The Coordinate Plane. Circles and Polygons on the Coordinate Plane. LESSON 13.1 Skills Practice. Problem Set
|
|
- Robert Burke
- 6 years ago
- Views:
Transcription
1 LESSON.1 Skills Practice Name Date The Coordinate Plane Circles and Polgons on the Coordinate Plane Problem Set Use the given information to show that each statement is true. Justif our answers b using theorems and b using algebra. 1. The center of circle O is at the origin. The coordinates of the given points are A(, ), B(, ), and C(, ). Show that n ABC is a right triangle. n ABC is an inscribed triangle in circle O with the hpotenuse as the diameter of the circle, therefore the triangle is a right triangle b the Right Triangle Diameter Theorem. AB 5 ( ) 1 ( ) 5 ( ) 5 5 AC 5 ( ) 1 ( ) 5 () 1 () BC 5 ( ) 1 ( ) 5 1 () ( ) 1 ( ) A C O B D Therefore, b the Converse of the Pthagorean Theorem, nabc is a right triangle. Chapter Skills Practice 75
2 LESSON.1 Skills Practice page. The center of circle O is at the origin. AZ and AT are tangent to circle O. The coordinates of the given points are A(, 3), T(, ), and Z(, ). Show that the lengths of AT and AZ are equal. A 3 T 3 Z O The center of circle C is at the origin. AB is tangent to circle C at (3, ). Show that the tangent line is perpendicular to CA. B ( 1, 7) A (3, ) C (, ) 7 Chapter Skills Practice
3 LESSON.1 Skills Practice page 3 Name Date. The center of circle O is at the origin. The coordinates of the given points are A(3, ), B(, 3), D(, 5), E( 3, ), and F( 1.5,.5). Show that EF FD AF FB. E A O F B D Chapter Skills Practice 77
4 LESSON.1 Skills Practice page 5. The center of circle O is at the origin. The coordinates of the given points are A( 5, 5), B(, 3), C(, 5), and D(, 5). Show that AD AB AC. A D B O C 7 Chapter Skills Practice
5 LESSON.1 Skills Practice page 5 Name Date. The center of circle O is at the origin. BD is perpendicular to OA at point C. The coordinates of the given points are A( 5, ), B(, 3), C(, ), and D(, 3). Show that OA bisects BD. B A C O D Chapter Skills Practice 79
6 LESSON.1 Skills Practice page Classif the polgon formed b connecting the midpoints of the sides of each quadrilateral. Show all our work. 7. The rectangle shown has vertices A(, ), B(, ), C(, ), and D(, ). Midpoint AB : U (, ) Midpoint BC : S (, ) Midpoint CD : T (, ) Midpoint DA : R (, ) D (, ) R T C (, ) S A (, ) U B (, ) Slope RT Slope US Slope TS 5 Slope RU RT and US are parallel since the have the same slope of. TS and RU are parallel since the have the same slope of. There are no perpendicular sides. The slopes are not opposite reciprocals. RT 5 ( ) 1 ( ) TS 5 ( ) 1 ( ) 5 ( ) 1 ( ) 5 ( ) 1 ( ) US 5 ( ) 1 ( ) 5 ( ) 1 ( ) 5 1 RU 5 ( ) 1 ( ) 5 ( ) 1 ( ) 5 1 All four sides of RTSU are congruent. Opposite sides are parallel and all sides are congruent, so the quadrilateral formed b connecting the midpoints of the rectangle is a rhombus. Chapter Skills Practice
7 LESSON.1 Skills Practice page 7 Name Date. The isosceles trapezoid shown has vertices A(, ), B(, ), C(, 3), and D(, 3). D (, 3) C (, 3) A (, ) B (, ) Chapter Skills Practice 1
8 LESSON.1 Skills Practice page 9. The parallelogram shown has vertices A(, 5), B(7, 5), C(3, ), and D(, ). A B D C Chapter Skills Practice
9 LESSON.1 Skills Practice page 9 Name Date. The rhombus shown has vertices A(, ), B(, 5), C(, ), and D(, 5). A D B C Chapter Skills Practice 3
10 LESSON.1 Skills Practice page 11. The square shown has vertices A(, ), B(, ), C(, ), and D(, ). D C B A Chapter Skills Practice
11 LESSON.1 Skills Practice page 11 Name Date 1. The kite shown has vertices A(, ), B(, ), C(, 3), and D(, ). A D B C Chapter Skills Practice 5
12 Chapter Skills Practice
