Basic Lesson: Pythagorean Theorem


 Elmer Wilson
 2 years ago
 Views:
Transcription
1 Basic Lesson: Pythagorean Theorem Basic skill One leg of a triangle is 10 cm and other leg is of 24 cm. Find out the hypotenuse? Here we have AB = 10 and BC = 24 Using the Pythagorean Theorem AC 2 = AB 2 + BC 2 Replacing value AB with 10 and BC with 24 in above formula we have AC 2 = AB 2 + BC 2 (x) 2 = (10) 2 + (24) 2 x= 676 = 26 Answer = 26 cm Basic skills Practice Find the length of a rod that has to be fixed diagonally in a room of dimensions 24 feet by 28 feet by 30 feet. Rod has to be fixed in a room diagonally which basically means diagonal of a cube. Diagonal of a cube = (l 2 +b 2 +h 2 ) Replacing values in above formula, Diagonal = ( ) = = 2260 = feet Answer = feet
2 Intermediate Lesson: Pythagorean Theorem Intermediate skills Practice A square with sides of 40 feet. What is the shortest distance between two opposite vertices? Here we have AB = 40 and BC = 40 Using the Pythagorean Theorem AC 2 = AB 2 + BC 2 Replacing value AB and BC with 40 in above formula we have AC 2 = AB 2 + BC 2 (40) 2 + (40) 2 = (x) 2 (x) 2 = = 3200 x= 3200 = (The diagonal of a square can also be calculated by using formula a 2, where a is the side of the square. Applying this formula for this problem; diagonal=40 x 2 = 40 x = In each case, answer is same) Answer = feet Intermediate skill To avoid the pond, Joe must walk 14 meters south and 48 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond? Suppose we have AC = 14 and AB = 48 If it were possible to walk through the pond, shortest distance could be calculated by using the Pythagorean Theorem AC 2 + AB 2 = BC 2 Replacing value AC with 14 and AB with 48 in the formula we have (14) 2 + (48) 2 = (BC) 2 (BC) 2 = = 2500 BC= 2500 = 50 Since, it is not possible to walk through the pond, Joe must walk 14m +48m = 62 Distance that would be saved if it were possible to walk through the pond = total distanceshortest distance= 6250=12 Answer = 12 m
3 Independent Practice 1: Pythagorean Theorem 1. A rectangle has a width of 6 feet and a length of 8 feet. Find the length of the diagonal in feet. 2. A rectangle has a width of 14 inches and a diagonal of 50 inches. Find the length of the rectangle in inches. 3. A 65 foot ladder is leaned against a wall. If the base of the ladder is 63 feet from the wall, how high up the wall will the ladder reach? Firefighters have a 37 feet extension ladder. In order to reach 35 feet up a building, how far away from the building should the feet of the ladder be placed? Princess Marie is locked in the tower of a castle. Tim volunteered to rescue the princess. If the tower window is 480 feet above the ground and you must place your ladder 31 feet from the base of the castle (because of the moat), what is the shortest length ladder, to the nearest foot, you will need to reach the princess? Tom wants to swim across a river that is 400 meters wide. He begins swimming perpendicular to the shore he started from but ends up 300 meters down river from where he started because of the current. How far did he actually swim from his starting point? In the South, settlers often fashioned tents as an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 6 meters high and 10 meters wide? 8. A baseball diamond is a square with sides of 80 feet. What is the shortest distance, to the nearest tenth of a foot, between home plate and second base? 9. To avoid the pond, Alex must walk 12 meters south and 35 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond? 10. A square with sides of 50 feet. What is the shortest distance between two opposite vertices? 11. Box measures 32 inches long, 6 inches wide and 8 inches high. What is the diagonal length of the box?
4 12. The sides of a triangle measure 14, 48, and 30. Is this triangle a right triangle? 13. The older floppy diskettes measured 7 and 3 inches on each side. What was the diagonal length of the diskette? 14. A right triangle has a hypotenuse of 17 and a leg of 15. Find the other leg of the triangle? 15. Two joggers run 12 miles north and then 8 miles west. What is the shortest distance to reach their starting point? 16. Slanted sides of a tent 34 feet long total and the bottom of the house is 30 feet across. What is the tallest point of this tent? 17. An equilateral triangle is plotted on a coordinate plane. Two of the vertices are (0,0) and (6,0). Which of the coordinates shown could be the vertex of the third side? 18. One leg of a right triangle is 62 units longer than the length of the other leg. If the hypotenuse is 82, then find the other two legs. 19. A cube has a width of 4 feet, height of 12 feet and a length of 8 feet. Find the length of the diagonal in feet. 20. A 15 foot ladder is leaned against a wall. If the base of the ladder is 9 feet from the wall, how high up the wall will the ladder reach?
