WYSE Academic Challenge Math Test (Regional) m x
|
|
- Jesse Doyle
- 5 years ago
- Views:
Transcription
1 WYSE Academic Challenge Math Test (Regional) Correct Answer: C For the height of the Loki kite we have = 7 sin For the height of the Thor kite we have = 50 sin The Thor kite is higher by. meter. See the diagrams below: Loki Thor 7m 50m o 8 o 45. Correct Answer: C The car is moving 0 mph to the east and 40 mph to the south. Using the Pythagorean Theorem, that means it s moving 50 mph in total.. Correct Answer: B Using cosθ = and r we have r = +, r = 4 cosθ r = 4 r = 4. Substituting for r y + y = y = 0. Completing the square we have y 4 what we need to find the linear feet for the border. π + =. The garden is circular with a radius of feet. The circumference is 4. Correct Answer: B r = 4π = An identity matri is its own transpose. An identity matri is its own inverse. An identity matri multiplied by itself is the same identity matri. 5. Correct Answer: C Let be the leg length of the triangle. =, =. The hypotenuse/ diameter is therefore 6. Correct Answer: D + =, the radius =, and area = π. This describes an arithmetic series with a = 40, d =, and n = 4 4 4( ) a = = 5. k k =. Then 06 Regional
2 Math - 7. Correct Answer: E The magnitude of.5 + is.5 i = 45. By DeMoivre s Theorem, the magnitude of a comple number raised to the nth power is the magnitude of that comple number, r, raised to the nth power. 45 cubed is 9,5. 8. Correct Answer: E ( 4) ( y + ) 9( 4) + 5( y + ) = 45 + =. The semi-major ais is a =. The 5 9 semi-minor ais is b = 5 and the distance from the center to the foci is c = 9 5 =. c The eccentricity is e = =. a 9. Correct Answer: C The domain is dependent upon where is positive. That is equivalent to the positive real numbers. 0. Correct Answer: B 0 Using = years after 000, the population can be modeled by y = , or the equivalent y = 0000 e. Solving 0000 = gives 7... Correct Answer: A θ 5 π ω = ; The angular speed. ω = = 5π. The linear speed t ν = r ω = 8 5π = Correct Answer: C There are letters in illegibility, one of which is repeated four times and one of which is repeated thrice. So the number of distinguishable strings is!,6,400 4!! =.. Correct Answer: B Converse of states that if two angles are vertical angles then the angles are congruent (true). Converse of states that if two angles have the same verte then the two angles are adjacent. This is false. The angles could be vertical. Converse of states if alternate interior angles are congruent then the two lines are parallel. This is true (Postulate 4.). Only the Converse of is false. 06 Regional
3 Math - 4. Correct Answer: B Bob does of the job every hour and Nate does of the job every hour. That means 6 that together, they do + = 7 of the job each hour. This means that it will take the 6 48 two of them = 48 = 6 6 hours to finish the job Correct Answer: C Let the starting amounts be A, B, and C. A =, so A =.5, B =, so B = 4, and 4 C =, so C =.5. The eaten amounts are A = 0.5, B =, and C =.5, for a total amount eaten of = Correct Answer: C The jog represents a right triangle with the legs of the triangle represented by 5 and. The shortest distance then would be the hypotenuse side to get back home. This is the 5 + =. typical 5,, right triangle 7. Correct Answer: A This is easiest to solve when we set f() to be equal to 5 and then solve for. = 5,so = 5 ( ). So = and then -7 = Correct Answer: E Since there are factors of ( ) and ( + ) there are no vertical asymptotes. in both the numerator and denominator, 9. Correct Answer: D Even functions are functions for which f(-) = f() is an identity. cos and sec are the two basic trig functions which are even. This makes both I and II even. Odd functions are functions for which f(-) = -f() is an identity. The other four basic trig functions are odd. This makes III odd, and since tan is odd, cos (tan ) would be even. 0. Correct Answer: A Kite, by definition. 06 Regional
4 Math - 4. Correct Answer: A ( + 5) ( ) ( + 5) + ( ) ( + 5) ( ) Correct Answer: D The eponential portion goes to infinity much, much faster than the linear portion goes to negative infinity, so the answer is infinity.. Correct Answer: D ln 0.6 ln 0.5 5r 0.065t 0.6p = pe r = = 0.065, 0.5 = e t = The half-life of a new married couple in the city is approimately 7 years. 4. Correct Answer: A The period of tan is π, so the period of tan would be A. The other transformations of the function are merely shifts, so the period does not change. 5. Correct Answer: E The overall number of possible draws is given by C(0,) = 0. The ways we can get all three the same color is all three blue C(,)= or all three green C(6,)=0. This makes the overall probability /0=7/ Correct Answer: B Solving the system of equations we have 7 + y 5 = 0 + 5y + 0 y = = = 5 =. Then y = 8. + ( 8) = 5. Then 7. Correct Answer: D f( ) = ( ) + = = Correct Answer: E log 4 b = b = 4 b = 4 9. Correct Answer: A The average rate of change of a function is the slope of the secant line between the two described points. In this case, the points are (0, 8) and (, 6) and the slope is thus A. 06 Regional
