Math 370 Exam 5 Review Name
|
|
- Michael Warner
- 5 years ago
- Views:
Transcription
1 Math 370 Exam 5 Review Name Graph the ellipse and locate the foci. 1) x2 6 + y2 = 1 1) Objective: (9.1) Graph Ellipses Not Centered at the Origin Graph the ellipse. 2) (x + 2)2 + (y + 1)2 9 = 1 2) Objective: (9.1) Graph Ellipses Not Centered at the Origin Convert the equation to the standard form for an ellipse by completing the square on x and y. 3) 16x y 2-32x - 150y = 0 3) Objective: (9.1) Graph Ellipses Not Centered at the Origin ) The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 0 feet and the height of the arch over the center of the roadway is 12 feet. Two trucks plan to use this road. They are both 8 feet wide. Truck 1 has an overall height of 11 feet and Truck 2 has an overall height of 12 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge. Objective: (9.1) Solve Applied Problems Involving Ellipses )
2 Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. 5) x 2 + y 2 = 25 25x y 2 = 00 5) Objective: (9.1) Additional Concepts Find the vertices and locate the foci for the hyperbola whose equation is given. 6) 9x 2-100y 2 = 900 6) Objective: (9.2) Locate a Hyperbola's Vertices and Foci Find the standard form of the equation of the hyperbola satisfying the given conditions. 7) Endpoints of transverse axis: (-3, 0), (3, 0); foci: (-8, 0), (8, 0) 7) Objective: (9.2) Write Equations of Hyperbolas in Standard Form Convert the equation to the standard form for a hyperbola by completing the square on x and y. 8) 9y 2-16x y + 6x = 0 8) Objective: (9.2) Write Equations of Hyperbolas in Standard Form Find the location of the center, vertices, and foci for the hyperbola described by the equation. 9) (y + 2)2 - (x - 2)2 9 = 1 9) Objective: (9.2) Graph Hyperbolas Not Centered at the Origin
3 10) A satellite following the hyperbolic path shown in the picture turns rapidly at (0, 2) and 10) then moves closer and closer to the line y = 3 x as it gets farther from the tracking station at 2 the origin. Find the equation that describes the path of the satellite if the center of the hyperbola is at (0, 0). (0, 2) y = 3 2 x Objective: (9.2) Solve Applied Problems Involving Hyperbolas Find the focus and directrix of the parabola with the given equation. 11) y 2 = x 11) Objective: (9.3) Graph Parabolas with Vertices at the Origin Graph the parabola. 12) y 2 = -16x 12) Objective: (9.3) Graph Parabolas with Vertices at the Origin
4 13) x 2 = 18y 13) Objective: (9.3) Graph Parabolas with Vertices at the Origin Find the standard form of the equation of the parabola using the information given. 1) Vertex: (6, -); Focus: (3, -) 1) Objective: (9.3) Write Equations of Parabolas in Standard Form Find the vertex, focus, and directrix of the parabola with the given equation. 15) (y - 3) 2 = -16(x - ) 15) Objective: (9.3) Graph Parabolas with Vertices Not at the Origin Graph the parabola with the given equation. 16) (x + 2) 2 = 8(y + 2) 16) Objective: (9.3) Graph Parabolas with Vertices Not at the Origin MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 17) A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 0 feet. Find the height of the arch at 10 feet from its center. A) 0.1 ft B) 2.3 ft C) 5.2 ft D) 39. ft Objective: (9.3) Solve Applied Problems Involving Parabolas 17) Parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. 18) x = t 3 + 1, y = 9 - t ; t = 2 18) Objective: (9.5) Use Point Plotting to Graph Plane Curves Described by Parametric Equations
5 Use point plotting to graph the plane curve described by the given parametric equations. 19) x = 2t - 1, y = t 2 + 5; - t 19) Objective: (9.5) Use Point Plotting to Graph Plane Curves Described by Parametric Equations 20) x = 5 sin t, y = 5 cos t; 0 t 2 20) Objective: (9.5) Use Point Plotting to Graph Plane Curves Described by Parametric Equations Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations. 21) x = 6 cos t, y = 6 sin t; 0 t 2 21) Objective: (9.5) Eliminate the Parameter 22) x = 2 + sec t, y = tan t; 0 < t < 2 22) Objective: (9.5) Eliminate the Parameter Eliminate the parameter. Write the resulting equation in standard form. 23) An ellipse: x = cos t, y = sin t 23) Objective: (9.5) Eliminate the Parameter Find a set of parametric equations for the conic section or the line. 2) Hyperbola: Vertices: (3, 0); Vertices: (-3, 0); Foci: (5, 0) and (-5, 0) 2) Objective: (9.5) Find Parametric Equations for Functions
