(2) = 137 /13 (45 / dt)log(2) = log(137 /13) dt = 13.24
|
|
- Shauna Cooper
- 6 years ago
- Views:
Transcription
1 Correct answer: A 4 WYSE Academic Challenge Sectional Mathematics 008 Solution Set ( sin α + sinα cosα + cos α ) ( + sin( )) ( + ) (sinα + cosα ) α Correct answer: D If Xthe number of girls, then we want P(0)+P()++P(4) OR -[P(5)+P(6)], that is 57/64 3 Correct answer: C 3 We can treat the right side of the equation as a + ar + ar + ar +, where a and a r Sums of this form converge to, which would simplify to x r x x x x 3 This makes the equation x x Solve to get x 3 x (x )(x 3) x, x 3, x 4 (incidentally, x can t be a solution because it would create division by 0 in the right side 4 Correct answer: D In a trapezoid circumscribed about a circle, the sum of the lengths of the legs equal the sum of lengths of the bases; therefore, a+ b 4 The height of the trapezoid equals the diameter of the circle Therefore, the area equals A (a+ b) h Correct answer: B The equation can be re-written as log 3(x + 4x), 4± 6 4()( 9) OR x + 4x 9 0 x Correct answer: C For vectors of the form ai + bj, length is a + b 3 + ( ) 36 7 Correct answer: A f(x) 0x 5x f (x) 60x 60x 60x (x ) The second derivative equals zero at x 0 and x It changes its sign at x, so the only inflection point is at x 8 Correct answer: D 45/ dt () 37 /3 (45 / dt)log() log(37 /3) dt Sectional Solution Set
2 9 Correct answer: A Although we could convert to Cartesian coordinates and find the distance, it is easier to use law of cosines on the triangle created by the two points and (0,0) The distance is a + b abcosθ where a /3, b /4, and θ π / 3 π /4 π / (/ 3) (/ 4) (/ 3)(/ 4)cos( π /) 0 Correct answer: E x y 6x 4y 3(x x) y + 4y+ y ± 3(x ) This is a pair of straight lines Correct answer: A The derivative of a constant is zero Correct answer: E 3(x ) (y + ) kx Let now be x 0 The equation is of the form y Pe We have the two points (-0, 4000) and (0, 48000) This means P and we can solve for k using k( 0) e x, so k and the equation is y 48000e Solve for when x 40 to get y Correct answer: B p p (p ) p + ( p ) p p, since p < 0 4 Correct answer: A 4 The expression may be re written as: (x + 3)(x 4) Vertical asymptotes are x -3 and x 4, so the sum Correct answer: C 4x 4x y + 4y 0 4(x x) (y 4y) 0 4(x x ) (y 4y + 4 4) 0 4(x x + 05) (y 4y + 4) (x 05) (y ) 7 4(x 05) (y ) (x 05) (y ) This means we end up with 7 7 7/4 7 ( ) ( ) 7 ( ) ( ) a 7/4, b, and c 7 / / Sectional Solution Set
3 6 Correct answer: B 3 + i x i 3 + i + i i + i 3 + 6i + i + i (i ) 3 + 7i i 5 7 Correct answer: E 8 < 6 x < 8 4< x < < x < 7 8 Correct answer: D A Amy s $, B Betsy s $, C Charlie s $, x $ left 08A x, 035B x, 053C x A + B + C 00000, so x/08 + x/035 + x/ Solve to get x A 0593 so A Correct answer: D The equation has a solution only if a 0 There are two cases x 0x a This equation can be rewritten as x 0x a 0 with the discriminant D ( 0) 4 a 00 4a x 0x a This equation can be represented as x 0x + a 0 with the discriminant D ( 00) 4 ( a) a The second discriminant is positive for a 0, so the second equation has two solutions for any non-negative value of a Therefore, the first equation must have exactly one solution, so the discriminant must be equal to 0: 00 4a 0 Therefore, a 5 0 Correct answer: A f( x+ 5) ( x+ 5 ) + (x+ 5 x ) x x Correct answer: B 85% of 38%, or 33%, of all trees die and are attacked 6% of 6%, or 6%, of all trees die and are not attacked This means , or 484% of all trees die The 33% represents 33 / 484, or 66708% of those that have died Correct answer: C A s( s a)( s b)( s c) wheres ( a+ b+ c)/ A 8(8 4)(8 5)(8 7) 98 3 Correct answer: B Ans B: x x + 3x + 5x 5 5 8x 0 5 and Correct answer: C SA 4π r, V 3 4/3π r Since 4 r 000, π r 8906, and V Sectional Solution Set