5 Math Correct Answer: E We can start by filling out the AM deliveries as Amy to Hamms (since Carol follows), Carol to Flower s R Us (to follow Amy), and Beth to Embry s (so she doesn t repeat). We then fill out the PM as none to Embry s (to satisfy I), Carol to GrowLots (to follow Anne), Beth to Hamm s (so she doesn t repeat) and Amy to Flowers R Us (by default). We can now list deliveries by person. Amy: F-H-G-F, Beth: G-E-F-H, and Carol: E-F-H-G. Beth and Carol went to all four. 06 Regional
Academic 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 informationWYSE MATH STATE 2012 SOLUTIONS. 1. Ans E: Trapezoids need only have one pair of parallel sides. Parallelograms are, by definition, forced to have two.
WYSE MATH STATE 01 SOLUTIONS 1. Ans E: Trapezoids need only have one pair of parallel sides. Parallelograms are, by definition, forced to have two.. Ans A: All the cans can be arranged in 10 P 10 = 10!
More informationMath 103 Selected Homework Solutions, Section 3.9
Math 103 Selected Homework Solutions, Section 3.9 9. Let s be the distance from the base of the light pole to the top of the man s shadow, and the distance from the light pole to the man. 15 s 6 s We know:
More information. Then 2 3 the circumference is 8π 25 in. 2(1) both of which violate the original assumptions. Therefore, we have no solution.
WYSE MATH SECTIONAL 04 SOLUTIONS Ans B: (a) and (d) are equivalent Therefore since the determinant of the product of matrices is the product of their determinants, it too cannot be zero If three square
More informationAlgebra/Trigonometry Review Notes
Algebra/Trigonometry Review Notes MAC 41 Calculus for Life Sciences Instructor: Brooke Quinlan Hillsborough Community College ALGEBRA REVIEW FOR CALCULUS 1 TOPIC 1: POLYNOMIAL BASICS, POLYNOMIAL END BEHAVIOR,
More informationSummer Review Packet for Students Entering AP Calculus BC. Complex Fractions
Summer Review Packet for Students Entering AP Calculus BC Comple Fractions When simplifying comple fractions, multiply by a fraction equal to 1 which has a numerator and denominator composed of the common
More informationTrigonometric ratios:
0 Trigonometric ratios: The six trigonometric ratios of A are: Sine Cosine Tangent sin A = opposite leg hypotenuse adjacent leg cos A = hypotenuse tan A = opposite adjacent leg leg and their inverses:
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 informationMATH 1220 Midterm 1 Thurs., Sept. 20, 2007
MATH 220 Midterm Thurs., Sept. 20, 2007 Write your name and ID number at the top of this page. Show all your work. You may refer to one double-sided sheet of notes during the eam and nothing else. Calculators
More informationAccuplacer 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 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 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 informationRadicals and Pythagorean Theorem Date: Per:
Math 2 Unit 7 Worksheet 1 Name: Radicals and Pythagorean Theorem Date: Per: [1-12] Simplify each radical expression. 1. 75 2. 24. 7 2 4. 10 12 5. 2 6 6. 2 15 20 7. 11 2 8. 9 2 9. 2 2 10. 5 2 11. 7 5 2
More informationAs we know, the three basic trigonometric functions are as follows: Figure 1
Trigonometry Basic Functions As we know, the three basic trigonometric functions are as follows: sin θ = cos θ = opposite hypotenuse adjacent hypotenuse tan θ = opposite adjacent Where θ represents an
More informationAP Calculus Summer Assignment
AP Calculus Summer Assignment 07-08 Welcome to AP Calculus. This summer assignment will help you review some Algebraic and Trigonometric topics that you will need for some problems in Calculus. This summer
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 informationUNIT 5 SIMILARITY, RIGHT TRIANGLE TRIGONOMETRY, AND PROOF Unit Assessment
Unit 5 ircle the letter of the best answer. 1. line segment has endpoints at (, 5) and (, 11). point on the segment has a distance that is 1 of the length of the segment from endpoint (, 5). What are the
More informationSection 6.2 Trigonometric Functions: Unit Circle Approach
Section. Trigonometric Functions: Unit Circle Approach The unit circle is a circle of radius centered at the origin. If we have an angle in standard position superimposed on the unit circle, the terminal
More informationA. Incorrect! For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1.
