6 3 ) Problems Expand and simplify each of the following algebraic expressions as much as possible. 8. ( x + 2)( x + 2) (x 2 1x ) 2
|
|
- Baldric Woods
- 5 years ago
- Views:
Transcription
1 MA 143 Precalculus Essentials - Fall 2013 Assignment 1. Review of Exponents, Radicals and Fractions Dr. E. Jacobs Read Section 1.1, 1.2, 1.3 and 1.4 Section 1.1/Problems 25-30, Section 1.2/Problems 15-26, Section 1.3/Problems 13-60, Section 1.4/Problems No problems from this assignment will be collected. However, you will get a quiz on problems similar to the problems below: Problems 1-6. Express each of the following in simplest form. I want the exact answers. Decimal approximations are not sufficient. ( ) /4 Problems Expand and simplify each of the following algebraic expressions as much as possible. 7. ( x + 2)( x 2) 8. ( x + 2)( x + 2) 9. ( x ) 2 x 2 (x 2 1x ) y 1 x x y y x Note: A quiz on this material will be given on Friday, August 30. Your score on the quiz will be counted as your score on Assignment 1.
2 Assignment 2. Introduction to Functions Read Section 2.1 Section 2.1/Problems Note: For each of these problems, express each answer in its simplest form. 1. If f(x) = x 2 + 2x, calculate f(1) and f(a 1). 2. If F (x) = 3x + 1, calculate F (2x) and F (x + 2) 3. If G(x) = x 1 3, calculate and simplify the expression G(3x + 1) 4. For each of the following functions, calculate and simplify the expression f(x+h) f(x) h a. f(x) = 4x + 3 b. f(x) = 1 x 2 5. Let f(x) be defined as follows: Graph y = f(x) for 2 x 2. f(x) = { x 2 for x < 0 x + 1 for x 0
3 Assignment 3. Linear Functions Read Section 1.10 Section 1.10/Problems 5-12, 19-38, Find the equation of each of the following lines: a. The line through (0, 3) and (2, 5) b. The line through (2, 4) and (3, 0) 2. Find the equation of the line that passes through the point (2, 8) and is parallel to the line y + 2x = 3 3. The relationship between temperature measured in degrees Celsius (x) and degrees Fahrenheit (y) is known to be linear - that is, it has the form y = mx + b. Water boils at 100 C and 212 F and freezes at 0 C and 32 F. Calculate m and b 4. Suppose your salary was $28,500 in 2003 and $32,900 in Assume your salary follows a linear growth pattern. a) Write a linear equation giving your salary S in terms of the year t where t = 0 corresponds to the year b) Use the linear equation to predict your salary in A small business purchases a piece of equipment for $875. After 5 years the equipment will be outdated, having no value. Write a linear equation giving the value of the equipment y in terms of the time x. Assume that 0 x 5.
4 Assignment 4. Domains, Graphs, Asymptotes, Average Rate of Change Read Section 2.1, 2.2, 2.4, 3.7 Section 2.1/Problems 35-64, 71, 75-78, Section 2.2/Problems 4-28, 33-38, Section 2.4/Problems 1-22, Section 3.7/Problems 21-72, An internet electronics company charges $20 shipping for orders under $80 but provides free shipping for orders that are $80 or more. Thus, if P (x) is the total price for an order of x dollars, P (x) is given by the formula: P (x) = Graph this function on the interval 0 x 100. { x + 20 for x < 80 x for x Find the domain for each of the following functions: a. f(x) = 1 x 6 1 d. G(x) = (x + 1) b. g(x) = 2x 4 c. F (x) = x2 2 x e. H(x) = x The average rate of change of a function f between x and x+h is given by the expression f(x+h) f(x) h. Calculate the average rate of change for each of the following functions. Your answer in each case will be an expression involving both x and h. Simplify each answer as much as possible. a. f(x) = 4x b. f(x) = 4x 2 c. f(x) = 10x 3 d. f(x) = 4x x 3 e. f(x) = 2 x 4. Graph each of the following functions. Make sure that your graph shows all the vertical and horizontal asymptotes, if any. a. y = 2 x 2 b. y = 1 x c. y = 8x2 +x 2x 2 +1 d. y = x (x 2) 2 e. y = x2 x 2 4
5 Assignment 5. Preview of Calculus - Limits and Derivatives Read Section Section 13.2/Problems 11-22, Section 13.3/Problems 3-7, 9-10, 15-22, Section 13.4/Problems 5-16 Problems 1-4. Calculate each of the following limits. I suggest that you refer to your graphs of the functions in problem 4 on Assignment 4 to verify your answers. 1 8x 2 + x 1. lim 2. lim x x x 2x lim x x (x 2) 2 4. lim x x 2 x 2 4 Problems 5-8. If we take h to be closer and closer to 0, then the average rate of change gets closer and closer to the instantaneous rate of change. In calculus notation, this is described as: f f(x + h) f(x) (x) = lim h 0 h Calculate the instantaneous rate of change for each of the following functions using this limit formula. Your answer in each case will be an expression involving only x. Simplify each answer as much as possible. 5. f(x) = 4x 2 6. f(x) = 10x 3 7. f(x) = 4x x 3 8. f(x) = 2 x 9. For the function f(x) = 4x 2, find the equation of the line that is tangent to the curve at x = If c and n are constants, then derivative of cx n can be found immediately with the formula cnx n 1. Use this formula to find the derivatives of each of the following: a. y = x4 2 b. y = 2 x c. y = 2x x d. y = 1 x