6 25) A baseball pitcher throws a baseball with an initial velocity of 136 feet per second at an angle of 20 to the horizontal. The ball leaves the pitcher's hand at a height of feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball? Objective: (9.5) Understand the Advantages of Parametric Representations 25) Identify the conic section that the polar equation represents. Describe the location of a directrix from the focus located at the pole. 2 26) r = 26) 1-2 cos Objective: (9.6) Define Conics in Terms of a Focus and a Directrix 27) r = sin 27) Objective: (9.6) Define Conics in Terms of a Focus and a Directrix 28) r = sin 28) Objective: (9.6) Define Conics in Terms of a Focus and a Directrix Graph the polar equation. 9 29) r = 3-3 cos Identify the directrix and vertex. 29) Objective: (9.6) Graph the Polar Equations of Conics
7 12 30) r = - cos Identify the directrix and vertices. 30) Objective: (9.6) Graph the Polar Equations of Conics 31) r = cos Identify the directrix and vertices. 31) Objective: (9.6) Graph the Polar Equations of Conics Use a graphing utility to graph the equation. 3 32) r = 32) 1 - cos - Objective: (9.6) Tech: Conic Sections in Polar Coordinates Write the first four terms of the sequence whose general term is given. 33) an = n ) Objective: (10.1) Find Particular Terms of a Sequence from the General Term
8 3) an = (-) n 3) Objective: (10.1) Find Particular Terms of a Sequence from the General Term 35) an = n + 3 2n ) Objective: (10.1) Find Particular Terms of a Sequence from the General Term 36) A deposit of $8000 is made in an account that earns 9% interest compounded quarterly. The balance in the account after n quarters is given by the sequence an = n n = 1, 2, 3,... Find the balance in the account after 6 years. Objective: (10.1) Find Particular Terms of a Sequence from the General Term 36) Write the first four terms of the sequence defined by the recursion formula. 37) a1 = -3 and an = an-1-3 for n 2 37) Objective: (10.1) Use Recursion Formulas Write the first four terms of the sequence whose general term is given. n 38) an = (n - 1)! 38) Objective: (10.1) Use Factorial Notation Evaluate the factorial expression. 9! 39) 7! 2! 39) Objective: (10.1) Use Factorial Notation 0) n(n + 2 )! (n + 3 )! Objective: (10.1) Use Factorial Notation 0) Find the indicated sum ) i - i = 7 1) 2) 5 i = 1 (i + 1)! (i + 2)! 2) Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 3) )
9 ) a a a ) 5) a + ar + ar ar 11 5) Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation. 6) (a + 1) + (a + c) + (a + c 2 ) (a + c n ) 6) Write the first five terms of the arithmetic sequence. 7) a1 = -15; d = 3 7) Objective: (10.2) Write Terms of an Arithmetic Sequence Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. 8) Find a 31 when a1 = -6, d = ) Objective: (10.2) Use the Formula for the General Term of an Arithmetic Sequence Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence. 9) a1 = -3, d = 0.5 9) Objective: (10.2) Use the Formula for the General Term of an Arithmetic Sequence 50) To train for a race, Will begins by jogging 13 minutes one day per week. He increases his jogging time by minutes each week. Write the general term of this arithmetic sequence, and find how many whole weeks it takes for him to reach a jogging time of one hour. Objective: (10.2) Use the Formula for the General Term of an Arithmetic Sequence 50) Find the indicated sum. 51) Find the sum of the first 30 terms of the arithmetic sequence: 10, 5, 0, -5,... 51) Objective: (10.2) Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence 52) Find the sum of the odd integers between 30 and ) Objective: (10.2) Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 53) 29 i = 1 (2i - 1) 53) Objective: (10.2) Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence
10 5) A theater has 3 rows with 27 seats in the first row, 30 in the second row, 33 in the third row, and so forth. How many seats are in the theater? Objective: (10.2) Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence 5) Write the first five terms of the geometric sequence. 55) a1 = -6; r = - 55) Objective: (10.3) Write Terms of a Geometric Sequence Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. 56) Find a6 when a1 = 9600, r = ) Write a formula for the general term (the nth term) of the geometric sequence. 57) 3, - 3 2, 3, - 3 8, 3 16,... 57) The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 58) an = n ) 59) an = 3 2 n 59) 60) an = 5n 2-60) 61) A hockey player signs a contract with a starting salary of $810,000 per year and an annual increase of 6.5% beginning in the second year. What will the athlete's salary be, to the nearest dollar, in the eighth year? 61) Use the formula for the sum of the first n terms of a geometric sequence to solve. 62) Find the sum of the first 8 terms of the geometric sequence: -8, -16, -32, -6, -128, ) Objective: (10.3) Use the Formula for the Sum of the First n Terms of a Geometric Sequence Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 63) i 63) i = 1 Objective: (10.3) Use the Formula for the Sum of the First n Terms of a Geometric Sequence