Algebra - Problem Drill 19: Basic Trigonometry - Right Triangle No. 1 of 10 1. Which of the following points lies on the unit circle? (A) 1, 1 (B) 1, (C) (D) (E), 3, 3, For a point to lie on the unit circle,
More information6.2 Trigonometric Integrals and Substitutions
Arkansas Tech University MATH 9: Calculus II Dr. Marcel B. Finan 6. Trigonometric Integrals and Substitutions In this section, we discuss integrals with trigonometric integrands and integrals that can
More informationMATH 32 FALL 2012 FINAL EXAM - PRACTICE EXAM SOLUTIONS
MATH 3 FALL 0 FINAL EXAM - PRACTICE EXAM SOLUTIONS () You cut a slice from a circular pizza (centered at the origin) with radius 6 along radii at angles 4 and 3 with the positive horizontal axis. (a) (3
More informationName: Math Analysis Chapter 3 Notes: Exponential and Logarithmic Functions
Name: Math Analysis Chapter 3 Notes: Eponential and Logarithmic Functions Day : Section 3-1 Eponential Functions 3-1: Eponential Functions After completing section 3-1 you should be able to do the following:
More informationMAC 1114: Trigonometry Notes
MAC 1114: Trigonometry Notes Instructor: Brooke Quinlan Hillsborough Community College Section 7.1 Angles and Their Measure Greek Letters Commonly Used in Trigonometry Quadrant II Quadrant III Quadrant
More informationMath 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 informationPRACTICE TEST 1 Math Level IC
SOLID VOLUME OTHER REFERENCE DATA Right circular cone L = cl V = volume L = lateral area r = radius c = circumference of base h = height l = slant height Sphere S = 4 r 2 V = volume r = radius S = surface
More informationAlpha Applications. Answers: 12. A 20. B 13. C 4. D 5. C 6. B 27. A 8. C 9. B 10. D 11. E 14. C 15. B 16. B 17. D 18. D 19. C
Answers: A B C 4 D 5 C 6 B 7 A 8 C 9 B 0 D E A C 4 C 5 B 6 B 7 D 8 D 9 C 0 B D A C 4 B 5 A 6 D 7 A 8 B 9 C 0 C Solutions: The decay is governed by m m0e ln k 60 kt Therefore, k60 e 60k ln ln Let s and
More informationA List of Definitions and Theorems
Metropolitan Community College Definition 1. Two angles are called complements if the sum of their measures is 90. Two angles are called supplements if the sum of their measures is 180. Definition 2. One
More informationCalculus - Chapter 2 Solutions
Calculus - Chapter Solutions. a. See graph at right. b. The velocity is decreasing over the entire interval. It is changing fastest at the beginning and slowest at the end. c. A = (95 + 85)(5) = 450 feet
More informationCALCULUS 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 informationDiagnostic Tests Study Guide
California State Universit, Sacramento Department of Mathematics and Statistics Diagnostic Tests Stud Guide Descriptions Stud Guides Sample Tests & Answers Table of Contents: Introduction Elementar Algebra
More informationSample Final Exam Problems Solutions Math 107
Sample Final Eam Problems Solutions Math 107 1 (a) We first factor the numerator and the denominator of the function to obtain f() = (3 + 1)( 4) 4( 1) i To locate vertical asymptotes, we eamine all locations
More information1. 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 informationIntroductory Algebra Chapter 9 Review
Introductory Algebra Chapter 9 Review Objective [9.1a] Find the principal square roots and their opposites of the whole numbers from 0 2 to 2 2. The principal square root of a number n, denoted n,is the
More informationChapter 2 Polynomial and Rational Functions