4 5 Correct answer: D Let a be the length of the legs of the triangle Then, the length of the hypotenuse is a p and the perimeter equals a+ a+ a a(+ ) p Therefore, a and + p p p 3 A a a p ( + ) Correct answer: E P(g from A and w from B) OR P(w from A and w from B)(3/7)(5/7)+(4/7)(6/7) (5+4)/49 39/49 7 Correct answer: B The height of the rectangle is 7 inches, and the width of the rectangle is 5 3 inches This means the perimeter is , or 33 inches 8 Correct answer: C Let us square the equation 7 a + a 3+ a a : 7 a + a 7 a + a 3+ a a + 3+ a a 4 Therefore, 7 a + a 3+ a a 6, so 9 Correct answer: A 7 a + a 3+ a a 3 5(r) 450e 34 5r ln(34 / 450) r r 0% - Go To Next Page Sectional Solution Set
5 30 Correct answer: A The perimeter of A is exactly 3 inches Since the area of triangle A is twice the area of B, each side of A is times as long as the matching side on triangle B Some students may have memorized this fact or will do proof through example The general proof of this argument is rather complex: We can express the area of a triangle in terms of any one side squared times a trigonometric expression of the three angles For example, in the following triangle, x is the length of one side, and a, b, and c are the angle measures: b a c By law of sines, the left side has length of xsinc sinb x The height of the triangle would then be xsinc sina sinb This means the area of the triangle can be expressed as xsinc 05 x sina sinb sinc sina x sinb Any similar triangle would have an area that sinc sina includes an identical value for sinb If a similar triangle has twice the area and has side y in the same spot as side x on our triangle, then: sincsina sincsina y x sinb sinb, y x, y x This ratio will hold for all three sides 3 Correct answer: D sin x sin(x) cos x cos(x) + sin x sin(x) cos(x x) + tan x tanx + sec(x) cos x cos(x) cos x cosx cos x cos(x) cosx 3 Correct answer: E 00 ( ) Correct answer: D Rectangular solid 4 * 3 * 4 cubic feet height of prism is 5 39 feet, so prism is 05 * 3 * 39 * cubic feet This makes the overall volume equal to 3937 cubic feet 008 Sectional Solution Set
6 34 Correct answer: E Let a and b be legs of the right triangle Then A ab 5 and a + b 4 Therefore ab 00 and a + b 576 If we add these two equations, we will get a + ab + b ( a + b) Therefore, a + b 6, so the perimeter equals p a + b Correct answer: E This is a binomial probability We could add up P () + P (3) + + P (0), but it s easier to calculate (P (0) + P ()) (095^0 + 0 * 095^9 * 005) Correct answer: B x 3 x 5 a 3a 5 (a 5)(a+ ) a 5 x 5 Let x a, then x + x a + a (a )(a+ ) a x 37 Correct answer: B 3 + (x 5) 80, so x 3 4x + 3 7, Correct answer: D x x (3y 5) 3 x+ 3 3y 5 y 39 Correct answer: A By matrix algebra, C AB U This means [ U] 40 Correct answer: C 3 9 4, so x - Let x sin a, then we need to find co s(x), knowing that a sinx Let us express cos(x) in terms of sin x : ( ) cos(x) cos x sin x sin x sin x sin x a 008 Sectional Solution Set
Math 005A Prerequisite Material Answer Key
Math 005A Prerequisite Material Answer Key 1. a) P = 4s (definition of perimeter and square) b) P = l + w (definition of perimeter and rectangle) c) P = a + b + c (definition of perimeter and triangle)
More informationUsing this definition, it is possible to define an angle of any (positive or negative) measurement by recognizing how its terminal side is obtained.