5 Independent Practice 2: Pythagorean Theorem Sam regularly takes a shortcut across Mr. Hilton's lawn instead of walking on the sidewalk (7 m by 24 m) on his way home from school. How much distance is saved by Joe cutting across the lawn? Tom has covered a distance of 35 meters south and 7 meters east. What can be shortest distance can he walk? Find the length of a diagonal of a cube that has sides measuring 12 cm each. An 11feet pole casts a shadow of 60 feet. What is the distance between the end of the shadow and the top of pole? A spider has taken up residence in a small cardboard box which measures 3 inches by 7 inches by 5 inches. What is the length, in inches, of a straight spider web that will carry the spider from the lower right front corner of the box to the upper left back corner of the box? David rides his bike 24 km south and then 4 km west. How far is he from his starting point? Town A is 9 miles from town B, and 12 miles from town C. Town A, B and C are forming a right triangle at A. A road connects towns B and C directly. Find the length of this road. A garden is in the shape of a right triangle. It has one side that is 22 ft long, and has a hypotenuse of 122 ft, what is the width of the garden Jack's TV screen is 12 inches long. If the diagonal measures 37 inches, how long is the width of Jack's TV? The foot of a ladder is placed 14 feet from a wall. If the top of the ladder rests 9 feet up on the wall, how long is the ladder? If each of the legs of an isosceles right triangle is 12 inches long, approximate the length of the hypotenuse to the nearest whole number. 12. Find the length of the diagonal of a square whose sides is 16 meters.
6 A hotair balloon is held in place by the ground crew at a point that is 40 ft from a point directly beneath the balloon. If the rope is of length 41 ft, how far above ground level is the balloon? There is a building with an 11 ft high window. Jack wants to use a ladder to go up to the window, and he decides to keep the ladder 60 ft away from the building to have a good slant. How long should the ladder be? If a leg of a triangle is 10 ft long, and another leg is 8 ft long, what is the length of the hypotenuse? 16. Diagonal of a cube is m. Find the length of the cube Nancy drives her car 15 km south and then 16 km west. How far is she from her starting point? Find x A cartoon in shape of a cube measures 4 inches. What is the diagonal length of the box? If the sum of the sides of a right triangle is 194 inches and the hypotenuse is 170 inches, find the two sides.
7 Homework: Pythagorean Theorem Basic skills Practice Find the length of a rod that has to be fixed diagonally in a room of dimensions 24 feet by 28 feet by 30 feet. Rod has to be fixed in a room diagonally which basically means diagonal of a cube Diagonal of a cube = (l 2 +b 2 +h 2 ) Replacing values in above formula, Diagonal = ( ) = = 2260 = feet Answer = feet 1. A cube has a side of 14 cm. How long is the diagonal? A 145 feet ladder is leaned against a wall. If the base of the ladder is 24 feet from the wall, how high up the wall will the ladder reach If each of the leg of an isosceles right triangle is 20 m long, approximate the length of the hypotenuse to the nearest whole number. Find the length of the diagonal of a square whose sides is 38 meters. AB=12x, AC=5x, BC=65. Find the value of x House A is 38 miles from house B, and 360 miles from house C. House A, B and C are forming a right triangle at A. A road connects houses B and C directly. Find the length of this road. There is a building with a 120 ft high window. Lisa wants to use a ladder to go up to the window, and she decides to keep the ladder 22 ft away from the building to have a good slant. How long should the ladder be? A ground is in the shape of a right triangle. It has one side that is 31 ft long, and has a hypotenuse of 481 ft. 9. Daisy Duck has a nest on the edge of the pond. From her favorite feeding spot, she can either waddle on land around the pond to the nest (70 meters by 240 meters), or she can swim across the pond to the nest. Daisy waddles more quickly than she swims. She waddles at the rate of 25 m/min and she swims at the rate of 10 m/min. Which route is quicker to travel from the feeding spot to the nest? Waddling on land or swimming in the pond?
8 If a leg of a triangle is 30 ft long, and another leg is 224 ft long, what is the length of the hypotenuse? A hall s screen is 62 inches long. If the diagonal measures 80 inches, and length of hall is 42 inches how long is the width of hall s screen? A cartoon measures 12 inches long, 8 inches wide and 18 inches high. What is the diagonal length of the box?