SECTION.1 Linear and Quadratic Functions Chapter Polynomial and Rational Functions Section.1: Linear and Quadratic Functions Linear Functions Quadratic Functions Linear Functions Definition of a Linear
More informationMath 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 informationNew York State Mathematics Association of Two-Year Colleges
New York State Mathematics Association of Two-Year Colleges Math League Contest ~ Fall 06 Directions: You have one hour to take this test. Scrap paper is allowed. The use of calculators is NOT permitted,
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 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 informationVisit us at: for a wealth of information about college mathematics placement testing!
North Carolina Early Mathematics Placement Testing Program, 9--4. Multiply: A. 9 B. C. 9 9 9 D. 9 E. 9 Solution and Answer to Question # will be provided net Monday, 9-8-4 North Carolina Early Mathematics
More informationUsing the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles
Math 154 Chapter 9.6: Applications of Radical Equations Objectives: Finding legs of right triangles Finding hypotenuse of right triangles Solve application problems involving right triangles Pythagorean
More information1 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 informationCrash Course in Trigonometry
Crash Course in Trigonometry Dr. Don Spickler September 5, 003 Contents 1 Trigonometric Functions 1 1.1 Introduction.................................... 1 1. Right Triangle Trigonometry...........................
More information2. Use your graphing calculator to graph each of the functions below over the interval 2, 2
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(-),
More informationReview Sheet for Exam 1 SOLUTIONS
Math b Review Sheet for Eam SOLUTIONS The first Math b midterm will be Tuesday, February 8th, 7 9 p.m. Location: Schwartz Auditorium Room ) The eam will cover: Section 3.6: Inverse Trig Appendi F: Sigma
More informationMath 2260 Exam #2 Solutions. Answer: The plan is to use integration by parts with u = 2x and dv = cos(3x) dx: dv = cos(3x) dx
Math 6 Eam # Solutions. Evaluate the indefinite integral cos( d. Answer: The plan is to use integration by parts with u = and dv = cos( d: u = du = d dv = cos( d v = sin(. Then the above integral is equal
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 informationTrigonometry Trigonometry comes from the Greek word meaning measurement of triangles Angles are typically labeled with Greek letters
Trigonometry Trigonometry comes from the Greek word meaning measurement of triangles Angles are typically labeled with Greek letters α( alpha), β ( beta), θ ( theta) as well as upper case letters A,B,
More information1993 AP Calculus AB: Section I
99 AP Calculus AB: Section I 90 Minutes Scientific Calculator Notes: () The eact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among
More informationMATH 104 MID-TERM EXAM SOLUTIONS. (1) Find the area of the region enclosed by the curves y = x 1 and y = x 1
MATH MID-TERM EXAM SOLUTIONS CLAY SHONKWILER ( Find the area of the region enclosed by the curves y and y. Answer: First, we find the points of intersection by setting the two functions equal to eachother:.
More informationThe answers below are not comprehensive and are meant to indicate the correct way to solve the problem. sin
Math : Practice Final Answer Key Name: The answers below are not comprehensive and are meant to indicate the correct way to solve the problem. Problem : Consider the definite integral I = 5 sin ( ) d.