Angle in Standard Position With the Cartesian plane, we define an angle in Standard Position if it has its vertex on the origin and one of its sides ( called the initial side ) is always on the positive
More informationMath 104 Midterm 3 review November 12, 2018
Math 04 Midterm review November, 08 If you want to review in the textbook, here are the relevant sections: 4., 4., 4., 4.4, 4..,.,. 6., 6., 6., 6.4 7., 7., 7., 7.4. Consider a right triangle with base
More informationInverse Trig Functions
6.6i Inverse Trigonometric Functions Inverse Sine Function Does g(x) = sin(x) have an inverse? What restriction would we need to make so that at least a piece of this function has an inverse? Given f (x)
More information(b) x = (d) x = (b) x = e (d) x = e4 2 ln(3) 2 x x. is. (b) 2 x, x 0. (d) x 2, x 0
1. Solve the equation 3 4x+5 = 6 for x. ln(6)/ ln(3) 5 (a) x = 4 ln(3) ln(6)/ ln(3) 5 (c) x = 4 ln(3)/ ln(6) 5 (e) x = 4. Solve the equation e x 1 = 1 for x. (b) x = (d) x = ln(5)/ ln(3) 6 4 ln(6) 5/ ln(3)
More informationc) xy 3 = cos(7x +5y), y 0 = y3 + 7 sin(7x +5y) 3xy sin(7x +5y) d) xe y = sin(xy), y 0 = ey + y cos(xy) x(e y cos(xy)) e) y = x ln(3x + 5), y 0
Some Math 35 review problems With answers 2/6/2005 The following problems are based heavily on problems written by Professor Stephen Greenfield for his Math 35 class in spring 2005. His willingness to
More informationMCR3U - Practice Mastery Test #6
Name: Class: Date: MCRU - Practice Mastery Test #6 Multiple Choice Identify the choice that best completes the statement or answers the question.. Factor completely: 4x 2 2x + 9 a. (2x ) 2 b. (4x )(x )
More informationTrig Identities, Solving Trig Equations Answer Section
Trig Identities, Solving Trig Equations Answer Section MULTIPLE CHOICE. ANS: B PTS: REF: Knowledge and Understanding OBJ: 7. - Compound Angle Formulas. ANS: A PTS: REF: Knowledge and Understanding OBJ:
More informationMath 12 Final Exam Review 1
Math 12 Final Exam Review 1 Part One Calculators are NOT PERMITTED for this part of the exam. 1. a) The sine of angle θ is 1 What are the 2 possible values of θ in the domain 0 θ 2π? 2 b) Draw these angles
More informationMATH 1241 FINAL EXAM FALL 2012 Part I, No Calculators Allowed
MATH 11 FINAL EXAM FALL 01 Part I, No Calculators Allowed 1. Evaluate the limit: lim x x x + x 1. (a) 0 (b) 0.5 0.5 1 Does not exist. Which of the following is the derivative of g(x) = x cos(3x + 1)? (a)
More informationFor a semi-circle with radius r, its circumfrence is πr, so the radian measure of a semi-circle (a straight line) is
Radian Measure Given any circle with radius r, if θ is a central angle of the circle and s is the length of the arc sustained by θ, we define the radian measure of θ by: θ = s r For a semi-circle with
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 informationSET 1. (1) Solve for x: (a) e 2x = 5 3x
() Solve for x: (a) e x = 5 3x SET We take natural log on both sides: ln(e x ) = ln(5 3x ) x = 3 x ln(5) Now we take log base on both sides: log ( x ) = log (3 x ln 5) x = log (3 x ) + log (ln(5)) x x
More informationDirections: Fill in the following in the appropriate spaces on the answer sheet and darken the corresponding
MATH 55 FINAL -FORM A Fall 0 Directions: Fill in the following in the appropriate spaces on the answer sheet and darken the corresponding ovals:. Last name, first and middle initials.. Student Z Number.
More informationH I G H E R S T I L L. Extended Unit Tests Higher Still Higher Mathematics. (more demanding tests covering all levels)
M A T H E M A T I C S H I G H E R S T I L L Higher Still Higher Mathematics Extended Unit Tests 00-0 (more demanding tests covering all levels) Contents Unit Tests (at levels A, B and C) Detailed marking
More informationCK- 12 Algebra II with Trigonometry Concepts 1
14.1 Graphing Sine and Cosine 1. A.,1 B. (, 1) C. 3,0 D. 11 1, 6 E. (, 1) F. G. H. 11, 4 7, 1 11, 3. 3. 5 9,,,,,,, 4 4 4 4 3 5 3, and, 3 3 CK- 1 Algebra II with Trigonometry Concepts 1 4.ans-1401-01 5.