6 Assignment 6. Quadratic Functions Read Section 3.1 Section 3.1/Problems 33-42, 45-48, 55, 56, 61, 64, 69, 75, It is always possible to use the method of completing the square to write a quadratic function in the standard form y = a(x h) 2 + k. Write each of the following quadratic functions in standard form and find the value of x that either maximizes or minimizes the function. a. f(x) = x 2 + 6x + 10 b. g(x) = 3 x 1 2 x2 2. A rocket is shot straight up into the air with an initial velocity of v 0 feet per second, and its height h(t) in feet above the ground after t seconds is given by h(t) = 16t 2 + v 0 t a. The rocket hits the ground after 4 seconds. Calculate v 0. b. What is the maximum height attained by the rocket? 3. The number of miles M that an automobile can travel on one gallon of gasoline is a function of its speed v (in miles per hour). If M = 1 30 v2 + 5 v for 0 < v < 70 2 find the value of v that maximizes M 4. There are 2,400 feet of fencing available to make a rectangular horse corral. a. Find a function that models the area of the corral in terms of the width x of the corral. b. Find the dimensions of the rectangle that maximize the area of the corral. 5. A rain gutter is formed by bending up the sides of a 30-inch wide rectangular sheet of metal, as shown below. a. Find a function that models the cross-sectional area of the gutter in terms of x. b. Find the maximum cross-sectional area of the gutter.
7 Assignment 7. Radian Measure Read Section 6.1 Section 6.1/Problems 3-26, 51-67, Suppose s denotes the length of the arc intercepted on a circle of radius r by a central angle of θ radians. If s = 4π kilometers and θ = π/2 radians, find the radius r. 2. Convert each degree measure to radians. Do not use a calculator. Write your answers as rational multiples of π. a) 30 b) 45 c) 90 d) 120 e) Convert each radian measure to degrees. Do not use a calculator. 3π π π π 2π a) 5 b) 3 c) 4 d) 6 e) 3 4. What radius should be used for a circular monorail track if the track is to change its direction of 7 in a distance of 24 meters (measured along the arc of the track)? 5. A motorcycle is moving at a speed of 88 kilometers per hour. If the radius of its wheels is 0.38 meters, find the angle in degrees through whch a spoke of a wheel turns in 3 seconds. 6. A satellite is orbiting a certain planet in a perfectly circular orbit of radius 7680 kilometers. If it makes it two-thirds of a revolution every hour, find : a) its angular speed ω b) its linear speed v 7. A nautical mile may be defined as the arc length intercepted on the surface of the earth by a central angle of measure 1 minute (1/60 of a degree). The radius of the earth is feet. How many feet are there in a nautical mile? 8. A girl rides her bicycle to school at a speed of 12 miles per hour. If the wheel diameter is 26 inches, what is the angular speed of the wheels? 9. A rpm (revolutions per minute) phonograph record has a radius of 14.6 centimeters. What is the linear speed (in centimeters per second) of a point on the rim of the record? 10. The earth, which is approximately 93,000,000 miles from the sun, revolves about the sun in a nearly circular orbit in approximately 365 days. Find the approximate linear speed (in miles per hour) of the earth in its orbit.
8 Assignment 8. Trigonometric Functions Read Section 5.1, 5.2, 6.2 Section 6.2/Problems 3-8, Problems 1-3. In each of the following three problems, the angle θ is an acute angle in a right triangle. Find the values of the six trigonometric functions for each case. 1. The side opposite θ has length 3 and the side adjacent to θ has length The side opposite θ has length 2 and the hypotenuse has length The side opposite θ has length 2 3 and the side adjacent to θ has length A 30-foot ladder leaning against a vertical wall just reaches a window sill. If the ladder makes an angle of 47 with the level ground, how high is the window sill? (Round off your answer to the nearest foot). 5. A guy wire 8 meters long helps support a CB base antenna mounted on top of a flat roof. If the wire makes an angle of 49.5 with the horizontal roof, how far above the roof is it attached to the antenna? (Round off your answer to the nearest tenth of a meter).