9 Quiz: Pythagorean Theorem Lisa drives her car 48 km south and then 575 km east. How far is she from her starting point? Using the Pythagorean Theorem, find the area of an equilateral triangle whose side measures 4 units. Find the area to the nearest tenth of a square unit. If the legs of an isosceles right triangle are 12 inches long, approximate the length of the hypotenuse to the nearest whole number Dick rides his bike 64 km south and then 1023 km west. How far is he from his starting point? If a leg of a triangle is 23 ft long, and another leg is 264 ft long, what is the length of the hypotenuse? A garden is in the shape of a square of sides 22 feet. What is its hypotenuse? If a side of a triangle is 16 ft long, and another side is 63 ft long, what is the length of the hypotenuse? Town A is 8 miles from town B, and 15 miles from town C. Town A, B and C are forming a right triangle at A. A road connects towns B and C directly. Find the length of this road. Find the height of an equilateral triangle whose side measures 48 cm. 10. A cartoon measures 30 inches long, 4 inches wide and 12 inches high. What is the diagonal length of the box? Circle # Correct Percentage Score 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
10 Answer Keys Page 2  Independent Practice: 1 10 feet 2 48 inches 3 16 feet 4 12 feet feet meters meters feet feet inches 12 no inches miles feet 17 3, , feet feet Page 3  Independent Practice: 1 5 meters meters feet inches km 7 15 miles feet 9 35 inches inches meters 13 9 feet feet feet meters km inches 20 26, 168 inches Page 4  Home Work : cm feet m meters miles feet feet 9 waddle feet inches inches Page 5  Quiz : km units inches km feet feet 7 65 feet 8 17 miles cm inches
2.3 Maximum and Minimum Applications
Section.3 155.3 Maximum and Minimum Applications Maximizing (or minimizing) is an important technique used in various fields of study. In business, it is important to know how to find the maximum profit
More informationFactoring, Solving. Equations, and Problem Solving REVISED PAGES
05W4801AM1.qxd 8/19/08 8:45 PM Page 241 Factoring, Solving Equations, and Problem Solving 5 5.1 Factoring by Using the Distributive Property 5.2 Factoring the Difference of Two Squares 5.3 Factoring
More informationMATH 90 CHAPTER 6 Name:.
MATH 90 CHAPTER 6 Name:. 6.1 GCF and Factoring by Groups Need To Know Definitions How to factor by GCF How to factor by groups The Greatest Common Factor Factoring means to write a number as product. a
More informationSection 2.4 Law of Sines and Cosines
Section.4 Law of Sines and osines Oblique Triangle A triangle that is not a right triangle, either acute or obtuse. The measures of the three sides and the three angles of a triangle can be found if at
More information13. Write the decimal approximation of 9,000,001 9,000,000, rounded to three significant
æ If 3 + 4 = x, then x = 2 gold bar is a rectangular solid measuring 2 3 4 It is melted down, and three equal cubes are constructed from this gold What is the length of a side of each cube? 3 What is the
More informationFree PreAlgebra Lesson 55! page 1
Free PreAlgebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can
More informationBasic Math for the Small Public Water Systems Operator
Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the
More informationSection 2.3 Solving Right Triangle Trigonometry
Section.3 Solving Rigt Triangle Trigonometry Eample In te rigt triangle ABC, A = 40 and c = 1 cm. Find a, b, and B. sin 40 a a c 1 a 1sin 40 7.7cm cos 40 b c b 1 b 1cos40 9.cm A 40 1 b C B a B = 90  A
More informationSECTION 16 Quadratic Equations and Applications
58 Equations and Inequalities Supply the reasons in the proofs for the theorems stated in Problems 65 and 66. 65. Theorem: The complex numbers are commutative under addition. Proof: Let a bi and c di be
More information121 Representations of ThreeDimensional Figures
Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 121 Representations of ThreeDimensional Figures Use isometric dot paper to sketch each prism. 1. triangular
More informationReview of Intermediate Algebra Content
Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6
More informationIntroduction and Mathematical Concepts
CHAPTER 1 Introduction and Mathematical Concepts PREVIEW In this chapter you will be introduced to the physical units most frequently encountered in physics. After completion of the chapter you will be
More information(15.) To find the distance from point A to point B across. a river, a base line AC is extablished. AC is 495 meters
(15.) To find the distance from point A to point B across a river, a base line AC is extablished. AC is 495 meters long. Angles
More information9 Areas and Perimeters
9 Areas and Perimeters This is is our next key Geometry unit. In it we will recap some of the concepts we have met before. We will also begin to develop a more algebraic approach to finding areas and perimeters.
More informationTEST A CHAPTER 6, EQUATIONS, INEQUALITIES, PROBLEM SOLVING. 1. Factor x 25x + 6. 2. Factor x 24x  5.