More information1.3 Basic Trigonometric Functions
www.ck1.org Chapter 1. Right Triangles and an Introduction to Trigonometry 1. Basic Trigonometric Functions Learning Objectives Find the values of the six trigonometric functions for angles in right triangles.
More informationcorrelated to the Indiana Academic Standards for Precalculus CC2
correlated to the Indiana Academic Standards for Precalculus CC2 6/2003 2003 Introduction to Advanced Mathematics 2003 by Richard G. Brown Advanced Mathematics offers comprehensive coverage of precalculus
More informationAcademic Challenge 2009 Regional Mathematics Solution Set. #2 Ans. C. Let a be the side of the cube. Then its surface area equals 6a = 10, so
Academic Challenge 009 Regional Mathematics Solution Set #1 Ans. C: x 4 = x 9 = -5 # Ans. C. Let a be the side of the cube. Then its surface area equals 6a = 10, so a = 10 / 6 and volume V = a = ( 10 /
More information5, tan = 4. csc = Simplify: 3. Simplify: 4. Factor and simplify: cos x sin x cos x
Precalculus Final Review 1. Given the following values, evaluate (if possible) the other four trigonometric functions using the fundamental trigonometric identities or triangles csc = - 3 5, tan = 4 3.
More informationLone Star College-CyFair Formula Sheet
Lone Star College-CyFair Formula Sheet The following formulas are critical for success in the indicated course. Student CANNOT bring these formulas on a formula sheet or card to tests and instructors MUST
More informationAP CALCULUS SUMMER WORKSHEET
AP CALCULUS SUMMER WORKSHEET DUE: First Day of School, 2011 Complete this assignment at your leisure during the summer. I strongly recommend you complete a little each week. It is designed to help you
More informationWithout fully opening the exam, check that you have pages 1 through 11.
Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response
More informationMLC Practice Final Exam
Name: Section: Recitation/Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response
More informationFind all solutions cos 6. Find all solutions. 7sin 3t Find all solutions on the interval [0, 2 ) sin t 15cos t sin.
7.1 Solving Trigonometric Equations with Identities In this section, we explore the techniques needed to solve more complex trig equations: By Factoring Using the Quadratic Formula Utilizing Trig Identities
More informationMath Fall 08 Final Exam Review
Math 173.7 Fall 08 Final Exam Review 1. Graph the function f(x) = x 2 3x by applying a transformation to the graph of a standard function. 2.a. Express the function F(x) = 3 ln(x + 2) in the form F = f
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 informationCAMI Education links: Maths NQF Level 4
CONTENT 1.1 Work with Comple numbers 1. Solve problems using comple numbers.1 Work with algebraic epressions using the remainder and factor theorems CAMI Education links: MATHEMATICS NQF Level 4 LEARNING
More informationAcademic Challenge 2012 Regional Math Solutions. (x 2)(x 3) 2. Ans C: As the rational expression for f(x) everywhere x is not 3 factors into
Academic Challenge 0 Regional Math Solutions Ans C: 8 4 ( 70)( 55) = = 4 9 7 6 ( )( ) Ans C: As the rational epression for f() everywhere is not factors into, it is evident that f() = ecept at = Thus,
More informationState Precalculus/Trigonometry Contest 2008
State Precalculus/Trigonometry Contest 008 Select the best answer for each of the following questions and mark it on the answer sheet provided. Be sure to read all the answer choices before making your
More informationAnswer Key. 7.1 Tangent Ratio. Chapter 7 Trigonometry. CK-12 Geometry Honors Concepts 1. Answers
7.1 Tangent Ratio 1. Right triangles with 40 angles have two pairs of congruent angles and therefore are similar. This means that the ratio of the opposite leg to adjacent leg is constant for all 40 right
More information2 Trigonometric functions
Theodore Voronov. Mathematics 1G1. Autumn 014 Trigonometric functions Trigonometry provides methods to relate angles and lengths but the functions we define have many other applications in mathematics..1
More informationExam 3: December 3 rd 7:00-8:30
MTH 111 - Fall 01 Exam Review (Solutions) Exam : December rd 7:00-8:0 Name: This exam review contains questions similar to those you should expect to see on Exam. The questions included in this review,