13 LESSON. Skills Practice Name Date Bring On the Algebra Deriving the Equation for a Circle Problem Set Write an equation in standard form of each circle. 1. a circle with center point at the origin when r r a circle with center point at the origin when r a circle with center point (, 5) when r 5 1. a circle with center point (, 1) when r 5 7 Chapter Skills Practice 7
14 LESSON. Skills Practice page 5. (, ) (, ). (3, 7) (, 3) Write the equation of each circle in standard form. Then identif the center point and radius of the circle ( 1 1 9) 1 ( 1 1) ( 1 3) 1 ( 1) 5 9 center: (3, 1), radius: 3 Chapter Skills Practice
15 LESSON. Skills Practice page 3 Name Date Chapter Skills Practice 9
16 LESSON. Skills Practice page Determine if each equation represents a circle. If so, describe the location of the center and radius ( 1 1 ) 1 ( 1 1 ) ( 1 ) 1 ( 1 ) 5 5 center: (, ), radius: Chapter Skills Practice
17 LESSON. Skills Practice page 5 Name Date Determine an equation of the circle that meets the given conditions. 17. Same center as circle A, ( 1 3) 1 ( 1 5) 5 9, but with a circumference that is twice that of circle A The radius of circle A is 9, or 3. To calculate the circumference of A, substitute 3 for r in the formula for the circumference of a circle. C 5 r 5 (3) C 5 A circle with twice the circumference of circle A has circumference ( ), or 1 units. To calculate its radius, substitute 1 for C in the formula for the circumference of a circle, and then solve for r. C 5 r 1 5 r 5 r The radius of the circle is. So an equation of the circle with the same center as circle A but with a circumference that is twice that of circle A is ( 1 3) 1 ( 1 5) 5, or ( 1 3) 1 ( 1 5) Same center as circle B, ( ) 1 ( 1 ) 5 9, but with a circumference that is three times that of circle B Chapter Skills Practice 91
18 9 Chapter Skills Practice
19 LESSON.3 Skills Practice Name Date Is That Point on the Circle? Determining Points on a Circle Problem Set For each circle A, determine whether the given point P lies on the circle. Eplain our reasoning. 1. P (5, 3) r 3 A (, ) 5 a 1 b 5 c r r 3 5 r r 5 3 < 5. Because the length of line segment AP is approimatel 5. units instead of units, line segment AP is not a radius of circle A; therefore, point P does not lie on circle A.. P (, ) A (, ) Chapter Skills Practice 93
20 LESSON.3 Skills Practice page 3. P (5, Œ39) A (, ). A (, ) P (, 7) 9 Chapter Skills Practice
21 LESSON.3 Skills Practice page 3 Name Date P (3, 11 Œ3 ) 5 1 A (1, 1) P (7, ) A (, 3) Chapter Skills Practice 95
22 LESSON.3 Skills Practice page Use smmetr to determine the coordinates of each labeled point on the circle. Give eact values, not approimations P (, ) 1 P (17, 5 Œ3 ) (, ) B (, ) (, ) B (, ) (, ) (3, 15) 15 9 C(, 3) C (3, ) (3 Œ, Œ) (, ) (1, ) (, 7.5) (, ) (1, ) (5, 1) Chapter Skills Practice
23 LESSON. Skills Practice Name Date The Parabola Equation of a Parabola Vocabular 1. locus of points a. A 1 D 5 or B 1 C 5. parabola 3. focus of a parabola. directri of a parabola 5. general form of a parabola. standard form of a parabola 7. ais of smmetr. verte of a parabola 9. concavit b. 5 p or 5 p c. describes the orientation of the curvature of the parabola d. a set of points in a plane that are equidistant from a fied point and a fied line e. the maimum or minimum point of a parabola f. a set of points that share a propert g. a line that passes through the parabola and divides the parabola into two smmetrical parts that are mirror images of each other h. the fied point from which all points of a parabola are equidistant i. the fied line from which all points of a parabola are equidistant Chapter Skills Practice 97
