b) i i. a) P ; b). a) no y-intercept, -intercept:,0 ; 6 Horizontal Asymptote: y 0; Vertical Asymptotes: 0; b) y-intercept: 0,0 -intercepts: 0,0 &,0 Horizontal Asymptote: y Vertical Asymptotes: ; c) y-intercept: 0, -intercepts:,0 Slant Asymptote: y ; Vertical Asymptotes: ;. a), b), 9,, f) c),, d),,0 e) 9,. a. w 7 c. r 7 d. g. or h. ln or 0 i. ln 7 e. f. ln ln ln ln ln ln

10 6. a. $80.9 $ a).7 yrs b).69 yrs c).8 yrs d). yrs e). yrs 0.t 8. a. nt 70e n 0 c. t.7 years 9. a. s. inches c. (radians) A.7 in r.676 miles s.68 miles A. m d. r 6. meters A m 8 0. a. sin 7 sin c. sin 7 d. sin 0 e. sin f. sin cos tan csc sec cot cos tan csc sec cot 7 7 cos tan csc sec cot 7 0 cos tan csc 0 sec cot 0 cos tan csc sec cot cos tan csc sec cot. a. is in Quadrant III; is in Quadrant II; sin 6 csc 6 sin cos csc sec 8 c. is in Quadrant IV; sin cos csc sec 8 6 tan 8 6 sec cot cos tan 8 8 cot tan cot. a C.9. a. ABC 0.8 TC feet

11 sin sec csc sec tan sin cos sin tan cot sin sin RHS sin sin cos sin RHS sin cos sin sin. a. RHS cos sin sin sin cos sin sin RHS cos sin cos RHS sin cos sin sin RHS cos sin cos cos cos sin cos cos sin sec sec tan tan (sec tan ) sin cos cos sin sin cos c. tan vsin v tan v sin v sin v sin v RHS sin v sin v sin v RHS sin v sin v sin v RHS sin v sin v sin v RHS sin v RHS cos v sin v RHS sin v sin v sin v d. cot cot y cot( y) cot cot y cos( y) RHS sin( y) cos cos y sin sin y sin cos y cos sin y cos cos y sin sin y sin cos y cos sin y RHS sin ysin sin ysin cos cos y sin sin y cot cot y cos y cos cot cot y sin y sin RHS sin sin sin sec csc sin LHS sin cos sin cos sin RHS sin sin e. LHS cos 0 f. LHS cos RHS sin cos sin cos csc sec sec csc 6. a. 6 c. d.

12 7. a. c. 8. a.,,, k c.,,, 9. a., or,, or, 0 0. a. 8 8i i. a. i j 6ij c. 6 d. 7 e. f a., y 6 7 6, y, z. Boat s speed in still water = mph; Current s speed = 6mph. 80 boes of Strawberries; boes of Kiwi fruit feet y y 0 8. Transverse ais: the -ais; Vertices:,0 ; Foci:,0 ; Asymptotes: y 9. a. 0 k k 999 k k k 0. a c. 99 d. 6

x x x 2. Use your graphing calculator to graph each of the functions below over the interval 2,2

x x x 2. Use your graphing calculator to graph each of the functions below over the interval 2,2 MSLC Math 48 Final Eam Review Disclaimer: This should NOT be used as your only guide for what to study.. Use the piece-wise defined function 4 4 if 0 f( ) to answer the following: if a) Compute f(-), f(-),

More information

Math 1160 Final Review (Sponsored by The Learning Center) cos xcsc tan. 2 x. . Make the trigonometric substitution into

Math 1160 Final Review (Sponsored by The Learning Center) cos xcsc tan. 2 x. . Make the trigonometric substitution into Math 60 Final Review (Sponsored by The Learning Center). Simplify cot csc csc. Prove the following identities: cos csc csc sin. Let 7sin simplify.. Prove: tan y csc y cos y sec y cos y cos sin y cos csc

More information

* Circle these problems: 23-27, 37, 40-44, 48, No Calculator!

* Circle these problems: 23-27, 37, 40-44, 48, No Calculator! AdvPreCal 1 st Semester Final Eam Review Name 1. Solve using interval notation: 7 8 * Circle these problems: -7, 7, 0-, 8, 6-66 No Calculator!. Solve and graph: 0. Solve using a number line and leave answer

More information

1 st Semester Final Review Date No

1 st Semester Final Review Date No CHAPTER 1 REVIEW 1. Simplify the epression and eliminate any negative eponents. Assume that all letters denote positive numbers. r s 6r s. Perform the division and simplify. 6 8 9 1 10. Simplify the epression.