More informationMATH 110: FINAL EXAM REVIEW
MATH 0: FINAL EXAM REVIEW Can you solve linear equations algebraically and check your answer on a graphing calculator? (.) () y y= y + = 7 + 8 ( ) ( ) ( ) ( ) y+ 7 7 y = 9 (d) ( ) ( ) 6 = + + Can you set
More informationNew Jersey Center for Teaching and Learning. Progressive Mathematics Initiative
Slide 1 / 150 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
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 informationInstructions. Do not open your test until instructed to do so!
st Annual King s College Math Competition King s College welcomes you to this year s mathematics competition and to our campus. We wish you success in this competition and in your future studies. Instructions
More informationMATH 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 informationChapter 6: Extending Periodic Functions
Chapter 6: Etending Periodic Functions Lesson 6.. 6-. a. The graphs of y = sin and y = intersect at many points, so there must be more than one solution to the equation. b. There are two solutions. From
More informationChapter 4 Trigonometric Functions
SECTION 4.1 Special Right Triangles and Trigonometric Ratios Chapter 4 Trigonometric Functions Section 4.1: Special Right Triangles and Trigonometric Ratios Special Right Triangles Trigonometric Ratios
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 informationOld Math 120 Exams. David M. McClendon. Department of Mathematics Ferris State University
Old Math 10 Exams David M. McClendon Department of Mathematics Ferris State University 1 Contents Contents Contents 1 General comments on these exams 3 Exams from Fall 016 4.1 Fall 016 Exam 1...............................
More informationMath 120. x x 4 x. . In this problem, we are combining fractions. To do this, we must have
Math 10 Final Eam Review 1. 4 5 6 5 4 4 4 7 5 Worked out solutions. In this problem, we are subtracting one polynomial from another. When adding or subtracting polynomials, we combine like terms. Remember
More informationChapter 3. Radian Measure and Circular Functions. Copyright 2005 Pearson Education, Inc.
Chapter 3 Radian Measure and Circular Functions Copyright 2005 Pearson Education, Inc. 3.1 Radian Measure Copyright 2005 Pearson Education, Inc. Measuring Angles Thus far we have measured angles in degrees
More informationWeBWorK demonstration assignment
WeBWorK demonstration assignment.( pt) Match the statements defined below with the letters labeling their equivalent expressions. You must get all of the answers correct to receive credit.. x is less than
More information(Section 4.7: Inverse Trig Functions) 4.82 PART F: EVALUATING INVERSE TRIG FUNCTIONS. Think:
PART F: EVALUATING INVERSE TRIG FUNCTIONS Think: (Section 4.7: Inverse Trig Functions) 4.82 A trig function such as sin takes in angles (i.e., real numbers in its domain) as inputs and spits out outputs
More informationMath 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 information2017 AP Calculus AB Summer Assignment
07 AP Calculus AB Summer Assignment Mrs. Peck ( kapeck@spotsylvania.k.va.us) This assignment is designed to help prepare you to start Calculus on day and be successful. I recommend that you take off the
More information3.1 Fundamental Identities
www.ck.org Chapter. Trigonometric Identities and Equations. Fundamental Identities Introduction We now enter into the proof portion of trigonometry. Starting with the basic definitions of sine, cosine,
More information( ) 7 ( 5x 5 + 3) 9 b) y = x x
New York City College of Technology, CUNY Mathematics Department Fall 0 MAT 75 Final Eam Review Problems Revised by Professor Kostadinov, Fall 0, Fall 0, Fall 00. Evaluate the following its, if they eist:
More informationPhysics 2A Chapter 1 - Vectors Fall 2017
These notes are eight pages. That includes some diagrams, but I realize reading them could get a bit tedious. So here is a quick summary: A vector quantity is one for which direction is relevant, like
More informationMath 102 Spring 2008: Solutions: HW #3 Instructor: Fei Xu
Math Spring 8: Solutions: HW #3 Instructor: Fei Xu. section 7., #8 Evaluate + 3 d. + We ll solve using partial fractions. If we assume 3 A + B + C, clearing denominators gives us A A + B B + C +. Then
More informationA: Super-Basic Algebra Skills. A1. True or false. If false, change what is underlined to make the statement true. a.
A: Super-Basic Algebra Skills A1. True or false. If false, change what is underlined to make the statement true. 1 T F 1 b. T F c. ( + ) = + 9 T F 1 1 T F e. ( + 1) = 16( + ) T F f. 5 T F g. If ( + )(
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 informationSolution: Let x be the amount of paint in one stripe. Let r and w be the amount of red and white paint respectively in a pink stripe. Then x = r + w.