24 LESSON. Skills Practice page Problem Set Determine the equation of the parabola (, ) 1 (, 1) (, 1) ( ) 1 (1 ) 5 ( ) 1 (1 ) 1 (1 ) 5 (1 ) 1 (1 ) 5 (1 ) (, ) 3 (3, ) 5 1 (3, ) Chapter Skills Practice
25 LESSON. Skills Practice page 3 Name Date 3. 5 (, ) 3 (, ) 5 1 (, ) (,.5) (,.5) (, ) 3 5 Chapter Skills Practice 99
26 LESSON. Skills Practice page Identif the verte, ais of smmetr, value of p, focus and directri for each parabola Verte: (, ) Ais of smmetr: 5 Value of p:.75 Focus: (,.75) Directri: (, 7.5) 3 5. (, ) 9 Chapter Skills Practice
27 LESSON. Skills Practice page 5 Name Date 7. Parabola c Chapter Skills Practice 91
28 LESSON. Skills Practice page Sketch each parabola Chapter Skills Practice
29 LESSON. Skills Practice page 7 Name Date Chapter Skills Practice 93
30 9 Chapter Skills Practice
31 LESSON.5 Skills Practice Name Date Simpl Parabolic More With Parabolas Problem Set Determine the equation of the parabola (, ) (, ) 3 5 (, ) ( ) 1 ( ) 5 ( ) 1 ( ) 1 ( ) 5 ( ) 1 ( ) 5 ( ) (3, 5) (, ) (, 3) Chapter Skills Practice 95
32 LESSON.5 Skills Practice page 3. (5, 1) 1 1 (, ) (, 5). (, ) 1 1 (, ) (3, ) 9 Chapter Skills Practice
33 LESSON.5 Skills Practice page 3 Name Date Identif the verte, ais of smmetr, value of p, focus and directri for each parabola Verte: (3, ) 1 (3, ) Ais of smmetr: 5 3 Value of p: Focus: (3, ) Directri: (, ) Chapter Skills Practice 97
34 LESSON.5 Skills Practice page Chapter Skills Practice
35 LESSON.5 Skills Practice page 5 Name Date Complete the table for each equation. Then, plot the points and graph the curve on the coordinate plane Chapter Skills Practice 99
36 LESSON.5 Skills Practice page Chapter Skills Practice
37 LESSON.5 Skills Practice page 7 Name Date Rewrite the equations in standard form ( ) 5 3( 1 ) Chapter Skills Practice 911
38 91 Chapter Skills Practice
Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in
Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.
More information0114ge. Geometry Regents Exam 0114
0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?
More informationSkills Practice Skills Practice for Lesson 9.1
Skills Practice Skills Practice for Lesson.1 Name Date Meeting Friends The Distance Formula Vocabular Define the term in our own words. 1. Distance Formula Problem Set Archaeologists map the location of
More informationQ.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or
STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. A variable rectangle PQRS has its sides parallel to fied directions. Q and S lie respectivel on the lines = a, = a and P lies on the ais. Then the locus of R
More informationLesson 9.1 Using the Distance Formula
Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)
More informationApplications. 12 The Shapes of Algebra. 1. a. Write an equation that relates the coordinates x and y for points on the circle.
Applications 1. a. Write an equation that relates the coordinates and for points on the circle. 1 8 (, ) 1 8 O 8 1 8 1 (13, 0) b. Find the missing coordinates for each of these points on the circle. If
More information1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.
Higher Maths Non Calculator Practice Practice Paper A. A sequence is defined b the recurrence relation u u, u. n n What is the value of u?. The line with equation k 9 is parallel to the line with gradient
More information0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationPREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared by IITians.
www. Class XI TARGET : JEE Main/Adv PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) ALP ADVANCED LEVEL PROBLEMS Straight Lines 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared b IITians.