More information

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y. BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH06 Review Sheet. Perform the indicated operations and simplif: n n 0 n + n ( 9 )( ) + + 6 + 9ab

More information

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y. BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH06 Review Sheet. Perform the indicated operations and simplif: n n 0 n + n ( 9 ) ( ) + + 6 + 9ab

More information

Honors Accelerated Pre-Calculus Midterm Exam Review Name: January 2010 Chapter 1: Functions and Their Graphs

Honors Accelerated Pre-Calculus Midterm Exam Review Name: January 2010 Chapter 1: Functions and Their Graphs Honors Accelerated Pre-Calculus Midterm Eam Review Name: January 010 Chapter 1: Functions and Their Graphs 1. Evaluate the function at each specified value of the independent variable and simplify. 1 f

More information

2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2

2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2 29 April PreCalculus Final Review 1. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line: y = 3x + 13 2. Determine the domain of the function. Verify your result with

More information

1. Evaluate the function at each specified value of the independent variable and simplify. f 2a.)

1. Evaluate the function at each specified value of the independent variable and simplify. f 2a.) Honors Pre-Calculus Midterm Eam Review Name: January 04 Chapter : Functions and Their Graphs. Evaluate the function at each specified value of the independent variable and simplify. f ( ) f () b. f ( )

More information

2018 Pre-Cal Spring Semester Review Name: Per:

2018 Pre-Cal Spring Semester Review Name: Per: 08 Pre-Cal Spring Semester Review Name: Per: For # 4, find the domain of each function. USE INTERVAL NOTATION!!. 4 f ( ) 5. f ( ) 6 5. f( ) 5 4. f( ) 4 For #5-6, find the domain and range of each graph.

More information

North Seattle Community College Computer Based Mathematics Instruction Math 102 Test Reviews

North Seattle Community College Computer Based Mathematics Instruction Math 102 Test Reviews North Seattle Community College Computer Based Mathematics Instruction Math 10 Test Reviews Click on a bookmarked heading on the left to access individual reviews. To print a review, choose print and the

More information

Math 370 Semester Review Name

Math 370 Semester Review Name Math 370 Semester Review Name 1) State the following theorems: (a) Remainder Theorem (b) Factor Theorem (c) Rational Root Theorem (d) Fundamental Theorem of Algebra (a) If a polynomial f(x) is divided

More information

MONTGOMERY HIGH SCHOOL CP Pre-Calculus Final Exam Review

MONTGOMERY HIGH SCHOOL CP Pre-Calculus Final Exam Review MONTGOMERY HIGH SCHOOL 01-015 CP Pre-Calculus Final Eam Review The eam will cover the following chapters and concepts: Chapter 1 Chapter 1.1 Functions.1 Power and Radical Functions 1. Analyzing Graphs

More information

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y. BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH06 Review Sheet. Perform the indicated operations and simplif: n n 0 n +n ( 9 )( ) + + 6 + 9ab a+b

More information

Name Please print your name as it appears on the class roster.

Name Please print your name as it appears on the class roster. Berkele Cit College Practice Problems Math 1 Precalculus - Final Eam Preparation Name Please print our name as it appears on the class roster. SHORT ANSWER. Write the word or phrase that best completes

More information

1. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y 3x

1. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y 3x MATH 94 Final Exam Review. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y x b) y x 4 c) y x 4. Determine whether or not each of the following

More information

Practice Test - Chapter 4

Practice Test - Chapter 4 Find the value of x. Round to the nearest tenth, if necessary. 1. An acute angle measure and the length of the hypotenuse are given, so the sine function can be used to find the length of the side opposite.

More information

MATH 175: Final Exam Review for Pre-calculus

MATH 175: Final Exam Review for Pre-calculus MATH 75: Final Eam Review for Pre-calculus In order to prepare for the final eam, you need too be able to work problems involving the following topics:. Can you graph rational functions by hand after algebraically

More information

MATH 2 - PROBLEM SETS

MATH 2 - PROBLEM SETS MATH - PROBLEM SETS Problem Set 1: 1. Simplify and write without negative eponents or radicals: a. c d p 5 y cd b. 5p 1 y. Joe is standing at the top of a 100-foot tall building. Mike eits the building

More information

2. Find the value of y for which the line through A and B has the given slope m: A(-2, 3), B(4, y), 2 3

2. Find the value of y for which the line through A and B has the given slope m: A(-2, 3), B(4, y), 2 3 . Find an equation for the line that contains the points (, -) and (6, 9).. Find the value of y for which the line through A and B has the given slope m: A(-, ), B(4, y), m.. Find an equation for the line

More information

2. Find the midpoint of the segment that joins the points (5, 1) and (3, 5). 6. Find an equation of the line with slope 7 that passes through (4, 1).