More information0113a2. Algebra 2/Trigonometry Regents Exam 0113
Algebra /Trigonometry Regents Exam 011 www.jmap.org 011a 1 What is the equation of the graph shown below? 4 What is the common ratio of the geometric sequence shown below?, 4, 8,16,... 1) 1 ) ) 4) 6 1)
More informationSum and difference formulae for sine and cosine. Elementary Functions. Consider angles α and β with α > β. These angles identify points on the
Consider angles α and β with α > β. These angles identify points on the unit circle, P (cos α, sin α) and Q(cos β, sin β). Part 5, Trigonometry Lecture 5.1a, Sum and Difference Formulas Dr. Ken W. Smith
More informationUnit 6 Trigonometric Identities
Unit 6 Trigonometric Identities Prove trigonometric identities Solve trigonometric equations Prove trigonometric identities, using: Reciprocal identities Quotient identities Pythagorean identities Sum
More informationTrigonometry - Part 1 (12 pages; 4/9/16) fmng.uk
Trigonometry - Part 1 (12 pages; 4/9/16) (1) Sin, cos & tan of 30, 60 & 45 sin30 = 1 2 ; sin60 = 3 2 cos30 = 3 2 ; cos60 = 1 2 cos45 = sin45 = 1 2 = 2 2 tan45 = 1 tan30 = 1 ; tan60 = 3 3 Graphs of y =
More informationChapter 1. Functions 1.3. Trigonometric Functions
1.3 Trigonometric Functions 1 Chapter 1. Functions 1.3. Trigonometric Functions Definition. The number of radians in the central angle A CB within a circle of radius r is defined as the number of radius
More informationx 2 x 2 4 x 2 x + 4 4x + 8 3x (4 x) x 2
MTH 111 - Spring 015 Exam Review (Solutions) Exam (Chafee Hall 71): April rd, 6:00-7:0 Name: 1. Solve the rational inequality x +. State your solution in interval notation. x DO NOT simply multiply both
More informationMA Practice Exam #2 Solutions
MA 123 - Practice Exam #2 Solutions Name: Instructions: For some of the questions, you must show all your work as indicated. No calculators, books or notes of any form are allowed. Note that the questions
More informationAP CALCULUS SUMMER WORKSHEET
AP CALCULUS SUMMER WORKSHEET DUE: First Day of School Aug. 19, 2010 Complete this assignment at your leisure during the summer. It is designed to help you become more comfortable with your graphing calculator,
More informationGeometry Honors Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Geometry Honors Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the conclusion of the following conditional? A number is divisible
More informationCandidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required.
Revision Checklist Unit C2: Core Mathematics 2 Unit description Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation;
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 informationWithout fully opening the exam, check that you have pages 1 through 11.
Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response
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 informationCore 3 (A2) Practice Examination Questions
Core 3 (A) Practice Examination Questions Trigonometry Mr A Slack Trigonometric Identities and Equations I know what secant; cosecant and cotangent graphs look like and can identify appropriate restricted
More informationResources: http://www.calcchat.com/book/calculus-9e/ http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/27.html http://www.calculus.org/ http://cow.math.temple.edu/ http://www.mathsisfun.com/calculus/
More informationCK- 12 Algebra II with Trigonometry Concepts 1
1.1 Pythagorean Theorem and its Converse 1. 194. 6. 5 4. c = 10 5. 4 10 6. 6 5 7. Yes 8. No 9. No 10. Yes 11. No 1. No 1 1 1. ( b+ a)( a+ b) ( a + ab+ b ) 1 1 1 14. ab + c ( ab + c ) 15. Students must
More informationsin x (B) sin x 1 (C) sin x + 1
ANSWER KEY Packet # AP Calculus AB Eam Multiple Choice Questions Answers are on the last page. NO CALCULATOR MAY BE USED IN THIS PART OF THE EXAMINATION. On the AP Eam, you will have minutes to answer
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 informationMath Trigonometry Final Exam
Math 1613 - Trigonometry Final Exam Name: Instructions: Please show all of your work. If you need more room than the problem allows, use a new plain white sheet of paper with the problem number printed
More informationPART ONE: Solve algebraically and check. Be sure to show all work.