More information1 What is the solution of the system of equations graphed below? y = 2x + 1
1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x
More informationSkills Practice Skills Practice for Lesson 1.1
Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Give an eample of each term.. quadratic function 9 0. vertical motion equation s
More information0811ge. Geometry Regents Exam
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationFind the area of the triangle. You try: D C. Determine whether each of the following statements is true or false. Solve for the variables.
lameda USD Geometr enchmark Stud Guide ind the area of the triangle. 9 4 5 D or all right triangles, a + b c where c is the length of the hpotenuse. 5 4 a + b c 9 + b 5 + b 5 b 5 b 44 b 9 he area of a
More informationIndicate whether the statement is true or false.
PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.
More information0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.
0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD
More informationPart (1) Second : Trigonometry. Tan
Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,
More informationAP Calculus BC : The Fundamental Theorem of Calculus
AP Calculus BC 415 5.3: The Fundamental Theorem of Calculus Tuesday, November 5, 008 Homework Answers 6. (a) approimately 0.5 (b) approimately 1 (c) approimately 1.75 38. 4 40. 5 50. 17 Introduction In
More informationA. 180 B. 108 C. 360 D. 540
Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior
More informationVerifying Properties of Quadrilaterals
Verifing roperties of uadrilaterals We can use the tools we have developed to find, classif, or verif properties of various shapes made b plotting coordinates on a Cartesian plane. Depending on the problem,
More informationPractice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E.
April 9, 01 Standards: MM1Ga, MM1G1b Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? (1,10) B. (,7) C. (,) (,) (,1). Points P, Q, R, and S lie on a line
More informationTest Corrections for Unit 1 Test
MUST READ DIRECTIONS: Read the directions located on www.koltymath.weebly.com to understand how to properly do test corrections. Ask for clarification from your teacher if there are parts that you are
More informationModule 3, Section 4 Analytic Geometry II
Principles of Mathematics 11 Section, Introduction 01 Introduction, Section Analtic Geometr II As the lesson titles show, this section etends what ou have learned about Analtic Geometr to several related
More informationLESSON #42 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART 2 COMMON CORE ALGEBRA II
LESSON #4 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART COMMON CORE ALGEBRA II You will recall from unit 1 that in order to find the inverse of a function, ou must switch and and solve for. Also,
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
More information0612ge. Geometry Regents Exam
0612ge 1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R. Which transformation produces an image that is similar to, but not congruent
More informationPOINT. Preface. The concept of Point is very important for the study of coordinate
POINT Preface The concept of Point is ver important for the stud of coordinate geometr. This chapter deals with various forms of representing a Point and several associated properties. The concept of coordinates
More informationSection 5.1. Perimeter and Area
Section 5.1 Perimeter and Area Perimeter and Area The perimeter of a closed plane figure is the distance around the figure. The area of a closed plane figure is the number of non-overlapping squares of
More informationCOORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE. To find the length of a line segment joining two points A(x 1, y 1 ) and B(x 2, y 2 ), use
COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE I. Length of a Line Segment: The distance between two points A ( x1, 1 ) B ( x, ) is given b A B = ( x x1) ( 1) To find the length of a line segment joining
More informationMATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1)
MATH : Final Eam Review Can ou find the distance between two points and the midpoint of a line segment? (.) () Consider the points A (,) and ( 6, ) B. (a) Find the distance between A and B. (b) Find the
More informationMATHEMATICS HSC Course Assessment Task 3 (Trial Examination) June 21, QUESTION Total MARKS
MATHEMATICS 0 HSC Course Assessment Task (Trial Eamination) June, 0 General instructions Working time hours. (plus 5 minutes reading time) Write using blue or black pen. Where diagrams are to be sketched,
More information0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?
0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100
More information0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?
0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle
More information10.2 INTRODUCTION TO CONICS: PARABOLAS
Section 0.2 Introduction to Conics: Parabolas 733 0.2 INTRODUCTION TO CONICS: PARABOLAS What ou should learn Recognize a conic as the intersection of a plane a double-napped cone. Write equations of parabolas
More informationTangent Lines Unit 10 Lesson 1 Example 1: Tell how many common tangents the circles have and draw them.