2. Find the midpoint of the segment that joins the points (5, 1) and (3, 5). 6. Find an equation of the line with slope 7 that passes through (4, 1). Math 129: Pre-Calculus Spring 2018 Practice Problems for Final Exam Name (Print): 1. Find the distance between the points (6, 2) and ( 4, 5). 2. Find the midpoint of the segment that joins the points (5,

More information

Math 370 Semester Review Name

Math 370 Semester Review Name Math 370 Semester Review Name These problems will give you an idea of what may be included on the final exam. Don't worry! The final exam will not be this long! 1) State the following theorems: (a) Remainder

More information

AFM Midterm Review I Fall Determine if the relation is a function. 1,6, 2. Determine the domain of the function. . x x

AFM Midterm Review I Fall Determine if the relation is a function. 1,6, 2. Determine the domain of the function. . x x AFM Midterm Review I Fall 06. Determine if the relation is a function.,6,,, 5,. Determine the domain of the function 7 h ( ). 4. Sketch the graph of f 4. Sketch the graph of f 5. Sketch the graph of f

More information

Honors Calculus Summer Preparation 2018

Honors Calculus Summer Preparation 2018 Honors Calculus Summer Preparation 08 Name: ARCHBISHOP CURLEY HIGH SCHOOL Honors Calculus Summer Preparation 08 Honors Calculus Summer Work and List of Topical Understandings In order to be a successful

More information

AP Calculus Summer Homework MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

AP Calculus Summer Homework MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. AP Calculus Summer Homework 2015-2016 Part 2 Name Score MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(p1, P2) between the points

More information

Trigonometric Identities Exam Questions

Trigonometric Identities Exam Questions Trigonometric Identities Exam Questions Name: ANSWERS January 01 January 017 Multiple Choice 1. Simplify the following expression: cos x 1 cot x a. sin x b. cos x c. cot x d. sec x. Identify a non-permissible

More information

Name Date. Show all work! Exact answers only unless the problem asks for an approximation.

Name Date. Show all work! Exact answers only unless the problem asks for an approximation. Advanced Calculus & AP Calculus AB Summer Assignment Name Date Show all work! Eact answers only unless the problem asks for an approimation. These are important topics from previous courses that you must

More information

MATH 175: Final Exam Review for Pre-calculus

MATH 175: Final Exam Review for Pre-calculus MATH 75: Final Eam Review for Pre-calculus In order to prepare for the final eam, you need to be able to work problems involving the following topics:. Can you find and simplify the composition of two

More information

Directions: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies.

Directions: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies. MATH 1113 Precalculus FINAL EXAM REVIEW irections: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies. Question: 1 QI: 758

More information

Midterm. Multiple Choice Identify the choice that best completes the statement or answers the question.

Midterm. Multiple Choice Identify the choice that best completes the statement or answers the question. Midterm Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Factor completely. If the polynomial cannot be factored, say it is prime. 10x 2-95x + 225 2. Solve

More information

Exam 2 Review F15 O Brien. Exam 2 Review:

Exam 2 Review F15 O Brien. Exam 2 Review: Eam Review:.. Directions: Completely rework Eam and then work the following problems with your book notes and homework closed. You may have your graphing calculator and some blank paper. The idea is to

More information

1 x. II. CHAPTER 2: (A) Graphing Rational Functions: Show Asymptotes using dotted lines, Intercepts, Holes(Coordinates, if any.)

1 x. II. CHAPTER 2: (A) Graphing Rational Functions: Show Asymptotes using dotted lines, Intercepts, Holes(Coordinates, if any.) FINAL REVIEW-014: Before using this review guide be sure to study your test and quizzes from this year. The final will contain big ideas from the first half of the year (chapters 1-) but it will be focused

More information

C) ) cos (cos-1 0.4) 5) A) 0.4 B) 2.7 C) 0.9 D) 3.5 C) - 4 5

C) ) cos (cos-1 0.4) 5) A) 0.4 B) 2.7 C) 0.9 D) 3.5 C) - 4 5 Precalculus B Name Please do NOT write on this packet. Put all work and answers on a separate piece of paper. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the

More information

2.) Find an equation for the line on the point (3, 2) and perpendicular to the line 6x - 3y = 1.