9 Assignment 9. Applications to Right Triangle Problems Read Section 6.2 Section 6.2/Problems 31-38, A jetliner is climbing so that its path is a straight line that makes an angle of 8.5 with the horizontal. How many meters does the jetliner rise while traveling 300 meters along its path? (Round off your answer to the nearest meter) 2. To measure the height of a cloud cover at night, a spotlight is aimed straight upward from the ground. The resulting spot of light on the clouds is viewed from a point on the level ground 850 meters from the spotlight, and the angle of elevation is measured at Find the height of the cloud cover to the nearest meter. 3. A lifeguard is seated on a high platform so that her eyes are 7 meters above sea level. Suddenly she spots the dorsal fin of a great white shark at a 4 angle of depression. Estimate, to the nearest meter, the horizontal distance between the platform and the shark. 4. Biologists studying the migration of birds are following a migrating flock in a light plane. The birds are flying at a constant altitude of 1200 feet and the plane is following at a constant altitude of 1700 feet. The biologists must maintain a distance of at least 600 feet between the plane and the flock in order to avoid disturbing the birds; therefore, they must monitor the angle of depression of the flock from the plane. Find the maximum allowable angle of depression, rounded off to the nearest angle. 5. A nature photographer using a telephoto lens photographs a rare bird roosting on a high branch of a tree at an angle of elevation of The distance between the lens and the bird is 330 feet. In order to obtain a more detailed photograph of the bird, the photographer cautiously moves closer to the base of the tree. The angle of elevation of the bird is now Find the new distance between the photographer s lens and the bird.
10 Assignment 10. Nonacute Angles Read Section 5.2, 6.3 Section 5.2/Problems 5-24, 65-72, Section 6.3/Problems Evaluate the six trigonometric functions of the angle θ in the standard position if the terminal side of θ contains the given point (x, y). Do not use a calculator - leave all answers in the form of a fraction or an integer. a. (2, 7) b. ( 2, 4) 2. If sec θ = 5 4 and csc θ = 5 3, use trigonometric identities to find sin θ, cos θ, tan θ and cot θ. 3. Find the values of the remaining five trigonometric functions if cos θ = θ in Q IV (Quadrant 4) 4. Find the quadrant containing θ for the given conditions: a. cos θ > 0 and sin θ < 0 b. sin θ > 0 and cot θ < 0 5. Let θ be the angle from the positive x-axis to the line 3y + 5x = 0, as shown in the diagram below. Find the values of sin θ and cos θ.
11 Assignment 11. Graphs of Trigonometric Functions, Vertical and Horizontal Shifts Read Section 2.5, 2.7, 5.3, 5.4 Section 2.5/Problems 4-33, Section 5.3/Problems 3-14, 17-38, 79, Section 5.4/Problems 4-7, 57 Problems 1-3. Refer to the graph of y = x and draw the graphs of each of the following functions by shifting the graph of y = x appropriately. 1. y = x 2 2. y = x y = x + 2 Problems 4-6. Sketch the graph of the function defined by each equation, find the amplitude and the period, and indicate one cycle on your graph. Start the cycle at a node for the sine functions and at a crest for the cosine function. You may use a graphing calculator or computer to help you draw the graph. 4. y = 2 sin x 5. y = 1 + cos πx 6. y = 2 sin x 3 Problems Write the equations of each of the following sine curves. Problem 7. Problem 8. Problem 9. Problem 10.