Tangent Lines Unit 10 Lesson 1 EQ: How can you verify that a segment is tangent to a circle? Circle: Center: Radius: Chord: Diameter: Secant: Tangent: Tangent Lines Unit 10 Lesson 1 Example 1: Tell how
More informationb UVW is a right-angled triangle, therefore VW is the diameter of the circle. Centre of circle = Midpoint of VW = (8 2) + ( 2 6) = 100
Circles 6F a U(, 8), V(7, 7) and W(, ) UV = ( x x ) ( y y ) = (7 ) (7 8) = 8 VW = ( 7) ( 7) = 64 UW = ( ) ( 8) = 8 Use Pythagoras' theorem to show UV UW = VW 8 8 = 64 = VW Therefore, UVW is a right-angled
More informationTable of Contents. Unit 6: Modeling Geometry. Answer Key...AK-1. Introduction... v
These materials ma not be reproduced for an purpose. The reproduction of an part for an entire school or school sstem is strictl prohibited. No part of this publication ma be transmitted, stored, or recorded
More informationabsolute value The distance of a number from zero on a real number line.
G L O S S A R Y A absolute value The distance of a number from zero on a real number line. acute angle An angle whose measure is less than 90. acute triangle A triangle in which each of the three interior
More informationTopic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths
Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)
N E W S O U T H W A L E S HIGHER SCHOOL CERTIFICATE EXAMINATION 996 MATHEMATICS /3 UNIT (COMMON) Time allowed Three hours (Plus minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL
More informationReady To Go On? Skills Intervention 10-1 Introduction to Conic Sections
Find this vocabular word in Lesson 10-1 and the Multilingual Glossar. Graphing Parabolas and Hperbolas on a Calculator A is a single curve, whereas a has two congruent branches. Identif and describe each
More informationThe telescopes at the W.M. Keck Observatory in Hawaii use hyperbolic mirrors.
UNIT 15 Conic Sections The telescopes at the W.M. Keck Observator in Hawaii use hperbolic mirrors. Copright 009, K1 Inc. All rights reserved. This material ma not be reproduced in whole or in part, including
More information4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF?
Name:!!!!!!!!!!!!! Geo(2) GEOMETRY (2) REVIEW FOR FINAL EXAM #2 1. If ABC is similar to ADE, then AB AD =? AE. Which replaces the? to make the statement true? A. AC!! B. AE!! C. DE!! D. BC 2. In ABC,
More informationCircles and Parabolas
Circles and Parabolas Discus throwing is an ancient sport at least 3000 years old. This sport has been part of the Olympics since the first Summer Olympics in 1896. Many ancient Greek and Roman statues
More informationChapter 3 Summary 3.1. Determining the Perimeter and Area of Rectangles and Squares on the Coordinate Plane. Example
Chapter Summar Ke Terms bases of a trapezoid (.) legs of a trapezoid (.) composite figure (.5).1 Determining the Perimeter and Area of Rectangles and Squares on the Coordinate Plane The perimeter or area
More informationStudy Guide. Exploring Circles. Example: Refer to S for Exercises 1 6.
9 1 Eploring ircles A circle is the set of all points in a plane that are a given distance from a given point in the plane called the center. Various parts of a circle are labeled in the figure at the
More informationRhombi, Rectangles and Squares
Rhombi, Rectangles and Squares Math Practice Return to the Table of Contents 1 Three Special Parallelograms All the same properties of a parallelogram apply to the rhombus, rectangle, and square. Rhombus
More informationIncoming Magnet Precalculus / Functions Summer Review Assignment
Incoming Magnet recalculus / Functions Summer Review ssignment Students, This assignment should serve as a review of the lgebra and Geometry skills necessary for success in recalculus. These skills were
More informationG.GPE.B.4: Quadrilaterals in the Coordinate Plane 2
Regents Exam Questions www.jmap.org Name: 1 In square GEOM, the coordinates of G are (2, 2) and the coordinates of O are ( 4,2). Determine and state the coordinates of vertices E and M. [The use of the
More information0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?