2.) Find an equation for the line on the point (3, 2) and perpendicular to the line 6x - 3y = 1. College Algebra Test File Summer 007 Eam #1 1.) Find an equation for the line that goes through the points (-5, -4) and (1, 4)..) Find an equation for the line on the point (3, ) and perpendicular to the

More information

D In, RS=10, sin R

D In, RS=10, sin R FEBRUARY 7, 08 Invitational Sickles The abbreviation NOTA means None of These Answers and should be chosen if choices A, B, C and D are not correct Solve for over the Real Numbers: ln( ) ln() The trigonometric

More information

1.1 Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 1) 162

1.1 Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 1) 162 Math 00 Midterm Review Dugopolski Trigonometr Edition, Chapter and. Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. ) ) - ) For the given angle,

More information

CALCULUS BASIC SUMMER REVIEW

CALCULUS BASIC SUMMER REVIEW NAME CALCULUS BASIC SUMMER REVIEW Slope of a non vertical line: rise y y y m run Point Slope Equation: y y m( ) The slope is m and a point on your line is, ). ( y Slope-Intercept Equation: y m b slope=

More information

Unit 10 Prerequisites for Next Year (Calculus)

Unit 10 Prerequisites for Next Year (Calculus) Unit 0 Prerequisites for Net Year (Calculus) The following Study Guide is the required INDEPENDENT review for you to work through for your final unit. You WILL have a test that covers this material after

More information

1. Which of the following defines a function f for which f ( x) = f( x) 2. ln(4 2 x) < 0 if and only if

1. Which of the following defines a function f for which f ( x) = f( x) 2. ln(4 2 x) < 0 if and only if . Which of the following defines a function f for which f ( ) = f( )? a. f ( ) = + 4 b. f ( ) = sin( ) f ( ) = cos( ) f ( ) = e f ( ) = log. ln(4 ) < 0 if and only if a. < b. < < < < > >. If f ( ) = (

More information

MATH 130 FINAL REVIEW

MATH 130 FINAL REVIEW MATH 130 FINAL REVIEW Problems 1 5 refer to triangle ABC, with C=90º. Solve for the missing information. 1. A = 40, c = 36m. B = 53 30', b = 75mm 3. a = 91 ft, b = 85 ft 4. B = 1, c = 4. ft 5. A = 66 54',

More information

f exist? Why or why not? Non-AP Calculus Summer Assignment 1. Use the graph at the right to answer the questions below. a. Find f (0).

f exist? Why or why not? Non-AP Calculus Summer Assignment 1. Use the graph at the right to answer the questions below. a. Find f (0). 1. Use the graph at the right to answer the questions below. 4 1 0 - - -1 0 1 4 5 6 7 8 9 10 11-1 - a. Find f (0). b. On what intervals is f( x) increasing? c. Find x so that f( x). d. Find the zeros of

More information

9) A) f-1(x) = 8 - x B) f-1(x) = x - 8 C)f-1(x) = x + 8 D) f-1(x) = x 8

9) A) f-1(x) = 8 - x B) f-1(x) = x - 8 C)f-1(x) = x + 8 D) f-1(x) = x 8 Review for Final Eam Name Algebra- Trigonometr MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polnomial completel. If a polnomial cannot

More information

Find the length of an arc that subtends a central angle of 45 in a circle of radius 8 m. Round your answer to 3 decimal places.

Find the length of an arc that subtends a central angle of 45 in a circle of radius 8 m. Round your answer to 3 decimal places. Chapter 6 Practice Test Find the radian measure of the angle with the given degree measure. (Round your answer to three decimal places.) 80 Find the degree measure of the angle with the given radian measure:

More information

Math 370 Exam 3 Review Name

Math 370 Exam 3 Review Name Math 370 Exam 3 Review Name The following problems will give you an idea of the concepts covered on the exam. Note that the review questions may not be formatted like those on the exam. You should complete

More information

3 Inequalities Absolute Values Inequalities and Intervals... 5

3 Inequalities Absolute Values Inequalities and Intervals... 5 Contents 1 Real Numbers, Exponents, and Radicals 3 1.1 Rationalizing the Denominator................................... 3 1.2 Factoring Polynomials........................................ 3 1.3 Algebraic

More information

Find: sinθ. Name: Date:

Find: sinθ. Name: Date: Name: Date: 1. Find the exact value of the given trigonometric function of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: sinθ c a θ a a =

More information

2018 Midterm Review Trigonometry: Midterm Review A Missive from the Math Department Trigonometry Work Problems Study For Understanding Read Actively