11 Round to the nearest dollar if needed. 6) To save for retirement, you decide to deposit $2250 into an IRA at the end of each year for the next 35 years. If the interest rate is 5% per year compounded annually, find the value of the IRA after 35 years. Objective: (10.3) Find the Value of an Annuity 6) Find the sum of the infinite geometric series, if it exists. 65) ) Objective: (10.3) Use the Formula for the Sum of an Infinite Geometric Series Express the repeating decimal as a fraction in lowest terms. 66) ) Objective: (10.3) Use the Formula for the Sum of an Infinite Geometric Series 67) A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only 60% as far as on the previous swing. How far will it swing altogether before coming to a complete stop? Round to the nearest inch when necessary. Objective: (10.3) Use the Formula for the Sum of an Infinite Geometric Series 67) Use mathematical induction to prove that the statement is true for every positive integer n. n(5n + 3) 68) (5n - 1) = 2 68) Objective: (10.) Prove Statements Using Mathematical Induction Evaluate the given binomial coefficient ) 69) Objective: (10.5) Evaluate a Binomial Coefficient Use the Binomial Theorem to expand the binomial and express the result in simplified form. 70) (5x + 2)3 70) Objective: (10.5) Expand a Binomial Raised to a Power 71) (x - 2) 71) Objective: (10.5) Expand a Binomial Raised to a Power Find the term indicated in the expansion. 72) (x - 3y)11; 8th term 72) Objective: (10.5) Find a Particular Term in a Binomial Expansion
Assignment Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Assignment.1-.3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The arch beneath a bridge is semi-elliptical, a one-way
More informationPrecalculus. Cumulative Review Conics, Polar, Parametric, Sequences & Series, Rational Functions. Conics
Name Precalculus Date Block Cumulative Review Conics, Polar, Parametric, Sequences & Series, Rational Functions Please do all work on a separate sheet of paper Conics Identify each equation If it is a
More informationMATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al. by hand.
MATH 1 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al 5.1 1. Mark the point determined by 6 on the unit circle. 5.3. Sketch a graph of y sin( x) by hand. 5.3 3. Find the
More informationMath 8 EXAM #5 Name: Any work or answers completed on this test form, other than the problems that require you to graph, will not be graded.
Math 8 EXAM #5 Name: Complete all problems in your blue book. Copy the problem into the bluebook then show all of the required work for that problem. Work problems out down the page, not across. Make only
More informationName: Date: 1. Match the equation with its graph. Page 1
Name: Date: 1. Match the equation with its graph. y 6x A) C) Page 1 D) E) Page . Match the equation with its graph. ( x3) ( y3) A) C) Page 3 D) E) Page 4 3. Match the equation with its graph. ( x ) y 1
More informationx y 2 2 CONIC SECTIONS Problem 1
CONIC SECTIONS Problem For the equations below, identify each conic section If it s a parabola, specify its vertex, focus and directrix If it s an ellipse, specify its center, vertices and foci If it s
More informationChapter 10. Exploring Conic Sections
Chapter 10 Exploring Conic Sections Conics A conic section is a curve formed by the intersection of a plane and a hollow cone. Each of these shapes are made by slicing the cone and observing the shape
More informationSummary of Formulas: see
To review the Conic Sections, Identify them and sketch them from the given equations, watch the following set of YouTube videos. They are followed by several practice problems for you to try, covering
More informationRewrite the equation in the left column into the format in the middle column. The answers are in the third column. 1. y 4y 4x 4 0 y k 4p x h y 2 4 x 0
Pre-Calculus Section 1.1 Completing the Square Rewrite the equation in the left column into the format in the middle column. The answers are in the third column. 1. y 4y 4x 4 0 y k 4p x h y 4 x 0. 3x 3y
More informationPreCalculus Chapter 9 Practice Test Name:
This ellipse has foci 0,, and therefore has a vertical major axis. The standard form for an ellipse with a vertical major axis is: 1 Note: graphs of conic sections for problems 1 to 1 were made with the
More informationMATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al
MATH Final Eam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al.. Mark the point determined by on the unit circle... Sketch a graph of y = sin( ) by hand... Find the amplitude, period,
More informationHonors Precalculus: Solving equations and inequalities graphically and algebraically. Page 1
Solving equations and inequalities graphically and algebraically 1. Plot points on the Cartesian coordinate plane. P.1 2. Represent data graphically using scatter plots, bar graphs, & line graphs. P.1