12 Assignment 12. Trigonometric Identities Read Section 7.1 Section 7.1/Problems 3-90 Problems 1-4. Use the fundamental identities to simplify each expression: 1. cot v sec v cot 2 y 1 + tan 2 y 3. (sec γ 1)(sec γ + 1) tan γ 4. cos γ 1 sin γ + cos γ 1 + sin γ 5. Rewrite the following trigonometric expression in terms of sines and cosines and simplify the result: sin y + tan y 1 + sec y Problems Show that each trigonometric equation is an identity. sin β csc β + cos β sec β = 1 7. (cos 2 t)(1 + tan 2 t) = 1 8. sin 2 v + tan 2 v + cos 2 v = sec 2 v 9. (cot β + csc β) 2 = sec β + 1 sec β cos( α) 1 + tan( α) sin( α) 1 + cot( α) = sin α + cos α
13 Assignment 13. Inverse Functions Read Section 2.7, 5.5, 6.4 Section 2.7/Problems 5-23, 37-60, Section 5.5/Problems 3-10, Section 6.4/Problems 3-6, Problems 1-3. Find the inverse of each of the following functions. 1. f(x) = 2 + 4x 2. f(x) = 4 x 2 (where x > 0) 3. f(x) = x x 2 Problems 4-6 answers in radians. Evaluate each expression without using a calculator or tables. Give ( 4. cos 1 1 ) 2 5. arccos tan 1 ( 1) 7. Use a calculator to evaluate each expression. Give answers in radians. a. arcsin b. sin 1 ( ) Problems 8-9. tables. Find the exact value of each expression without using a calculator or 8. tan(tan 1 3) 9. cos[arctan( 2)] 10. Rewrite as an algebraic expression in terms of x: sin(arctan x)
14 Assignment 14. Sine and Cosine of Sums and Differences, Double Angle Formulas Read Section 7.2, 7.3 Section 7.2/Problems 3-42, Section 7.3/Problems 3-16, Problems 1-5. Simplify each expression as much as possible. 1. cos(2π γ) ( ) 3π 2. csc 2 + β 3. sin(α β) cos β + cos(α β) sin β ( 4. sin t π ) ( + cos t π ) sin 2 t cos 2 t + cos 4t
15 Assignment 15. Trigonometric Equations Read Section 7.4, 7.5 Section 7.4/Problems 17-44, Section 7.5/Problems 3-34, 43, 45, 47, 51, 52 Problems 1-5. Solve each trigonometric equation with the side condition 0 θ < 360 or 0 t < 2π. Assume that when the variable is given as θ that the angle is measured in degrees and when the variable is given as t that the angle is measured in radians. Do not use a calculator or tables. 1. sin 2θ = cos 2t = 2 sin 2 t 3. cos θ + 3 sin θ = 1 4. sin θ + cos θ = 1 5. cot 2 t + csc 2 t = 3
16 Assignment 16. Exponential and Logarithm Functions Read Section 4.1, 4.2, 4.3 Section 4.1/Problems 9-16, Section 4.2/Problems 7-16, 21, 23, 31, Section 4.3/Problems 7-36, 86, Change each equation to its exponential form: a. log = 3 b. log 2 16 = 4 c. log 6 1 = 0 d. ln e = 1 2. Change each equation to its logarithmic form: a. 2 3 = 8 b = 10, 000 c = d. e 0 = 1 3. Evaluate each logarithm a. log 10 (1, 000, 000) b. log 2 64 c. log e 1 d. log Sketch the graph of each of the following equations: a. y = ( ) x 3 b. y = 2 ( ) x A drug is eliminated from the body through urine. The initial dose is 10 mg and the amount A(t) in the body t hours later is given by: A(t) = 10(0.8) t Determine when only 2 mg of the drug are left in the body.
17 Assignment 17. Properties of Logarithms, Applications of Logarithms and Exponentials Read Section 4.4, 4.5, 4.6 Section 4.4/Problems 7-52, 72, Section 4.5/Problems 3-28, 37-58, Section 4.6/Problems 1-33 Problems 1-6. Solve for x. Decimal approximations from a calculator are acceptable x = e x = log 10 ( x ) = log 2 x + log 2 ( 1 x 2 ) = 1 5. ln(ln x) = 0 6. ln ( e 2x) = 6 7. If the pollution of Lake Erie were stopped suddenly, it has been estimated that the level y of pollutants would decrease according to the formula: y = y 0 e t with time t in years and y 0 is the initial pollutant level (the pollutant level at which further pollution ceased). How many years would it take to clear 50% of the pollutants? 8. Chemists use a number denoted by ph to describe quantitatively the acidity or basicity of solutions. By definition, ph = log 10 [ H + ] where [H + ] denotes the hydrogen ion concentration (in moles per liter). In vinegar, the hydrogen ion concentration is [H + ] Approximate the ph of vinegar. 9. The population N(t) (in millions) of India t years after 1985 may be approximated by the formula: N(t) = 762e 0.022t How many years does it take for the population to triple? 10. If the interest is compounded continuously at the rate of 6% per year, the compound interest formula takes the form: P (t) = P 0 e 0.06t where P 0 denotes the initial deposit. Approximate the number of years it takes an initial deposit of $5,000 to grow to $40,000.
18 Assignment 18. Additional Topics Read Section 12.1, 13.5 and 9.1 Section 12.1/Problems 55-60, 41-48, Section 13.5/Problems 13-14, Section 9.1/Problems 1-74 This assignment should be completed by the last day of the course. At this point, it will be too late for your instructor to grade any homework, so no problems will be collected. However, you will be responsible for this material on the final exam.