2018 Midterm Review Trigonometry: Midterm Review A Missive from the Math Department Trigonometry Work Problems Study For Understanding Read Actively Summer . Fill in the blank to correctl complete the sentence..4 written in degrees and minutes is..4 written in degrees and minutes is.. Find the complement and the supplement of the given angle. The complement

More information

Trigonometry 1st Semester Review Packet (#2) C) 3 D) 2

Trigonometry 1st Semester Review Packet (#2) C) 3 D) 2 Trigonometry 1st Semester Review Packet (#) Name Find the exact value of the trigonometric function. Do not use a calculator. 1) sec A) B) D) ) tan - 5 A) -1 B) - 1 D) - Find the indicated trigonometric

More information

Math 122 Final Review Guide

Math 122 Final Review Guide Math 122 Final Review Guide Some questions are a combination of ideas from more than one section. Listed are the main sections that a question relates to. 5.4 1. Convert 97 to radians. 5.3 2. If 1035 is

More information

PreCalculus First Semester Exam Review

PreCalculus First Semester Exam Review PreCalculus First Semester Eam Review Name You may turn in this eam review for % bonus on your eam if all work is shown (correctly) and answers are correct. Please show work NEATLY and bo in or circle

More information

Honors Pre-calculus Midterm Review

Honors Pre-calculus Midterm Review Honors Pre-calculus Midterm Review Name: Chapter 1: Functions and Their Graphs 1. Evaluate the function f(x) = x 2 + 1 at each specified value of the independent variable and simplify. a. f( 3) b. f(x

More information

Accuplacer College Level Math Study Guide

Accuplacer College Level Math Study Guide Testing Center Student Success Center Accuplacer Study Guide The following sample questions are similar to the format and content of questions on the Accuplacer College Level Math test. Reviewing these

More information

Math 140 Study Guide. Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 1)

Math 140 Study Guide. Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 1) Math 40 Study Guide Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. ) 0 4) If csc q =, find cot q. A) C) B) 8 Find sin A and cos A. A) sin A = 3 ; cos A

More information

Use a calculator to find the value of the expression in radian measure rounded to 2 decimal places. 1 8) cos-1 6

Use a calculator to find the value of the expression in radian measure rounded to 2 decimal places. 1 8) cos-1 6 Math 180 - chapter 7 and 8.1-8. - New Edition - Spring 09 Name Find the value of the expression. 1) sin-1 0.5 ) tan-1-1 ) cos-1 (- ) 4) sin-1 Find the exact value of the expression. 5) sin [sin-1 (0.7)]

More information

Algebra II Standard Term 4 Review packet Test will be 60 Minutes 50 Questions

Algebra II Standard Term 4 Review packet Test will be 60 Minutes 50 Questions Algebra II Standard Term Review packet 2017 NAME Test will be 0 Minutes 0 Questions DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document.

More information

2018 MIDTERM EXAM REVIEW

2018 MIDTERM EXAM REVIEW Name: Hour: 2018 MIDTERM EXAM REVIEW PRE-CALCULUS Please keep in mind that this exam is worth 20% of your overall grade for this SEMESTER and your semester grade is averaged into your overall GPA. Schedule

More information

( 3 ) = (r) cos (390 ) =

( 3 ) = (r) cos (390 ) = MATH 7A Test 4 SAMPLE This test is in two parts. On part one, you may not use a calculator; on part two, a (non-graphing) calculator is necessary. When you complete part one, you turn it in and get part

More information

Instructor: Imelda Valencia Course: A3 Honors Pre Calculus

Instructor: Imelda Valencia Course: A3 Honors Pre Calculus Student: Date: Instructor: Imelda Valencia Course: A3 Honors Pre Calculus 01 017 Assignment: Summer Homework for those who will be taking FOCA 017 01 onl available until Sept. 15 1. Write the epression

More information

Math 2412 Pre Calculus TEST 2 Prep Fall 2011

Math 2412 Pre Calculus TEST 2 Prep Fall 2011 Math 41 Pre Calculus TEST Prep Fall 011 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the eact value under the given conditions. 1) sin α

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the appropriate identity to find the indicated function value. Rationalize the denominator,

More information

AP CALCULUS AB,...) of Topical Understandings ~

AP CALCULUS AB,...) of Topical Understandings ~ Name: Precalculus Teacher: AP CALCULUS AB ~ (Σer) ( Force Distance) and ( L, L,...) of Topical Understandings ~ As instructors of AP Calculus, we have etremely high epectations of students taking our courses.