More informationChapter 10 Test Review
Name: Class: Date: Chapter 10 Test Review Short Answer 1. Write an equation of a parabola with a vertex at the origin and a focus at ( 2, 0). 2. Write an equation of a parabola with a vertex at the origin
More information, minor axis of length 12. , asymptotes y 2x. 16y
Math 4 Midterm 1 Review CONICS [1] Find the equations of the following conics. If the equation corresponds to a circle find its center & radius. If the equation corresponds to a parabola find its focus
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Pre-Calculus Mid Term Review. January 2014 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the graph of the function f, plotted with a solid
More informationConic Sections. College Algebra
Conic Sections College Algebra Conic Sections A conic section, or conic, is a shape resulting from intersecting a right circular cone with a plane. The angle at which the plane intersects the cone determines
More informationConic Sections and Analytic Geometry
Chapter 9 Conic Sections and Analytic Geometry Chapter 9 Conic Sections and Analytic Geometry 9.1 The Ellipse 9.2 The Hyperbola 9.3 The Parabola 9.4 Rotation of Axes 9.5 Parametric Equations 9.6 Conic
More informationThe point (x, y) lies on the circle of radius r and center (h, k) iff. x h y k r
NOTES +: ANALYTIC GEOMETRY NAME LESSON. GRAPHS OF EQUATIONS IN TWO VARIABLES (CIRCLES). Standard form of a Circle The point (x, y) lies on the circle of radius r and center (h, k) iff x h y k r Center:
More informationChapter 9 Topics in Analytic Geometry
Chapter 9 Topics in Analytic Geometry What You ll Learn: 9.1 Introduction to Conics: Parabolas 9.2 Ellipses 9.3 Hyperbolas 9.5 Parametric Equations 9.6 Polar Coordinates 9.7 Graphs of Polar Equations 9.1
More information1.1 calculator viewing window find roots in your calculator 1.2 functions find domain and range (from a graph) may need to review interval notation
1.1 calculator viewing window find roots in your calculator 1.2 functions find domain and range (from a graph) may need to review interval notation functions vertical line test function notation evaluate
More information3. Solve the following. Round to the nearest thousandth.
This review does NOT cover everything! Be sure to go over all notes, homework, and tests that were given throughout the semester. 1. Given g ( x) i, h( x) x 4x x, f ( x) x, evaluate the following: a) f
More informationFigures adapted from Mathworld.wolfram.com and vectosite.net.
MTH 11 CONIC SECTIONS 1 The four basic types of conic sections we will discuss are: circles, parabolas, ellipses, and hyperbolas. They were named conic by the Greeks who used them to describe the intersection
More informationMATH 1020 WORKSHEET 10.1 Parametric Equations
MATH WORKSHEET. Parametric Equations If f and g are continuous functions on an interval I, then the equations x ft) and y gt) are called parametric equations. The parametric equations along with the graph
More informationChapter 8.1 Conic Sections/Parabolas. Honors Pre-Calculus Rogers High School
Chapter 8.1 Conic Sections/Parabolas Honors Pre-Calculus Rogers High School Introduction to Conic Sections Conic sections are defined geometrically as the result of the intersection of a plane with a right
More informationMA 154 PRACTICE QUESTIONS FOR THE FINAL 11/ The angles with measures listed are all coterminal except: 5π B. A. 4
. If θ is in the second quadrant and sinθ =.6, find cosθ..7.... The angles with measures listed are all coterminal except: E. 6. The radian measure of an angle of is: 7. Use a calculator to find the sec
More information7. r = r = r = r = r = 2 5
Exercise a: I. Write the equation in standard form of each circle with its center at the origin and the given radius.. r = 4. r = 6 3. r = 7 r = 5 5. r = 6. r = 6 7. r = 0.3 8. r =.5 9. r = 4 0. r = 3.
More informationGeometry: Conic Sections
Conic Sections Introduction When a right circular cone is intersected by a plane, as in figure 1 below, a family of four types of curves results. Because of their relationship to the cone, they are called
More informationSemester 2 Review Units 4, 5, and 6
Precalculus Semester 2 Review Units 4, 5, and 6 NAME: Period: UNIT 4 Simplify each expression. 1) (sec θ tan θ)(1 + tan θ) 2) cos θ sin 2 θ 1 3) 1+tan θ 1+cot θ 4) cos 2θ cosθ sin θ 5) sec 2 x sec 2 x
More informationObjectives and Homework List
MAC 1140 Objectives and Homework List Each objective covered in MAC1140 is listed below. Along with each objective is the homework list used with MyMathLab (MML) and a list to use with the text (if you
More informationPre-Calculus. 2) Find the equation of the circle having (2, 5) and (-2, -1) as endpoints of the diameter.