0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30
More informationC=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle
10.1 Circles and Circumference Chapter 10 Circles Circle the locus or set of all points in a plane that are A equidistant from a given point, called the center When naming a circle you always name it by
More informationPractice Problems for Test II
Math 117 Practice Problems for Test II 1. Let f() = 1/( + 1) 2, and let g() = 1 + 4 3. (a) Calculate (b) Calculate f ( h) f ( ) h g ( z k) g( z) k. Simplify your answer as much as possible. Simplify your
More informatione x for x 0. Find the coordinates of the point of inflexion and justify that it is a point of inflexion. (Total 7 marks)
Chapter 0 Application of differential calculus 014 GDC required 1. Consider the curve with equation f () = e for 0. Find the coordinates of the point of infleion and justify that it is a point of infleion.
More informationGeometry Note Cards EXAMPLE:
Geometry Note Cards EXAMPLE: Lined Side Word and Explanation Blank Side Picture with Statements Sections 12-4 through 12-5 1) Theorem 12-3 (p. 790) 2) Theorem 12-14 (p. 790) 3) Theorem 12-15 (p. 793) 4)
More informationUNIT 3 CIRCLES AND VOLUME Lesson 1: Introducing Circles Instruction
Prerequisite Skills This lesson requires the use of the following skills: performing operations with fractions understanding slope, both algebraically and graphically understanding the relationship of
More information9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson
Chapter 9 Lesson 9-1 The Function with Equation = a BIG IDEA The graph of an quadratic function with equation = a, with a 0, is a parabola with verte at the origin. Vocabular parabola refl ection-smmetric
More information9. AD = 7; By the Parallelogram Opposite Sides Theorem (Thm. 7.3), AD = BC. 10. AE = 7; By the Parallelogram Diagonals Theorem (Thm. 7.6), AE = EC.
3. Sample answer: Solve 5x = 3x + 1; opposite sides of a parallelogram are congruent; es; You could start b setting the two parts of either diagonal equal to each other b the Parallelogram Diagonals Theorem
More informationName: Richard Montgomery High School Department of Mathematics. Summer Math Packet. for students entering. Algebra 2/Trig*
Name: Richard Montgomer High School Department of Mathematics Summer Math Packet for students entering Algebra 2/Trig* For the following courses: AAF, Honors Algebra 2, Algebra 2 (Please go the RM website
More informationAre You Ready? Find Area in the Coordinate Plane
SKILL 38 Are You Read? Find Area in the Coordinate Plane Teaching Skill 38 Objective Find the areas of figures in the coordinate plane. Review with students the definition of area. Ask: Is the definition
More information2014 Caryn White: Caryn Loves Math 1
2014 Caryn White: Caryn Loves Math 1 Coordinate Plane Geometry: Quadrilateral Task Cards By Caryn White Table of Contents Copy Right Informations:... 2 Instructions and Ideas... 3 Task Cards... 5 Wanted
More informationRMT 2013 Geometry Test Solutions February 2, = 51.
RMT 0 Geometry Test Solutions February, 0. Answer: 5 Solution: Let m A = x and m B = y. Note that we have two pairs of isosceles triangles, so m A = m ACD and m B = m BCD. Since m ACD + m BCD = m ACB,
More informationMultiple Choice. 3. The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
Accelerated Coordinate Algebra/Analtic Geometr answers the question. Page 1 of 5 Multiple Choice 1. The dashed triangle is an image of the solid triangle. What is the scale factor of the image?. The polgons
More information5.2 Solving Quadratic Equations by Factoring
Name. Solving Quadratic Equations b Factoring MATHPOWER TM, Ontario Edition, pp. 78 8 To solve a quadratic equation b factoring, a) write the equation in the form a + b + c = b) factor a + b + c c) use
More information3.5. Did you ever think about street names? How does a city or town decide what to. composite figures
.5 Composite Figures on the Coordinate Plane Area and Perimeter of Composite Figures on the Coordinate Plane LEARNING GOALS In this lesson, ou will: Determine the perimeters and the areas of composite
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 informationQUESTION BANK ON STRAIGHT LINE AND CIRCLE
QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,
More informationAPPENDIXES. B Coordinate Geometry and Lines C. D Trigonometry E F. G The Logarithm Defined as an Integral H Complex Numbers I
APPENDIXES A Numbers, Inequalities, and Absolute Values B Coordinate Geometr and Lines C Graphs of Second-Degree Equations D Trigonometr E F Sigma Notation Proofs of Theorems G The Logarithm Defined as
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More information9.3. Practice C For use with pages Tell whether the triangle is a right triangle.