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) ±

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) ± Final Review for Pre Calculus 009 Semester Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation algebraically. ) v + 5 = 7 - v

More information

Math 141: Trigonometry Practice Final Exam: Fall 2012

Math 141: Trigonometry Practice Final Exam: Fall 2012 Name: Math 141: Trigonometry Practice Final Eam: Fall 01 Instructions: Show all work. Answers without work will NOT receive full credit. Clearly indicate your final answers. The maimum possible score is

More information

R3.6 Solving Linear Inequalities. 3) Solve: 2(x 4) - 3 > 3x ) Solve: 3(x 2) > 7-4x. R8.7 Rational Exponents

R3.6 Solving Linear Inequalities. 3) Solve: 2(x 4) - 3 > 3x ) Solve: 3(x 2) > 7-4x. R8.7 Rational Exponents Level D Review Packet - MMT This packet briefly reviews the topics covered on the Level D Math Skills Assessment. If you need additional study resources and/or assistance with any of the topics below,

More information

Review for the Final Exam

Review for the Final Exam -1- T 9K8uDt5aU 9SPogf0tEwNaHrdea ALFLWCR.6 m AAylNl9 7rOiBg4hMtYss UrTecs8eMrkvSe1du.E L omgakd2ev zwaiitrhz VINnafCiEnjibtAeD GAWl2g7ezb7rXa3 l2v.i Worksheet by Kuta Software LLC 05.20.10 Algebra 2 Name

More information

8 Systems of Linear Equations

8 Systems of Linear Equations 8 Systems of Linear Equations 8.1 Systems of linear equations in two variables To solve a system of linear equations of the form { a1 x + b 1 y = c 1 x + y = c 2 means to find all its solutions (all pairs

More information

West Essex Regional School District. AP Calculus AB. Summer Packet

West Essex Regional School District. AP Calculus AB. Summer Packet West Esse Regional School District AP Calculus AB Summer Packet 05-06 Calculus AB Calculus AB covers the equivalent of a one semester college calculus course. Our focus will be on differential and integral

More information

Math 175: Chapter 6 Review: Trigonometric Functions

Math 175: Chapter 6 Review: Trigonometric Functions Math 175: Chapter 6 Review: Trigonometric Functions In order to prepare for a test on Chapter 6, you need to understand and be able to work problems involving the following topics. A. Can you sketch an

More information

Calculus Summer Packet

Calculus Summer Packet Calculus Summer Packet Congratulations on reaching this level of mathematics in high school. I know some or all of you are bummed out about having to do a summer math packet; but keep this in mind: we

More information

AP Calculus BC Summer Review

AP Calculus BC Summer Review AP Calculus BC 07-08 Summer Review Due September, 07 Name: All students entering AP Calculus BC are epected to be proficient in Pre-Calculus skills. To enhance your chances for success in this class, it

More information

Pre-Calculus MATH 119 Fall Section 1.1. Section objectives. Section 1.3. Section objectives. Section A.10. Section objectives

Pre-Calculus MATH 119 Fall Section 1.1. Section objectives. Section 1.3. Section objectives. Section A.10. Section objectives Pre-Calculus MATH 119 Fall 2013 Learning Objectives Section 1.1 1. Use the Distance Formula 2. Use the Midpoint Formula 4. Graph Equations Using a Graphing Utility 5. Use a Graphing Utility to Create Tables

More information

KCATM 2013 Algebra Team Test. E) No Solution. C x By. E) None of the Above are correct C) 9,19

KCATM 2013 Algebra Team Test. E) No Solution. C x By. E) None of the Above are correct C) 9,19 KCTM 03 lgebra Team Test School ) Solve the inequality: 6 3 4 5 5 3,,3 3, 3 E) No Solution Both and B are correct. ) Solve for : By C C B y C By B C y C By E) None of the bove are correct 3) Which of the

More information

PreCalculus Final Exam Review Revised Spring 2014

PreCalculus Final Exam Review Revised Spring 2014 PreCalculus Final Eam Review Revised Spring 0. f() is a function that generates the ordered pairs (0,0), (,) and (,-). a. If f () is an odd function, what are the coordinates of two other points found

More information

Honors Precalculus Notes Packet

Honors Precalculus Notes Packet Honors Precalculus Notes Packet 04-05 Academic Magnet High School Contents Unit : Inequalities, Equations, and Graphs... Unit : Functions and Graphs... 6 Unit 3: New Functions from Old... 37 Unit 4: Polynomial

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Math 170 Final Exam Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the function at the given value of the independent variable and

More information

TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet.

TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet. MATH TEST 4 REVIEW TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet. PART NON-CALCULATOR DIRECTIONS: The problems

More information

Math 153 Final Exam Extra Review Problems

Math 153 Final Exam Extra Review Problems Math 153 Final Exam Extra Review Problems This is not intended to be a comprehensive review of every type of problem you are responsible for solving, but instead is meant to give you some extra problems

More information

Math 142: Trigonometry and Analytic Geometry Practice Final Exam: Fall 2012

Math 142: Trigonometry and Analytic Geometry Practice Final Exam: Fall 2012 Name: Math 14: Trigonometry and Analytic Geometry Practice Final Eam: Fall 01 Instructions: Show all work. Answers without work will NOT receive full credit. Clearly indicate your final answers. The maimum

More information

Math 1050 Final Exam Form A College Algebra Fall Semester Student ID ID Verification Section Number

Math 1050 Final Exam Form A College Algebra Fall Semester Student ID ID Verification Section Number Math 1050 Final Eam Form A College Algebra Fall Semester 2010 Instructor Name Student ID ID Verification Section Number Time Limit: 120 minutes Graphing calculators without CAS are allowed. All problems

More information

Pre-Exam. 4 Location of 3. 4 sin 3 ' = b Location of 180 ' = c Location of 315

Pre-Exam. 4 Location of 3. 4 sin 3 ' = b Location of 180 ' = c Location of 315 MATH-330 Pre-Exam Spring 09 Name Rocket Number INSTRUCTIONS: You must show enough work to justify your answer on ALL problems except for Problem 6. Correct answers with no work or inconsistent work shown

More information

Honors Precalculus A. Semester Exam Review

Honors Precalculus A. Semester Exam Review Semester Eam Review Honors Precalculus A Semester Eam Review 015-016 MCPS 015 016 1 Semester Eam Review The semester A eamination for Honors Precalculus consists of two parts. Part 1 is selected response

More information

Group/In-Class Exercises 8/18/09 g0401larson8etrig.tst 4.1 Radian and Degree Measure

Group/In-Class Exercises 8/18/09 g0401larson8etrig.tst 4.1 Radian and Degree Measure Group/In-Class Exercises 8/8/09 g040larson8etrig.tst 4. Radian and Degree Measure Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The given angle

More information

MA Review Worksheet for Exam 1, Summer 2016

MA Review Worksheet for Exam 1, Summer 2016 MA 15800 Review Worksheet for Eam 1, Summer 016 1) Choose which of the following relations represent functions and give the domain and/or range. a) {(,5), (,5), ( 1,5)} b) equation: y 4 1 y 4 (5, ) 1 (

More information

ARE YOU READY 4 CALCULUS

ARE YOU READY 4 CALCULUS ARE YOU READY 4 CALCULUS TEACHER NAME: STUDENT NAME: PERIOD: 50 Problems - Calculator allowed for some problems SCORE SHEET STUDENT NAME: Problem Answer Problem Answer 1 26 2 27 3 28 4 29 5 30 6 31 7 32

More information

IUPUI Department of Mathematical Sciences Departmental Final Examination PRACTICE FINAL EXAM VERSION #1 MATH Trigonometry

IUPUI Department of Mathematical Sciences Departmental Final Examination PRACTICE FINAL EXAM VERSION #1 MATH Trigonometry IUPUI Department of Mathematical Sciences Departmental Final Examination PRACTICE FINAL EXAM VERSION #1 MATH 15400 Trigonometry Exam directions similar to those on the departmental final. 1. DO NOT OPEN

More information

Name: Top Ten Things You ve Learned #10: Graphing Lines, Parabolas, and other Functions I. No Calculator: Sketch a graph of each equation

Name: Top Ten Things You ve Learned #10: Graphing Lines, Parabolas, and other Functions I. No Calculator: Sketch a graph of each equation Name: #: Graphing Lines, Parabolas, and other Functions I. No Calculator: Sketch a graph of each equation... - - - - - -.. 6. - - - - - - 7. 8. 9. - - - - - - ... a f - - - - - - II. Use a graphing calculator

More information

MAT 1050 GROUP FINAL EXAM HOMEWORK

MAT 1050 GROUP FINAL EXAM HOMEWORK MAT 00 GROUP FINAL EXAM HOMEWORK SHOW ALL WORK DO NOT USE A CALCULATOR The problems come from the following final eams: W0, F, F0, W, W, F, W, f Adding/Subtracting Algebraic Epressions Simplif b adding

More information

PRE-CALCULUS FORM IV. Textbook: Precalculus with Limits, A Graphing Approach. 4 th Edition, 2005, Larson, Hostetler & Edwards, Cengage Learning.