Pre-Calculus Conic Review Name Block Date Circles: 1) Determine the center and radius of each circle. a) ( x 5) + ( y + 6) = 11 b) x y x y + 6 + 16 + 56 = 0 ) Find the equation of the circle having (,
More informationTo sketch the graph we need to evaluate the parameter t within the given interval to create our x and y values.
Module 10 lesson 6 Parametric Equations. When modeling the path of an object, it is useful to use equations called Parametric equations. Instead of using one equation with two variables, we will use two
More information9.3 Hyperbolas and Rotation of Conics
9.3 Hyperbolas and Rotation of Conics Copyright Cengage Learning. All rights reserved. What You Should Learn Write equations of hyperbolas in standard form. Find asymptotes of and graph hyperbolas. Use
More informationPractice Test - Chapter 7
Write an equation for an ellipse with each set of characteristics. 1. vertices (7, 4), ( 3, 4); foci (6, 4), ( 2, 4) The distance between the vertices is 2a. 2a = 7 ( 3) a = 5; a 2 = 25 The distance between
More informationMastery. PRECALCULUS Student Learning Targets
PRECALCULUS Student Learning Targets Big Idea: Sequences and Series 1. I can describe a sequence as a function where the domain is the set of natural numbers. Connections (Pictures, Vocabulary, Definitions,
More informationPre-Calculus Guided Notes: Chapter 10 Conics. A circle is
Name: Pre-Calculus Guided Notes: Chapter 10 Conics Section Circles A circle is _ Example 1 Write an equation for the circle with center (3, ) and radius 5. To do this, we ll need the x1 y y1 distance formula:
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Precalculus Fall 204 Midterm Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find an equation in standard form for the hyperbola that
More informationStudy Guide and Review
Graph the hyperbola given by each equation. 30. = 1 The equation is in standard form, and h = 6 and k = 3. Because a 2 = 30 and b 2 = 8, a = 5.5 and b =. The values of a and b can be used to find c. c
More informationCK 12 Algebra II with Trigonometry Concepts 1
10.1 Parabolas with Vertex at the Origin Answers 1. up 2. left 3. down 4.focus: (0, 0.5), directrix: y = 0.5 5.focus: (0.0625, 0), directrix: x = 0.0625 6.focus: ( 1.25, 0), directrix: x = 1.25 7.focus:
More informationAssignment Assignment for Lesson 14.1
Assignment Assignment for Lesson.1 Name Date The Origin of Parabolas Parabolas Centered at the Origin 1. Consider the parabola represented by the equation y 2 12x 0. a. Write the equation of the parabola
More informationMid-Chapter Quiz: Lessons 7-1 through 7-3
Write an equation for and graph a parabola with the given focus F and vertex V 1. F(1, 5), V(1, 3) Because the focus and vertex share the same x coordinate, the graph is vertical. The focus is (h, k +
More informationChapter 11. Parametric Equations And Polar Coordinates
Instructor: Prof. Dr. Ayman H. Sakka Chapter 11 Parametric Equations And Polar Coordinates In this chapter we study new ways to define curves in the plane, give geometric definitions of parabolas, ellipses,
More informationCatholic Central High School
Catholic Central High School Algebra II Practice Examination II Instructions: 1. Show all work on the test copy itself for every problem where work is required. Points may be deducted if insufficient or
More information= ( )= To find the domain, we look at the vertical asymptote(s) (where denominator equals zero) , =0
Precalculus College Algebra Review for Final Name It is also a good idea to go back through your old tests and quizzes to review. 1. Find (+1) given ()=3 +1 2. Determine () given ()=+2 and ()= (+1)=3(+1)
More informationConic Sections: Parabolas
Conic Sections: Parabolas Why are the graphs of parabolas, ellipses, and hyperbolas called 'conic sections'? Because if you pass a plane through a double cone, the intersection of the plane and the cone
More informationb) develop mathematical thinking and problem solving ability.