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 informationFind 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 informationPractice 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 informationMth 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 information2018 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 informationExam Review 2 nd Semester 6-1 Operations on Functions
NAME DATE PERIOD Exam Review 2 nd Semester 6-1 Operations on Functions Find (f + g)(x), (f g)(x), (f g)(x), and (x) for each f(x) and g(x). 1. f(x) = 8x 3; g(x) = 4x + 5 2. f(x) = + x 6; g(x) = x 2 If
More information3 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 informationChapter 1: Trigonometric Functions 1. Find (a) the complement and (b) the supplement of 61. Show all work and / or support your answer.
Trig Exam Review F07 O Brien Trigonometry Exam Review: Chapters,, To adequately prepare for the exam, try to work these review problems using only the trigonometry knowledge which you have internalized
More informationCh6prac 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 informationMULTIPLE 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. Determine algebraically whether the function is even, odd, or neither even nor odd. ) f(x)
More informationMULTIPLE 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 information1.1 Angles, Degrees, and Arcs
MA140 Trig 2015 Homework p. 1 Name: 1.1 Angles, Degrees, and Arcs Find the fraction of a counterclockwise revolution that will form an angle with the indicated number of degrees. 3(a). 45 3(b). 150 3(c).
More informationDirections: 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 informationMath 370 Exam 2 Review Name
Math 70 Exam 2 Review Name Be sure to complete these problems before the review session. 10 of these questions will count as a quiz in Learning Catalytics. Round 1 will be individual. Round 2 will be in
More informationTrigonometry Final Exam Review
Name Period Trigonometry Final Exam Review 2014-2015 CHAPTER 2 RIGHT TRIANGLES 8 1. Given sin θ = and θ terminates in quadrant III, find the following: 17 a) cos θ b) tan θ c) sec θ d) csc θ 2. Use a calculator
More informationSANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET
SANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET 017-018 Name: 1. This packet is to be handed in on Monday August 8, 017.. All work must be shown on separate paper attached to the packet. 3.
More informationAlgebra II Final Exam Semester II Practice Test
Name: Class: Date: Algebra II Final Exam Semester II Practice Test 1. (10 points) A bacteria population starts at,03 and decreases at about 15% per day. Write a function representing the number of bacteria
More informationMath 1303 Part II. The opening of one of 360 equal central angles of a circle is what we chose to represent 1 degree
Math 1303 Part II We have discussed two ways of measuring angles; degrees and radians The opening of one of 360 equal central angles of a circle is what we chose to represent 1 degree We defined a radian
More informationARE 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 information2. 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 informationPractice Test - Chapter 4
Find the value of x. Round to the nearest tenth, if necessary. Find the measure of angle θ. Round to the nearest degree, if necessary. 1. An acute angle measure and the length of the hypotenuse are given,
More informationName Date Period. Calculater Permitted MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PreAP Precalculus Spring Final Exam Review Name Date Period Calculater Permitted MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression.
More informationMONTGOMERY 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 informationAP 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 information1 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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 3 x 9 D) 27. y 4 D) -8x 3 y 6.
Precalculus Review - Spring 018 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the exponential expression. Assume that variables represent
More informationMath 121: Calculus 1 - Fall 2013/2014 Review of Precalculus Concepts
Introduction Math 121: Calculus 1 - Fall 201/2014 Review of Precalculus Concepts Welcome to Math 121 - Calculus 1, Fall 201/2014! This problems in this packet are designed to help you review the topics
More informationFall 07/MAT 150/Exam 1 Name: Show all your work. 2. (8pts) Solve the inequality and write the solution in interval notation: x 7 2.
Fall 07/MAT 150/Exam 1 Name: Show all your work. 1. (6pts) Solve for x: a 2 x + b = b 2 x a 2. (8pts) Solve the inequality and write the solution in interval notation: x 7 2. 3. (12pts) Find the equation
More informationMath 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 informationA) 13 B) 9 C) 22 D) log 9
Math 70 Exam 2 Review Name Be sure to complete these problems before the review session. Participation in our review session will count as a quiz grade. Please bring any questions you have ready to ask!
More information1. 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 informationHonors 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 informationAP Calculus Free-Response Questions 1969-present AB
AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions
More informationMath 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 informationSection 6.1 Sinusoidal Graphs
Chapter 6: Periodic Functions In the previous chapter, the trigonometric functions were introduced as ratios of sides of a right triangle, and related to points on a circle We noticed how the x and y values
More informationNorth 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 informationPreCalculus Second Semester Review Ch. P to Ch. 3 (1st Semester) ~ No Calculator
PreCalculus Second Semester Review Ch. P to Ch. 3 (1st Semester) ~ No Calculator Solve. Express answer using interval notation where appropriate. Check for extraneous solutions. P3 1. x x+ 5 1 3x = P5.