PRE-CALCULUS FORM IV. Textbook: Precalculus with Limits, A Graphing Approach. 4 th Edition, 2005, Larson, Hostetler & Edwards, Cengage Learning. PRE-CALCULUS FORM IV Tetbook: Precalculus with Limits, A Graphing Approach. 4 th Edition, 2005, Larson, Hostetler & Edwards, Cengage Learning. Course Description: This course is designed to prepare students

More information

1.1 Angles and Degree Measure

1.1 Angles and Degree Measure J. Jenkins - Math 060 Notes. Angles and Degree Measure An angle is often thought of as being formed b rotating one ra awa from a fied ra indicated b an arrow. The fied ra is the initial side and the rotated

More information

Ch6prac 1.Find the degree measure of the angle with the given radian measure. (Round your answer to the nearest whole number.) -2

Ch6prac 1.Find the degree measure of the angle with the given radian measure. (Round your answer to the nearest whole number.) -2 Ch6prac 1.Find the degree measure of the angle with the given radian measure. (Round your answer to the nearest whole number.) -2 2. Find the degree measure of the angle with the given radian measure.

More information

Math 0210 Common Final Review Questions (2 5 i)(2 5 i )

Math 0210 Common Final Review Questions (2 5 i)(2 5 i ) Math 0 Common Final Review Questions In problems 1 6, perform the indicated operations and simplif if necessar. 1. ( 8)(4) ( )(9) 4 7 4 6( ). 18 6 8. ( i) ( 1 4 i ) 4. (8 i ). ( 9 i)( 7 i) 6. ( i)( i )

More information

Math 231 Final Exam Review

Math 231 Final Exam Review Math Final Eam Review Find the equation of the line tangent to the curve 4y y at the point (, ) Find the slope of the normal line to y ) ( e at the point (,) dy Find d if cos( y) y 4 y 4 Find the eact

More information

MTH 122: Section 204. Plane Trigonometry. Test 1

MTH 122: Section 204. Plane Trigonometry. Test 1 MTH 122: Section 204. Plane Trigonometry. Test 1 Section A: No use of calculator is allowed. Show your work and clearly identify your answer. 1. a). Complete the following table. α 0 π/6 π/4 π/3 π/2 π

More information

Test # 33 QUESTIONS MATH131 091700 COLLEGE ALGEBRA Name atfm131bli www.alvarezmathhelp.com website MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

More information

MATH 115 Precalculus Spring, 2015, V1.2

MATH 115 Precalculus Spring, 2015, V1.2 MULTIPLE CHOICE 1. Solve, and express the answer in interval notation: 6 5x 4. 1. A. (, 2] [2/5, ) B. [2/5, 2] C. (, 2/5] D. (, 2/5] [2, ) 2. Which of the following polynomials has a graph which exhibits

More information

( ) 2 + 2x 3! ( x x ) 2

( ) 2 + 2x 3! ( x x ) 2 Review for The Final Math 195 1. Rewrite as a single simplified fraction: 1. Rewrite as a single simplified fraction:. + 1 + + 1! 3. Rewrite as a single simplified fraction:! 4! 4 + 3 3 + + 5! 3 3! 4!

More information

College Prep Math Final Exam Review Packet

College Prep Math Final Exam Review Packet College Prep Math Final Exam Review Packet Name: Date of Exam: In Class 1 Directions: Complete each assignment using the due dates given by the calendar below. If you are absent from school, you are still

More information

Mth 133 Trigonometry Review Problems for the Final Examination

Mth 133 Trigonometry Review Problems for the Final Examination Mth 1 Trigonometry Review Problems for the Final Examination Thomas W. Judson Stephen F. Austin State University Fall 017 Final Exam Details The final exam for MTH 1 will is comprehensive and will cover

More information

PreCalculus. American Heritage Upper School Summer Math Packet

PreCalculus. American Heritage Upper School Summer Math Packet ! PreCalculus American Heritage Upper School Summer Math Packet All Upper School American Heritage math students are required to complete a summer math packet. This packet is intended for all students

More information

( )( ) Algebra 136 Semester 2 Review. ( ) 6. g( h( x) ( ) Name. In 1-6, use the functions below to find the solutions.

( )( ) Algebra 136 Semester 2 Review. ( ) 6. g( h( x) ( ) Name. In 1-6, use the functions below to find the solutions. Algebra 136 Semester Review In 1-6, use the functions below to find the solutions. Name f ( x) = 3x x + g( x) = x 3 h( x) = x + 3 1. ( f + h) ( x). ( h g) ( x) 3. h x g ( ) 4. ( gh) ( x). f g( x) ( ) 6.

More information