Submission for Pre-Calculus MATH 20095 1. Course s instructional goals and objectives: The purpose of this course is to a) develop conceptual understanding and fluency with algebraic and transcendental
More informationName. Center axis. Introduction to Conic Sections
Name Introduction to Conic Sections Center axis This introduction to conic sections is going to focus on what they some of the skills needed to work with their equations and graphs. year, we will only
More informationUnit 8, Ongoing Activity, Little Black Book of Algebra II Properties
Unit 8, Ongoing Activity, Little Black Book of Algebra II Properties Little Black Book of Algebra II Properties Unit 8 Conic Sections 8.1 Circle write the definition, provide examples of both the standard
More informationMultivariable Calculus
Multivariable Calculus Chapter 10 Topics in Analytic Geometry (Optional) 1. Inclination of a line p. 5. Circles p. 4 9. Determining Conic Type p. 13. Angle between lines p. 6. Parabolas p. 5 10. Rotation
More information13.1 2/20/2018. Conic Sections. Conic Sections: Parabolas and Circles
13 Conic Sections 13.1 Conic Sections: Parabolas and Circles 13.2 Conic Sections: Ellipses 13.3 Conic Sections: Hyperbolas 13.4 Nonlinear Systems of Equations 13.1 Conic Sections: Parabolas and Circles
More informationName: Class: Date: Conics Multiple Choice Pre-Test. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: Conics Multiple Choice Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1 Graph the equation x 2 + y 2 = 36. Then describe the
More informationStandard Equation of a Circle
Math 335 Trigonometry Conics We will study all 4 types of conic sections, which are curves that result from the intersection of a right circular cone and a plane that does not contain the vertex. (If the
More informationMAC Learning Objectives. Module 12 Polar and Parametric Equations. Polar and Parametric Equations. There are two major topics in this module:
MAC 4 Module 2 Polar and Parametric Equations Learning Objectives Upon completing this module, you should be able to:. Use the polar coordinate system. 2. Graph polar equations. 3. Solve polar equations.
More informationLesson 8 Introduction to Quadratic Functions
Lesson 8 Introduction to Quadratic Functions We are leaving exponential and logarithmic functions behind and entering an entirely different world. As you work through this lesson, you will learn to identify
More informationUnit 12 Topics in Analytic Geometry - Classwork
Unit 1 Topics in Analytic Geometry - Classwork Back in Unit 7, we delved into the algebra and geometry of lines. We showed that lines can be written in several forms: a) the general form: Ax + By + C =
More informationMath 155, Lecture Notes- Bonds
Math 155, Lecture Notes- Bonds Name Section 10.1 Conics and Calculus In this section, we will study conic sections from a few different perspectives. We will consider the geometry-based idea that conics
More informationP.5 Rational Expressions
P.5 Rational Expressions I Domain Domain: Rational expressions : Finding domain a. polynomials: b. Radicals: keep it real! i. sqrt(x-2) x>=2 [2, inf) ii. cubert(x-2) all reals since cube rootscan be positive
More informationCatholic Central High School
Catholic Central High School Algebra II Practice Examination I Instructions: 1. Show all work on the test copy itself for every problem where work is required. Points may be deducted if insufficient or
More informationCHAPTER 2. Polynomials and Rational functions
CHAPTER 2 Polynomials and Rational functions Section 2.1 (e-book 3.1) Quadratic Functions Definition 1: A quadratic function is a function which can be written in the form (General Form) Example 1: Determine
More informationSemester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them.
Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Chapter 9 and 10: Right Triangles and Trigonometric Ratios 1. The hypotenuse of a right
More informationAlgebra II. Slide 1 / 181. Slide 2 / 181. Slide 3 / 181. Conic Sections Table of Contents
Slide 1 / 181 Algebra II Slide 2 / 181 Conic Sections 2015-04-21 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 181 Review of Midpoint and Distance Formulas Introduction
More informationFinal Exam Review Algebra Semester 1
Final Exam Review Algebra 015-016 Semester 1 Name: Module 1 Find the inverse of each function. 1. f x 10 4x. g x 15x 10 Use compositions to check if the two functions are inverses. 3. s x 7 x and t(x)
More informationCollege Algebra Exam File - Fall Test #1
College Algebra Exam File - Fall 010 Test #1 1.) For each of the following graphs, indicate (/) whether it is the graph of a function and if so, whether it the graph of one-to one function. Circle your
More informationAlgebra 2CP S1 Final Exam Information. Your final exam will consist of two parts: Free Response and Multiple Choice
Algebra 2CP Name Algebra 2CP S1 Final Exam Information Your final exam will consist of two parts: Free Response and Multiple Choice Part I: Free Response: Five questions, 10 points each (50 points total),
More information8.2 Graph and Write Equations of Parabolas
8.2 Graph and Write Equations of Parabolas Where is the focus and directrix compared to the vertex? How do you know what direction a parabola opens? How do you write the equation of a parabola given the
More informationPart I. There are 5 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer.