1. Before starting to paint, Paul had 130 ounces of blue paint, 164 ounces of red paint and 188 ounces of white paint. Paul painted four equally sized stripes on the wall, making a blue stripe, a red stripe,
More informationa) i b) ii c) iii d) i and ii e) ii and iii a) b) c) d) e)
Math Field Day 07 Page Suppose the graph of a line has a negative y intercept and a positive intercept If the slope is given by m, which of the following could be true? i m > 0 ii m < 0 iii m = 0 a) i
More informationAP Calculus BC Summer Assignment School Year
AP Calculus BC Summer Assignment School Year 018-019 Objective of the summer assignment: i. To build on students readiness in foundational skills and knowledge ii. To review prerequisites topics for the
More informationChapter 5 The Next Wave: MORE MODELING AND TRIGONOMETRY
ANSWERS Mathematics (Mathematical Analysis) page 1 Chapter The Next Wave: MORE MODELING AND TRIGONOMETRY NW-1. TI-8, points; Casio, points a) An infinite number of them. b) 17p, - 7p c) Add p n to p, p
More informationSolutions Math is Cool HS Championships Mental Math
Mental Math 9/11 Answer Solution 1 30 There are 5 such even numbers and the formula is n(n+1)=5(6)=30. 2 3 [ways] HHT, HTH, THH. 3 6 1x60, 2x30, 3x20, 4x15, 5x12, 6x10. 4 9 37 = 3x + 10, 27 = 3x, x = 9.
More informationMA Practice Questions for the Final Exam 07/10 .! 2! 7. 18! 7.! 30! 12 " 2! 3. A x y B x y C x xy x y D.! 2x! 5 y E.
MA 00 Practice Questions for the Final Eam 07/0 ) Simplify:! y " [! (y " )].!! 7. 8! 7.! 0! "! A y B y C y y D.!! y E. None of these ) Which number is irrational? A.! B..4848... C. 7 D.. E.! ) The slope
More informationC H A P T E R 9 Topics in Analytic Geometry
C H A P T E R Topics in Analtic Geometr Section. Circles and Parabolas.................... 77 Section. Ellipses........................... 7 Section. Hperbolas......................... 7 Section. Rotation
More information221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM
Math Refresher Session 3 1 Area, Perimeter, and Volume Problems Area, Perimeter, and Volume 301. Formula Problems. Here, you are given certain data about one or more geometric figures, and you are asked
More informationUnit 6: 10 3x 2. Semester 2 Final Review Name: Date: Advanced Algebra
Semester Final Review Name: Date: Advanced Algebra Unit 6: # : Find the inverse of: 0 ) f ( ) = ) f ( ) Finding Inverses, Graphing Radical Functions, Simplifying Radical Epressions, & Solving Radical Equations
More informationBy Alex O Brien, updated on 6/24/2014
HEBRON HIGH SCHOOL AP CALCULUS SUMMER ASSIGNMENT AP Calculus AB/BC Mathematics fun for all! By Ale O Brien, updated on 6/4/04 The purpose of this assignment is to make certain that you have much of the
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 informationGRE. Advanced GRE Math Questions
Advanced GRE Math Questions Quantitative Arithmetic 1. What is the sum of all integers x, such that 7 < x 5? 7 7 6 6 7 1. C Quantitative Fractions and Ratios 1. The current ratio of boys to girls at a
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 informationChapter 3. Radian Measure and Circular Functions. Section 3.1: Radian Measure. π 1.57, 1 is the only integer value in the
Chapter Radian Measure and Circular Functions Section.: Radian Measure. Since θ is in quadrant I, 0 < θ
More information(c) n (d) n 2. (a) (b) (c) (d) (a) Null set (b) {P} (c) {P, Q, R} (d) {Q, R} (a) 2k (b) 7 (c) 2 (d) K (a) 1 (b) 3 (c) 3xyz (d) 27xyz
318 NDA Mathematics Practice Set 1. (1001)2 (101)2 (110)2 (100)2 2. z 1/z 2z z/2 3. The multiplication of the number (10101)2 by (1101)2 yields which one of the following? (100011001)2 (100010001)2 (110010011)2