More informationMath 121: Calculus 1 - Winter 2012/2013 Review of Precalculus Concepts
Introduction Math 11: Calculus 1 - Winter 01/01 Review of Precalculus Concepts Welcome to Math 11 - Calculus 1, Winter 01/01! This problems in this packet are designed to help you review the topics from
More informationMath 121: Calculus 1 - Fall 2012/2013 Review of Precalculus Concepts
Introduction Math 11: Calculus 1 - Fall 01/01 Review of Precalculus Concepts Welcome to Math 11 - Calculus 1, Fall 01/01! This problems in this packet are designed to help you review the topics from Algebra
More informationPre-Calculus 40 Final Outline/Review:
2016-2017 Pre-Calculus 40 Final Outline/Review: Non-Calculator Section: 16 multiple choice (32 pts) and 6 open ended (24 pts). Calculator Section: 8 multiple choice (16 pts) and 11 open ended (36 pts).
More information2018 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 informationn power Name: NOTES 2.5, Date: Period: Mrs. Nguyen s Initial: LESSON 2.5 MODELING VARIATION
NOTES 2.5, 6.1 6.3 Name: Date: Period: Mrs. Nguyen s Initial: LESSON 2.5 MODELING VARIATION Direct Variation y mx b when b 0 or y mx or y kx y kx and k 0 - y varies directly as x - y is directly proportional
More informationMath 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 information5.1: Angles and Radian Measure Date: Pre-Calculus
5.1: Angles and Radian Measure Date: Pre-Calculus *Use Section 5.1 (beginning on pg. 482) to complete the following Trigonometry: measurement of triangles An angle is formed by two rays that have a common
More informationPrecalculus A - Final Exam Review Fall, 2014
Name: Precalculus A - Final Exam Review Fall, 2014 Period: Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 1) 85 2) -166 3) 3 Convert the radian
More information1. 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 informationPrecalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2
Precalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2 Lesson 6.2 Before we look at the unit circle with respect to the trigonometric functions, we need to get some
More information1.1 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 informationPre-Calculus Semester 1 Practice Final
Class: Date: Pre-Calculus Semester Practice Final Multiple Choice Identify the choice that best completes the statement or answers the question.. Evaluate the function at the specified value of the independent
More informationFree Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom
Free Response Questions 1969-010 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions
More information1.1 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 informationAP Calculus Summer Assignment Summer 2017 Expectations for Summer Assignment on the first day of the school year.
Summer 07 Expectations for Summer Assignment This packet is to be submitted to your Calculus BC teacher on the first day of the school year. All work must be shown in the packet OR on separate paper attached
More informationCALCULUS ASSESSMENT REVIEW
CALCULUS ASSESSMENT REVIEW DEPARTMENT OF MATHEMATICS CHRISTOPHER NEWPORT UNIVERSITY 1. Introduction and Topics The purpose of these notes is to give an idea of what to expect on the Calculus Readiness
More informationAP Calculus Summer Assignment - Part 1
2017-2018 AP CALCULUS SUMMER ASSIGNMENT Linear Functions AP Calculus Summer Assignment - Part 1 Determine the equation of the line that passes through the given points 1. (0,-1) and (5,9) 2. (-2,-1) and
More information25 More Trigonometric Identities Worksheet
5 More Trigonometric Identities Worksheet Concepts: Trigonometric Identities Addition and Subtraction Identities Cofunction Identities Double-Angle Identities Half-Angle Identities (Sections 7. & 7.3)
More informationLevel 1 Advanced Mathematics Final Exam June 19, 2007
Level Advanced Mathematics Final Exam June 9, 007 NAME: Instructions WRITE ANSWERS IN THE SPACES PROVIDED AND SHOW ALL WORK. Partial credit will not be given if work is not shown. Ask for extra paper if
More informationJim Lambers Math 1B Fall Quarter Final Exam Solution (Version A)
Jim Lambers Math 1B Fall Quarter 004-05 Final Exam Solution (Version A) 1. Suppose that a culture initially contains 500 bacteria, and that the population doubles every hours. What is the population after
More informationThis is your first impression to me as a mathematician. Make it good.
Calculus Summer 2016 DVHS (AP or RIO) Name : Welcome! Congratulations on reaching this advanced level of mathematics. Calculus is unlike the mathematics you have already studied, and yet it is built on
More informationHalldorson Honors Pre Calculus Name 4.1: Angles and Their Measures
.: Angles and Their Measures. Approximate each angle in terms of decimal degrees to the nearest ten thousandth. a. θ = 5 '5" b. θ = 5 8'. Approximate each angle in terms of degrees, minutes, and seconds
More informationMULTIPLE 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 informationA Short Course in Basic Trigonometry. Marcel B. Finan Arkansas Tech University c All Rights Reserved
A Short Course in Basic Trigonometry Marcel B. Finan Arkansas Tech University c All Rights Reserved PREFACE Trigonometry in modern time is an indispensable tool in Physics, engineering, computer science,
More informationHonors Precalculus Semester 1 Review
Honors Precalculus Semester 1 Review Name: UNIT 1 1. For each sequence, find the explicit and recursive formulas. Show your work. a) 45, 39, 33, 27 b) 8 3, 16 9 32 27, 64 81 Explicit formula: Explicit
More informationTriangles and Vectors
Chapter 3 Triangles and Vectors As was stated at the start of Chapter 1, trigonometry had its origins in the study of triangles. In fact, the word trigonometry comes from the Greek words for triangle measurement.