LESSON 9.3 NAME DATE For use with pages 543 549 Tell whether the triangle is a right triangle. 1. 21 2. 3. 75 6 2 2 17 72 63 66 16 2 4. 110 5. 4.3 6. 96 2 4.4 10 3 3 4.5 Decide whether the numbers can
More informationPractice Assessment Task SET 3
PRACTICE ASSESSMENT TASK 3 655 Practice Assessment Task SET 3 Solve m - 5m + 6 $ 0 0 Find the locus of point P that moves so that it is equidistant from the points A^-3, h and B ^57, h 3 Write x = 4t,
More information8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no
Lesson 8.1.1 8-6. a: 110 b: 70 c: 48 d: 108 8-7. a: no b: yes c: no d: yes e: no f: yes g: yes h: no 8-8. b: The measure of an exterior angle of a triangle equals the sum of the measures of its remote
More information4.2 Parabolas. Explore Deriving the Standard-Form Equation. Houghton Mifflin Harcourt Publishing Company. (x - p) 2 + y 2 = (x + p) 2
COMMON CORE. d Locker d LESSON Parabolas Common Core Math Standards The student is epected to: COMMON CORE A-CED.A. Create equations in two or more variables to represent relationships between quantities;
More informationSpecial Mathematics Notes
Special Mathematics Notes Tetbook: Classroom Mathematics Stds 9 & 10 CHAPTER 6 Trigonometr Trigonometr is a stud of measurements of sides of triangles as related to the angles, and the application of this
More informationName: GEOMETRY: EXAM (A) A B C D E F G H D E. 1. How many non collinear points determine a plane?
GMTRY: XM () Name: 1. How many non collinear points determine a plane? ) none ) one ) two ) three 2. How many edges does a heagonal prism have? ) 6 ) 12 ) 18 ) 2. Name the intersection of planes Q and
More informationUse this space for computations. 1 In trapezoid RSTV below with bases RS and VT, diagonals RT and SV intersect at Q.
Part I Answer all 28 questions in this part. Each correct answer will receive 2 credits. For each statement or question, choose the word or expression that, of those given, best completes the statement
More informationUnit 10 Geometry Circles. NAME Period
Unit 10 Geometry Circles NAME Period 1 Geometry Chapter 10 Circles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (10-1) Circles and Circumference
More information0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.
0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,
More informationMarquette University
Marquette University 2 0 7 C O M P E T I T I V E S C H O L A R S H I P E X A M I N A T I O N I N M A T H E M A T I C S Do not open this booklet until you are directed to do so.. Fill out completely the
More information5-4. Focus and Directrix of a Parabola. Key Concept Parabola VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING
5- Focus and Directri of a Parabola TEKS FOCUS VOCABULARY TEKS ()(B) Write the equation of a parabola using given attributes, including verte, focus, directri, ais of smmetr, and direction of opening.
More information(b) the equation of the perpendicular bisector of AB. [3]
HORIZON EDUCATION SINGAPORE Additional Mathematics Practice Questions: Coordinate Geometr 1 Set 1 1 In the figure, ABCD is a rhombus with coordinates A(2, 9) and C(8, 1). The diagonals AC and BD cut at
More informationEdexcel GCE A Level Maths. Further Maths 3 Coordinate Systems
Edecel GCE A Level Maths Further Maths 3 Coordinate Sstems Edited b: K V Kumaran kumarmaths.weebl.com 1 kumarmaths.weebl.com kumarmaths.weebl.com 3 kumarmaths.weebl.com 4 kumarmaths.weebl.com 5 1. An ellipse
More informationJUST IN TIME MATERIAL GRADE 11 KZN DEPARTMENT OF EDUCATION CURRICULUM GRADES DIRECTORATE TERM
JUST IN TIME MATERIAL GRADE 11 KZN DEPARTMENT OF EDUCATION CURRICULUM GRADES 10 1 DIRECTORATE TERM 1 017 This document has been compiled by the FET Mathematics Subject Advisors together with Lead Teachers.