Math 109 Final Exam-Spring 016 Page 1 Part I. There are 5 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer. 1) Determine an equivalent
More informationModule 3: Stand Up Conics
MATH55 Module 3: Stand Up Conics Main Math concepts: Conic Sections (i.e. Parabolas, Ellipses, Hyperbolas), nd degree equations Auxilliary ideas: Analytic vs. Co-ordinate-free Geometry, Parameters, Calculus.
More informationTEKS Clarification Document. Mathematics Precalculus
TEKS Clarification Document Mathematics Precalculus 2012 2013 111.31. Implementation of Texas Essential Knowledge and Skills for Mathematics, Grades 9-12. Source: The provisions of this 111.31 adopted
More informationPrecalculus 2 Section 10.6 Parametric Equations
Precalculus 2 Section 10.6 Parametric Equations Parametric Equations Write parametric equations. Graph parametric equations. Determine an equivalent rectangular equation for parametric equations. Determine
More information7-5 Parametric Equations
3. Sketch the curve given by each pair of parametric equations over the given interval. Make a table of values for 6 t 6. t x y 6 19 28 5 16.5 17 4 14 8 3 11.5 1 2 9 4 1 6.5 7 0 4 8 1 1.5 7 2 1 4 3 3.5
More informationMath 2412 Activity 4(Due with Final Exam)
Math Activity (Due with Final Exam) Use properties of similar triangles to find the values of x and y x y 7 7 x 5 x y 7 For the angle in standard position with the point 5, on its terminal side, find the
More informationFind the maximum value or minimum value for the function. 11. Solve the equation. 13.
ACCELERATED MATH IV SUMMER PACKET DUE THE FIRST DAY OF SCHOOL The problems in this packet are designed to help you review topics from previous mathematics courses that are essential to your success in
More informationCLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)?
CLEP Pre-Calculus Section : Time 0 Minutes 50 Questions For each question below, choose the best answer from the choices given. An online graphing calculator (non-cas) is allowed to be used for this section..
More informationPLANE TRIGONOMETRY Exam I September 13, 2007
Name Rec. Instr. Rec. Time PLANE TRIGONOMETRY Exam I September 13, 2007 Page 1 Page 2 Page 3 Page 4 TOTAL (10 pts.) (30 pts.) (30 pts.) (30 pts.) (100 pts.) Below you will find 10 problems, each worth
More informationQuadratic Functions CHAPTER. 1.1 Lots and Projectiles Introduction to Quadratic Functions p. 31
CHAPTER Quadratic Functions Arches are used to support the weight of walls and ceilings in buildings. Arches were first used in architecture by the Mesopotamians over 4000 years ago. Later, the Romans
More informationConic Sections. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics
Conic Sections MATH 211, Calculus II J. Robert Buchanan Department o Mathematics Spring 2018 Introduction The conic sections include the parabola, the ellipse, and the hyperbola. y y y x x x Parabola A
More informationWallingford Public Schools - HIGH SCHOOL COURSE OUTLINE
Wallingford Public Schools - HIGH SCHOOL COURSE OUTLINE Course Title: PreCalculus Course Number: 1523 (A) 1522 (H) Department: Mathematics Grade(s): 11-12 Level(s): Honors and Academic Objectives that
More informationWhat you will learn today
What you will learn today Conic Sections (in 2D coordinates) Cylinders (3D) Quadric Surfaces (3D) Vectors and the Geometry of Space 1/24 Parabolas ellipses Hyperbolas Shifted Conics Conic sections result
More informationOpenStax-CNX module: m The Ellipse. OpenStax College. Abstract
OpenStax-CNX module: m49438 1 The Ellipse OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section, you will: Write equations
More informationAdvanced Math Final Exam Review Name: Bornoty May June Use the following schedule to complete the final exam review.