More informationSummer Packet Greetings Future AP Calculus Scholar,
Summer Packet 2017 Greetings Future AP Calculus Scholar, I am excited about the work that we will do together during the 2016-17 school year. I do not yet know what your math capability is, but I can assure
More informationCHAPTER 6. Section Two angles are supplementary. 2. Two angles are complementary if the sum of their measures is 90 radians
SECTION 6-5 CHAPTER 6 Section 6. Two angles are complementary if the sum of their measures is 90 radians. Two angles are supplementary if the sum of their measures is 80 ( radians).. A central angle of
More informationGroup/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 informationAlgebra 2 Honors Final Exam StudyGuide
Name: Score: 0 / 80 points (0%) Algebra 2 Honors Final Exam StudyGuide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Simplify. 2. D Multiply the numerator
More information; approximate b to the nearest tenth and B or β to the nearest minute. Hint: Draw a triangle. B = = B. b cos 49.7 = 215.
M 1500 am Summer 009 1) Given with 90, c 15.1, and α 9 ; approimate b to the nearest tenth and or β to the nearest minute. Hint: raw a triangle. b 18., 0 18 90 9 0 18 b 19.9, 0 58 b b 1.0, 0 18 cos 9.7
More informationAP CALCULUS Summer Assignment 2014
Name AP CALCULUS Summer Assignment 014 Welcome to AP Calculus. In order to complete the curriculum before the AP Exam in May, it is necessary to do some preparatory work this summer. The following assignment
More informationStudy Guide for Benchmark #1 Window of Opportunity: March 4-11
Study Guide for Benchmark #1 Window of Opportunity: March -11 Benchmark testing is the department s way of assuring that students have achieved minimum levels of computational skill. While partial credit
More informationIUPUI 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 informationSolve the problem. 2) If tan = 3.7, find the value of tan + tan ( + ) + tan ( + 2 ). A) 11.1 B) 13.1 C) D) undefined
Assignment Bonus Chs 6,,8 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. In the problem, t is a real number and P = (x, y) is the point on the
More information2. 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 informationIntermediate Algebra Final Exam Review
Intermediate Algebra Final Exam Review Note to students: The final exam for MAT10, MAT 11 and MAT1 will consist of 30 multiple-choice questions and a few open-ended questions. The exam itself will cover
More informationMath 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 informationSection 6.1. Standard position- the vertex of the ray is at the origin and the initial side lies along the positive x-axis.
1 Section 6.1 I. Definitions Angle Formed by rotating a ray about its endpoint. Initial side Starting point of the ray. Terminal side- Position of the ray after rotation. Vertex of the angle- endpoint
More informationMTH 121 Fall 2007 Essex County College Division of Mathematics and Physics Worksheet #1 1
MTH Fall 007 Essex County College Division of Mathematics and Physics Worksheet # Preamble It is extremely important that you complete the following two items as soon as possible. Please send an email
More informationOn a separate sheet of paper, answer the following questions by showing ALL of your work.
Final Exam Review Cummulative Math 20-1 Ch.1 Sequence and Series Final Exam Review On a separate sheet of paper, answer the following questions by showing ALL of your work. 1. The common difference in
More information3 a = b = Period: a = b = Period: Phase Shift: V. Shift: Phase shift: V. Shift:
Name: Semester One Eam Review Pre-Calculus I. Second Nine Weeks Graphing Trig Functions: sketch the graph of the function, identif the parts being asked. 1. sin. cos( ) 1 Domain: Range: Domain: Range:
More informationLevel 1 Advanced Mathematics Final Exam June 19, 2007
NAME: Answer Key Level Advanced Mathematics Final Exam June 9, 007 Instructions WRITE ANSWERS IN THE SPACES PROVIDED AND SHOW ALL WORK. Partial credit will not be given if work is not shown. Ask for extra
More informationhttps://www.webassign.net/v4cgi/assignments/pre...
Practice Test 2 Part A Chap 1 Sections 5,6,7,8 (11514149) Question 12345678910111213141516171819202122232425262728293031323334353 Description This is one of two practice tests to help you prepare for Test
More informationHomework 3. (33-40) The graph of an exponential function is given. Match each graph to one of the following functions.