NAME AP CALCULUS BC SUMMER ASSIGNMENT 2017 DIRECTIONS: Each part must be completed separately on looseleaf. All work should be shown and done in a neat and precise manner. Any questions pertaining to the
More informationUnit 6 Trigonometric Identities Prove trigonometric identities Solve trigonometric equations
Unit 6 Trigonometric Identities Prove trigonometric identities Solve trigonometric equations Prove trigonometric identities, using: Reciprocal identities Quotient identities Pythagorean identities Sum
More information( ) 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 informationChapter 7: Techniques of Integration
Chapter 7: Techniques of Integration MATH 206-01: Calculus II Department of Mathematics University of Louisville last corrected September 14, 2013 1 / 43 Chapter 7: Techniques of Integration 7.1. Integration
More informationIndiana Academic Standards for Precalculus
PRECALCULUS correlated to the Indiana Academic Standards for Precalculus CC2 6/2003 2004 Introduction to Precalculus 2004 by Roland E. Larson and Robert P. Hostetler Precalculus thoroughly explores topics
More informationTrigonometric Functions () 1 / 28
Trigonometric Functions () 1 / 28 Trigonometric Moel On a certain ay, ig tie at Pacific Beac was at minigt. Te water level at ig tie was 9.9 feet an later at te following low tie, te tie eigt was 0.1 ft.
More informationTRIGONOMETRY OUTCOMES
TRIGONOMETRY OUTCOMES C10. Solve problems involving limits of trigonometric functions. C11. Apply derivatives of trigonometric functions. C12. Solve problems involving inverse trigonometric functions.
More informationAlpha Trigonometry Solutions MA National Convention. Answers:
Answers: 1 A C C D 5 A 6 C 7 B 8 A 9 A 10 A 11 C 1 D 1 E 1 B 15 C 16 C 17 D 18 C 19 B 0 C 1 E A C C 5 E 6 B 7 E 8 D 9 D 0 B 1 Solutions: 1 A Need to check each answer to 1 k60 and 1 (60 ) = 06. C An even
More informationSpherical trigonometry
Spherical trigonometry 1 The spherical Pythagorean theorem Proposition 1.1 On a sphere of radius, any right triangle AC with C being the right angle satisfies cos(c/) = cos(a/) cos(b/). (1) Proof: Let
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 information2018 TAME High School Practice Mathematics Test
018 TAME High School Practice Mathematics Test (1) Arturo took four exams and made grades of 65, 88, 9 and 75. If Arturo wants to have an average of at least 80, which of the following is the lowest grade
More informationThe American School of Marrakesh. AP Calculus AB Summer Preparation Packet
The American School of Marrakesh AP Calculus AB Summer Preparation Packet Summer 2016 SKILLS NEEDED FOR CALCULUS I. Algebra: *A. Exponents (operations with integer, fractional, and negative exponents)
More informationM152: Calculus II Midterm Exam Review
M52: Calculus II Midterm Exam Review Chapter 4. 4.2 : Mean Value Theorem. - Know the statement and idea of Mean Value Theorem. - Know how to find values of c making the theorem true. - Realize the importance
More informationMath-2A. Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms
Math-A Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms Describe the idea of area. Area attempts to answer the question how big is it? The area
More informationSpring 2015 Sample Final Exam
Math 1151 Spring 2015 Sample Final Exam Final Exam on 4/30/14 Name (Print): Time Limit on Final: 105 Minutes Go on carmen.osu.edu to see where your final exam will be. NOTE: This exam is much longer than
More informationThe goal of today is to determine what u-substitution to use for trigonometric integrals. The most common substitutions are the following:
Trigonometric Integrals The goal of today is to determine what u-substitution to use for trigonometric integrals. The most common substitutions are the following: Substitution u sinx u cosx u tanx u secx
More informationI) Simplifying fractions: x x. 1) 1 1 y x. 1 1 x 1. 4 x. 13x. x y xy. x 2. Factoring: 10) 13) 12) III) Solving: x 9 Prime (using only) 11)
AP Calculus Summer Packet Answer Key Reminders:. This is not an assignment.. This will not be collected.. You WILL be assessed on these skills at various times throughout the course.. You are epected to
More informationINSTRUCTOR SAMPLE E. Check that your exam contains 25 questions numbered sequentially. Answer Questions 1-25 on your scantron.