Advanced Math Final Exam Review Name: Bornoty May June 2013 Use the following schedule to complete the final exam review. Homework will e checked in every day. Late work will NOT e accepted. Homework answers
More information1Identify and generate
Then You related arithmetic sequences to linear functions. (Lesson -5) Now Geometric Sequences as Exponential Functions 1Identify and generate geometric sequences. 2Relate geometric sequences to exponential
More informationPractice Test - Chapter 9
Find the midpoint of the line segment with endpoints at the given coordinates 1 (8, 3), ( 4, 9) Substitute 8, 4, 3 and 9 for x 1, x 2, y 1 and y 2 respectively in the midpoint formula Find the distance
More informationEXERCISE SET 10.2 MATD 0390 DUE DATE: INSTRUCTOR
EXERCISE SET 10. STUDENT MATD 090 DUE DATE: INSTRUCTOR You have studied the method known as "completing the square" to solve quadratic equations. Another use for this method is in transforming the equation
More informationFind the midpoint of the line segment with endpoints at the given coordinates. 1. (8, 3), ( 4, 9) SOLUTION: Substitute 8, 4, 3 and 9 for x 1
Find the midpoint of the line segment with endpoints at the given coordinates. 1. (8, 3), ( 4, 9) Substitute 8, 4, 3 and 9 for x 1, x 2, y 1 and y 2 respectively in the midpoint formula. 2. Substitute
More informationAlgebra II Lesson 10-5: Hyperbolas Mrs. Snow, Instructor
Algebra II Lesson 10-5: Hyperbolas Mrs. Snow, Instructor In this section, we will look at the hyperbola. A hyperbola is a set of points P in a plane such that the absolute value of the difference between
More informationCHAPTER 8 QUADRATIC RELATIONS AND CONIC SECTIONS
CHAPTER 8 QUADRATIC RELATIONS AND CONIC SECTIONS Big IDEAS: 1) Writing equations of conic sections ) Graphing equations of conic sections 3) Solving quadratic systems Section: Essential Question 8-1 Apply
More informationSlide 2 / 222. Algebra II. Quadratic Functions
Slide 1 / 222 Slide 2 / 222 Algebra II Quadratic Functions 2014-10-14 www.njctl.org Slide 3 / 222 Table of Contents Key Terms Explain Characteristics of Quadratic Functions Combining Transformations (review)
More informationUnit 6 Quadratic Functions
Unit 6 Quadratic Functions 12.1 & 12.2 Introduction to Quadratic Functions What is A Quadratic Function? How do I tell if a Function is Quadratic? From a Graph The shape of a quadratic function is called
More information1.) Write the equation of a circle in standard form with radius 3 and center (-3,4). Then graph the circle.
Welcome to the world of conic sections! http://www.youtube.com/watch?v=bfonicn4bbg Some examples of conics in the real world: Parabolas Ellipse Hyperbola Your Assignment: Circle -Find at least four pictures
More information8th Grade Math. Parent Handbook
8th Grade Math Benchmark 1 Parent Handbook This handbook will help your child review material learned this quarter, and will help them prepare for their first Benchmark Test. Please allow your child to
More informationSection 6.1: Quadratic Functions and their Characteristics Vertical Intercept Vertex Axis of Symmetry Domain and Range Horizontal Intercepts
Lesson 6 Quadratic Functions and Equations Lesson 6 Quadratic Functions and Equations We are leaving exponential functions behind and entering an entirely different world. As you work through this lesson,
More informationSemester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them.
Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Chapter 9 and 10: Right Triangles and Trigonometric Ratios 1. The hypotenuse of a right
More informationALGEBRA 2 CP FINAL EXAM REVIEW
ALGEBRA CP FINAL EXAM REVIEW Algebra CP FINAL EXAM REVIEW Name CHAPTER - TRIGONOMETRY Note: always round sides to the nearest tenth and angles to the nearest degree. Find the values of the si trigonometric
More informationMath 126C: Week 3 Review
Math 126C: Week 3 Review Note: These are in no way meant to be comprehensive reviews; they re meant to highlight the main topics and formulas for the week. Doing homework and extra problems is always the
More informationChapter 6: Quadratic Functions
Chapter 6: Quadratic Functions Section 6.1 Chapter 6: Quadratic Functions Section 6.1 Exploring Quadratic Relations Terminology: Quadratic Relations: A relation that can be written in the standard form
More informationWillmar Public Schools Curriculum Map
Subject Area Mathematics Senior High Course Name Advanced Algebra 2B Date June 2010 Advanced Algebra 2B and Algebra 2B courses parallel each other in content and time. The Advanced Algebra 2B class is
More informationPut your initials on the top of every page, in case the pages become separated.
Math 1201, Fall 2016 Name (print): Dr. Jo Nelson s Calculus III Practice for 1/2 of Final, Midterm 1 Material Time Limit: 90 minutes DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED TO DO SO. This exam contains
More informationCollege Pre Calculus A Period. Weekly Review Sheet # 1 Assigned: Monday, 9/9/2013 Due: Friday, 9/13/2013
College Pre Calculus A Name Period Weekly Review Sheet # 1 Assigned: Monday, 9/9/013 Due: Friday, 9/13/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE
More information12/11/2018 Algebra II - Semester 1 Review
Name: Semester Review - Study Guide Score: 72 / 73 points (99%) Algebra II - Semester 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Name the property
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. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1)
More informationMath 125 Little Book Homework Chapters 7, 10, 11, and 12
Math 125 Little Book Homework Chapters 7, 10, 11, and 12 Do NOT copy the book follow the guidelines given for each section. NO CREDIT will be given if you copy the book! You earn 2 points if you turn in
More information