Homework Section 4. (-40) The graph of an exponential function is given. Match each graph to one of the following functions. (a)y = x (b)y = x (c)y = x (d)y = x (e)y = x (f)y = x (g)y = x (h)y = x (46,
More informationHalldorson Honors Pre Calculus Name 4.1: Angles and Their Measures
Halldorson Honors Pre Calculus Name 4.1: Angles and Their Measures 1. Approximate each angle in terms of decimal degrees to the nearest ten thousandth. a. θ = 56 34'53" b. θ = 35 48'. Approximate each
More informationAP CALCULUS BC Syllabus / Summer Assignment 2015
AP CALCULUS BC Syllabus / Summer Assignment 015 Name Congratulations! You made it to BC Calculus! In order to complete the curriculum before the AP Exam in May, it is necessary to do some preparatory work
More information(A) (12, 5) (B) ( 8, 15) (C) (3,6) (D) (4,4)
DR. YOU: 018 FALL 1 CHAPTER 1. ANGLES AND BASIC TRIG LECTURE 1-0 REVIEW EXAMPLE 1 YOUR TURN 1 Simplify the radical expression. Simplify the radical expression. (A) 108 (A) 50 First, find the biggest perfect
More informationMTH 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 informationTrigonometry (Ch. 4) Test Review - CALCULATOR ALLOWED
Name: Class: Date: ID: A Trigonometry (Ch. 4) Test Review - CALCULATOR ALLOWED 1. A guy wire runs from the ground to a cell tower. The wire is attached to the cell tower a = 190 feet above the ground.
More informationSummer Work Packet for MPH Math Classes
Summer Work Packet for MPH Math Classes Students going into AP Calculus AB Sept. 018 Name: This packet is designed to help students stay current with their math skills. Each math class expects a certain
More information1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Math120 - Precalculus. Final Review. Fall, 2011 Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
More informationChapter 13: Trigonometry Unit 1
Chapter 13: Trigonometry Unit 1 Lesson 1: Radian Measure Lesson 2: Coterminal Angles Lesson 3: Reference Angles Lesson 4: The Unit Circle Lesson 5: Trig Exact Values Lesson 6: Trig Exact Values, Radian
More informationAlgebra 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 information1. OBJECTIVE: Linear Equations
CUNY YORK COLLEGE FINAL EXAM REVIEW MATH 120: Precalculus Use the following questions to review for your final examimation for Math 120. Your ability to answer these questions will reflect what you learned
More informationGroup Final Spring Is the equation a valid form of one of the Pythagorean trigonometric identities? 1 cot ß = csc., π [D] None of these 6
Group Final Spring 010 1 1. Is the equation a valid form of one of the Pythagorean trigonometric identities? 1 cot ß = csc ß. Find the exact value of the expression. sin π cos π cos π sin π 1 4 1 4. Find
More informationMath 121 Final Exam Review Fall 2011
Math 11 Final Exam Review Fall 011 Calculators can be used. No Cell Phones. Your cell phones cannot be used for a calculator. Put YOUR NAME, UIN, INSTRUCTORS NAME, TA s NAME and DISCUSSION TIME on the
More informationSection 6.1 Angles and Radian Measure Review If you measured the distance around a circle in terms of its radius, what is the unit of measure?
Section 6.1 Angles and Radian Measure Review If you measured the distance around a circle in terms of its radius, what is the unit of measure? In relationship to a circle, if I go half way around the edge
More informationCHAPTER 1. ANGLES AND BASIC TRIG
DR. YOU: 017 FALL 1 CHAPTER 1. ANGLES AND BASIC TRIG LECTURE 1-0 REVIEW EXAMPLE 1 YOUR TURN 1 Simplify the radical expression. Simplify the radical expression. (A) 108 (A) 50 First, find the biggest perfect
More informationPre-calculus Notes: Chapter 5 The Trigonometric Functions. Use the word bank below to fill in the blanks below. You may use each term only once.
Name: Pre-calculus Notes: Chapter 5 The Trigonometric Functions Section 1 Angles and Degree Measure Use the word bank below to fill in the blanks below. You may use each term only once. degree vertex negative
More informationI. Degrees and Radians minutes equal 1 degree seconds equal 1 minute. 3. Also, 3600 seconds equal 1 degree. 3.
0//0 I. Degrees and Radians A. A degree is a unit of angular measure equal to /80 th of a straight angle. B. A degree is broken up into minutes and seconds (in the DMS degree minute second sstem) as follows:.
More informationRegina High School AP Calculus Miss Moon
Regina High School AP Calculus 018-19 Miss Moon Going into AP Calculus, there are certain skills that have been taught to you over the previous years that we assume you have. If you do not have these skills,
More information