MATH 41 FINAL EXAM NAME SECTION NUMBER INSTRUCTOR SAMPLE E On your scantron, write and bubble your PSU ID, Section Number, and Test Version. Failure to correctly code these items may result in a loss of
More informationSummer Review for Students Entering AP Calculus AB
Summer Review for Students Entering AP Calculus AB Class: Date: AP Calculus AB Summer Packet Please show all work in the spaces provided The answers are provided at the end of the packet Algebraic Manipulation
More informationQuadratic Applications Name: Block: 3. The product of two consecutive odd integers is equal to 30 more than the first. Find the integers.
Quadratic Applications Name: Block: This problem packet is due before 4pm on Friday, October 26. It is a formative assessment and worth 20 points. Complete the following problems. Circle or box your answer.
More informationMA FINAL EXAM Form A MAY 1, 2017
MA 6 FINAL EXAM Form A MAY, 7 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a # pencil on the scantron. a. If the cover of your exam is GREEN, write in the TEST/QUIZ NUMBER boxes and darken
More informationSum and Difference Identities
Sum and Difference Identities By: OpenStaxCollege Mount McKinley, in Denali National Park, Alaska, rises 20,237 feet (6,168 m) above sea level. It is the highest peak in North America. (credit: Daniel
More informationFriday 09/15/2017 Midterm I 50 minutes
Fa 17: MATH 2924 040 Differential and Integral Calculus II Noel Brady Friday 09/15/2017 Midterm I 50 minutes Name: Student ID: Instructions. 1. Attempt all questions. 2. Do not write on back of exam sheets.
More information8.6 Inverse Trigonometric Ratios
www.ck12.org Chapter 8. Right Triangle Trigonometry 8.6 Inverse Trigonometric Ratios Learning Objectives Use the inverse trigonometric ratios to find an angle in a right triangle. Solve a right triangle.
More information1 Solving equations 1.1 Kick off with CAS 1. Polynomials 1. Trigonometric symmetry properties 1.4 Trigonometric equations and general solutions 1.5 Literal and simultaneous equations 1.6 Review 1.1 Kick
More informationSolving equations UNCORRECTED PAGE PROOFS
1 Solving equations 1.1 Kick off with CAS 1. Polynomials 1.3 Trigonometric symmetry properties 1.4 Trigonometric equations and general solutions 1.5 Literal equations and simultaneous equations 1.6 Review
More informationCalculus I (Math 241) (In Progress)
Calculus I (Math 241) (In Progress) The following is a collection of Calculus I (Math 241) problems. Students may expect that their final exam is comprised, more or less, of one problem from each section,
More informationFinal Exam. Math 3 December 7, 2010
Final Exam Math 3 December 7, 200 Name: On this final examination for Math 3 in Fall 200, I will work individually, neither giving nor receiving help, guided by the Dartmouth Academic Honor Principle.
More informationREQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS
REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS The Department of Applied Mathematics administers a Math Placement test to assess fundamental skills in mathematics that are necessary to begin the study
More information1,cost 1 1,tant 0 1,cott ,cost 0 1,tant 0. 1,cott 1 0. ,cost 5 6,tant ,cott x 2 1 x. 1 x 2. Name: Class: Date:
Class: Date: Practice Test (Trigonometry) Instructor: Koshal Dahal Multiple Choice Questions SHOW ALL WORK, EVEN FOR MULTIPLE CHOICE QUESTIONS, TO RECEIVE CREDIT. 1. Find the values of the trigonometric
More informationAlgebra 2/Trig AIIT.17 Trig Identities Notes. Name: Date: Block:
Algebra /Trig AIIT.7 Trig Identities Notes Mrs. Grieser Name: Date: Block: Trigonometric Identities When two trig expressions can be proven to be equal to each other, the statement is called a trig identity
More informationLearning Objectives for Math 165
Learning Objectives for Math 165 Chapter 2 Limits Section 2.1: Average Rate of Change. State the definition of average rate of change Describe what the rate of change does and does not tell us in a given
More informationThanks for downloading this product from Time Flies!