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 998 MATHEMATICS / UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of equal value.
More informationDownloaded from
Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar
More information0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
More information11. Concentric Circles: Circles that lie in the same plane and have the same center.
Circles Definitions KNOW THESE TERMS 1. Circle: The set of all coplanar points equidistant from a given point. 2. Sphere: The set of all points equidistant from a given point. 3. Radius of a circle: The
More information2000 Solutions Euclid Contest
Canadian Mathematics Competition n activit of The Centre for Education in Mathematics and Computing, Universit of Waterloo, Waterloo, Ontario 000 s Euclid Contest (Grade) for The CENTRE for EDUCTION in
More information8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no
Lesson 8.1.1 8-6. a: 110 b: 70 c: 48 d: 108 8-7. a: no b: yes c: no d: yes e: no f: yes g: yes h: no 8-8. b: The measure of an exterior angle of a triangle equals the sum of the measures of its remote
More informationDistance. Warm Ups. Learning Objectives I can find the distance between two points. Football Problem: Bailey. Watson
Distance Warm Ups Learning Objectives I can find the distance between two points. Football Problem: Bailey Watson. Find the distance between the points (, ) and (4, 5). + 4 = c 9 + 6 = c 5 = c 5 = c. Using
More information2.1 The Rectangular Coordinate System
. The Rectangular Coordinate Sstem In this section ou will learn to: plot points in a rectangular coordinate sstem understand basic functions of the graphing calculator graph equations b generating a table
More information6 Linear and Quadratic Functions
6 Linear and Quadratic Functions 6. Prologue Definition 4 in Book I of Euclid s Elements (3rd centur BC) reads: A straight line is a line that lies evenl with the points on itself. No one knows for sure
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Tuesday, January 22, :15 to 4:15 p.m.
The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Tuesda, Januar, 00 1:15 to 4:15 p.m., onl Notice... Scientific calculators
More information( ) ( ) Geometry Team Solutions FAMAT Regional February = 5. = 24p.
. A 6 6 The semi perimeter is so the perimeter is 6. The third side of the triangle is 7. Using Heron s formula to find the area ( )( )( ) 4 6 = 6 6. 5. B Draw the altitude from Q to RP. This forms a 454590
More informationDiagnostic Assessment Number and Quantitative Reasoning
Number and Quantitative Reasoning Select the best answer.. Which list contains the first four multiples of 3? A 3, 30, 300, 3000 B 3, 6, 9, 22 C 3, 4, 5, 6 D 3, 26, 39, 52 2. Which pair of numbers has
More informationGeometry Honors Homework
Geometry Honors Homework pg. 1 12-1 Practice Form G Tangent Lines Algebra Assume that lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. 2. 3. The circle
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time)
N E W S O U T H W A L E S HIGHER SCHOOL CERTIFICATE EXAMINATION 996 MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions.
More informationGlossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards
Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important
More informationNotes: Review of Algebra I skills
Notes: Review of Algebra I skills http://www.monroeps.org/honors_geometry.aspx http://www.parklandsd.org/wp-content/uploads/hrs_geometry.pdf Name: Date: Period: Algebra Review: Systems of Equations * If
More informationThe region enclosed by the curve of f and the x-axis is rotated 360 about the x-axis. Find the volume of the solid formed.
Section A ln. Let g() =, for > 0. ln Use the quotient rule to show that g ( ). 3 (b) The graph of g has a maimum point at A. Find the -coordinate of A. (Total 7 marks) 6. Let h() =. Find h (0). cos 3.
More informationSTRATHFIELD GIRLS HIGH SCHOOL TRIAL HIGHER SCHOOL CERTIFICATE MATHEMATICS. Time allowed Three hours (Plus 5 minutes reading time)
STRATHFIELD GIRLS HIGH SCHOOL TRIAL HIGHER SCHOOL CERTIFICATE 00 MATHEMATICS Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of
More informationNumber Plane Graphs and Coordinate Geometry
Numer Plane Graphs and Coordinate Geometr Now this is m kind of paraola! Chapter Contents :0 The paraola PS, PS, PS Investigation: The graphs of paraolas :0 Paraolas of the form = a + + c PS Fun Spot:
More information