More informationMATH CIRCLE Session # 2, 9/29/2018
MATH CIRCLE Session # 2, 9/29/2018 SOLUTIONS 1. The n-queens Problem. You do NOT need to know how to play chess to work this problem! This is a classical problem; to look it up today on the internet would
More informationMathematical review trigonometry vectors Motion in one dimension
Mathematical review trigonometry vectors Motion in one dimension Used to describe the position of a point in space Coordinate system (frame) consists of a fixed reference point called the origin specific
More informationPART II Section A or 5
MATHEMATICS CONTEST 2017 ANSWER KEY PART I Section A 1. 338 2. 3 days 3. 113 4. 20% 5. 22 or (0, 22) 6. n =100 7. 5 Section B 8. 1 9. 3 3 square units 10. x =4 11. a + b =34 12. 2584 Section C 13. a =20,
More informationIntegration by Triangle Substitutions
Integration by Triangle Substitutions The Area of a Circle So far we have used the technique of u-substitution (ie, reversing the chain rule) and integration by parts (reversing the product rule) to etend
More informationObjectives and Essential Questions
VECTORS Objectives and Essential Questions Objectives Distinguish between basic trigonometric functions (SOH CAH TOA) Distinguish between vector and scalar quantities Add vectors using graphical and analytical
More informationChapter 8B - Trigonometric Functions (the first part)
Fry Texas A&M University! Spring 2016! Math 150 Notes! Section 8B-I! Page 79 Chapter 8B - Trigonometric Functions (the first part) Recall from geometry that if 2 corresponding triangles have 2 angles of
More information6-5 Study Guide and Intervention
6-5 Study Guide and Intervention Simplify Radicals Product Property of Radicals For any real numbers a and b, and any integer n > 1: 1. if n is even and a and b are both nonnegative, then n ab n a n b.
More informationAcademic Challenge 2010 State Mathematics Solution Set
Academic Challenge 00 State Mathematics Solution Set. Ans A: Let (0,0) be the Cross Roads intersection. Apple starts at (0,). Since the road Apple is at a 45 degree angle, the slope of this road will be.
More informationSolution. Using the point-slope form of the equation we have the answer immediately: y = 4 5 (x ( 2)) + 9 = 4 (x +2)+9
Chapter Review. Lines Eample. Find the equation of the line that goes through the point ( 2, 9) and has slope 4/5. Using the point-slope form of the equation we have the answer immediately: y = 4 5 ( (
More informationLesson 6 Plane Geometry Practice Test Answer Explanations
Lesson 6 Plane Geometry Practice Test Answer Explanations Question 1 One revolution is equal to one circumference: C = r = 6 = 1, which is approximately 37.68 inches. Multiply that by 100 to get 3,768
More informationdx dt = x 2 x = 120
Solutions to Review Questions, Exam. A child is flying a kite. If the kite is 90 feet above the child s hand level and the wind is blowing it on a horizontal course at 5 feet per second, how fast is the
More informationDepartment of Mathematical Sciences. Math 226 Calculus Spring 2016 Exam 2V2 DO NOT TURN OVER THIS PAGE UNTIL INSTRUCTED TO DO SO
Department of Mathematical Sciences Math 6 Calculus Spring 6 Eam V DO NOT TURN OVER THIS PAGE UNTIL INSTRUCTED TO DO SO NAME (Printed): INSTRUCTOR: SECTION NO.: When instructed, turn over this cover page
More informationMATH 32 FALL 2013 FINAL EXAM SOLUTIONS. 1 cos( 2. is in the first quadrant, so its sine is positive. Finally, csc( π 8 ) = 2 2.
MATH FALL 01 FINAL EXAM SOLUTIONS (1) (1 points) Evalute the following (a) tan(0) Solution: tan(0) = 0. (b) csc( π 8 ) Solution: csc( π 8 ) = 1 sin( π 8 ) To find sin( π 8 ), we ll use the half angle formula:
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 information