Thanks for downloading this product from Time Flies! I hope you enjoy using this product. Follow me at my TpT store! My Store: https://www.teacherspayteachers.com/store/time-flies 2018 Time Flies. All
More information. CALCULUS AB. Name: Class: Date:
Class: _ Date: _. CALCULUS AB SECTION I, Part A Time- 55 Minutes Number of questions -8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions: Solve each of the following problems, using
More informationMathematics, Algebra, and Geometry
Mathematics, Algebra, and Geometry by Satya http://www.thesatya.com/ Contents 1 Algebra 1 1.1 Logarithms............................................ 1. Complex numbers........................................
More information0615a2. Algebra 2/Trigonometry Regents Exam x 2 y? 4 x. y 2. x 3 y
Algebra /Trigonometry Regents Exam 065 www.jmap.org 065a Which list of ordered pairs does not represent a one-to-one function? ) (, ),(,0),(,),(4,) ) (,),(,),(,4),(4,6) ) (,),(,4),(,),(4,) 4) (,5),(,4),(,),(4,0)
More informationTrig Practice 08 and Specimen Papers
IB Math High Level Year : Trig: Practice 08 and Spec Papers Trig Practice 08 and Specimen Papers. In triangle ABC, AB = 9 cm, AC = cm, and Bˆ is twice the size of Ĉ. Find the cosine of Ĉ.. In the diagram
More informationWYSE ACADEMIC CHALLENGE State Math Exam 2009 Solution Set. 2. Ans E: Function f(x) is an infinite geometric series with the ratio r = :
WYSE ACADEMIC CHALLENGE State Math Eam 009 Solution Set 40. Ans A: ( C( 40,8 ) * C( 3,8 ) * C( 4,8 ) * C( 6,8 ) * C( 8,8 )) / 5 = 0.00084. Ans E: Function f() is an infinite geometric series with the ratio
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 informationπ = d Addition Formulae Revision of some Trigonometry from Unit 1Exact Values H U1 O3 Trigonometry 26th November 2013 H U2 O3 Trig Formulae
26th November 2013 H U1 O3 Trigonometry Addition Formulae Revision of some Trigonometry from Unit 1Exact Values 2 30 o 30 o 3 2 r π = d 180 1 1 45 o 45 o 2 45 o 45 o 1 1 60 o 60 o 1 2 1 180 x x 180 + x
More informationWYSE MATH REGIONAL 2014 SOLUTIONS. 1. Ans C: There are eight vertices in a cube and six in an octahedron.
WYSE MATH REGIONAL 04 SOLUTIONS. Ans C: There are eight vertices in a cube and six in an octahedron.. Ans E: There are C 9 ways to select the 9 doughnuts. This is 8,57,00 ways. There are 8 C ways to select
More informationChapter 5 Notes. 5.1 Using Fundamental Identities
Chapter 5 Notes 5.1 Using Fundamental Identities 1. Simplify each expression to its lowest terms. Write the answer to part as the product of factors. (a) sin x csc x cot x ( 1+ sinσ + cosσ ) (c) 1 tanx
More information4 The Trigonometric Functions
Mathematics Learning Centre, University of Sydney 8 The Trigonometric Functions The definitions in the previous section apply to between 0 and, since the angles in a right angle triangle can never be greater
More informationDear Future CALCULUS Student,
Dear Future CALCULUS Student, I am looking forward to teaching the AP Calculus AB class this coming year and hope that you are looking forward to the class as well. Here a few things you need to know prior
More informationMath 1310 Final Exam
Math 1310 Final Exam December 11, 2014 NAME: INSTRUCTOR: Write neatly and show all your work in the space provided below each question. You may use the back of the exam pages if you need additional space
More informationOne of the powerful themes in trigonometry is that the entire subject emanates from a very simple idea: locating a point on the unit circle.
2.24 Tanz and the Reciprocals Derivatives of Other Trigonometric Functions One of the powerful themes in trigonometry is that the entire subject emanates from a very simple idea: locating a point on the
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 information6.1 The Inverse Sine, Cosine, and Tangent Functions Objectives
Objectives 1. Find the Exact Value of an Inverse Sine, Cosine, or Tangent Function. 2. Find an Approximate Value of an Inverse Sine Function. 3. Use Properties of Inverse Functions to Find Exact Values
More information