TEST A CHAPTER 6, EQUATIONS, INEQUALITIES, PROBLEM SOLVING. Factor x 25x + 6. 2. Factor x 24x  5. 3. Solve: (x + 2)(x  3) = 0 x(x  3)(x + 4) = 0 4. Solve by factoring: x 2 + x + 2 = 0. 5. Solve by
More informationFactoring Polynomials
UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can
More informationFactoring and Applications
Factoring and Applications What is a factor? The Greatest Common Factor (GCF) To factor a number means to write it as a product (multiplication). Therefore, in the problem 48 3, 4 and 8 are called the
More informationPolynomial Degree and Finite Differences
CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial
More informationMany Word problems result in Quadratic equations that need to be solved. Some typical problems involve the following equations:
Many Word problems result in Quadratic equations that need to be solved. Some typical problems involve the following equations: Quadratic Equations form Parabolas: Typically there are two types of problems:
More information2.8 FUNCTIONS AND MATHEMATICAL MODELS
2.8 Functions and Mathematical Models 131 2.8 FUNCTIONS AND MATHEMATICAL MODELS At one time Conway would be making constant appeals to give him a year, and he would immediately respond with the date of
More informationFORMULA FOR FINDING THE SQUARE FEET OF A RECTANGLE L x W = A
UNIT I REAL ESTATE MATH AREA MEASUREMENTS FORMULA FOR FINDING THE SQUARE FEET OF A RECTANGLE L x W = A Where: A = Area L = Length W = Width If the length = 30 and the width = 20 20 x 30 = 600 Sq. Feet
More informationWarmUp Oct. 22. Daily Agenda:
Evaluate y = 2x 3x + 5 when x = 1, 0, and 2. Daily Agenda: Grade Assignment Go over Ch 3 Test; Retakes must be done by next Tuesday 5.1 notes / assignment Graphing Quadratic Functions 5.2 notes / assignment
More informationKeystone National Middle School Math Level 8 Placement Exam
Keystone National Middle School Math Level 8 Placement Exam 1) A cookie recipe calls for the following ingredients: 2) In the quadrilateral below, find the measurement in degrees for x? 1 ¼ cups flour
More informationFactor and Solve Polynomial Equations. In Chapter 4, you learned how to factor the following types of quadratic expressions.
5.4 Factor and Solve Polynomial Equations Before You factored and solved quadratic equations. Now You will factor and solve other polynomial equations. Why? So you can find dimensions of archaeological
More informationYOU CAN COUNT ON NUMBER LINES
Key Idea 2 Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and
More informationXV. Mathematics, Grade 10
XV. Mathematics, Grade 10 Grade 10 Mathematics Test The spring 2011 grade 10 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework
More information+ 4θ 4. We want to minimize this function, and we know that local minima occur when the derivative equals zero. Then consider
Math Xb Applications of Trig Derivatives 1. A woman at point A on the shore of a circular lake with radius 2 miles wants to arrive at the point C diametrically opposite A on the other side of the lake
More informationLIFE SCIENCE. Hoop House Construction for New Mexico: 12ft. x 40ft. Hoop House BRINGING TO YOUR HOME ECONOMICS COLLEGE OF AGRICULTURE AND
Hoop House Construction for New Mexico: 12ft. x 40ft. Hoop House COLLEGE OF AGRICULTURE AND HOME ECONOMICS BRINGING SCIENCE TO YOUR LIFE Hoop House Construction for New Mexico: 12ft. x 40ft. Hoop House
More informationTrigonometry WORKSHEETS
WORKSHEETS The worksheets available in this unit DO NOT constitute a course since no instructions or worked examples are offered, and there are far too many of them. They are offered here in the belief
More informationCollege of Charleston Math Meet 2008 Written Test Level 1
College of Charleston Math Meet 2008 Written Test Level 1 1. Three equal fractions, such as 3/6=7/14=29/58, use all nine digits 1, 2, 3, 4, 5, 6, 7, 8, 9 exactly one time. Using all digits exactly one
More informationFind the length of the arc on a circle of radius r intercepted by a central angle θ. Round to two decimal places.
SECTION.1 Simplify. 1. 7π π. 5π 6 + π Find the measure of the angle in degrees between the hour hand and the minute hand of a clock at the time shown. Measure the angle in the clockwise direction.. 1:0.
More informationA Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions
A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25
More informationSJO PW  Język angielski ogólnotechniczny, Poziom B2 Opracowanie: I. Zamecznik, M. Witczak, H. Maniecka, A. Hilgier,
GEOMETRY AND MEASUREMENT  Teacher s notes and key to tasks Introduction (5 minutes one week before the actual LESSON): 1. Elicit vocabulary connected with geometric figures ask the students (SS) to look
More informationAMC 10 Solutions Pamphlet TUESDAY, FEBRUARY 13, 2001 Sponsored by Mathematical Association of America University of Nebraska
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO AMERICAN MATHEMATICS COMPETITIONS nd Annual Mathematics Contest 10 AMC 10 Solutions Pamphlet TUESDAY, FEBRUARY 1, 001
More informationAnswer Key for the Review Packet for Exam #3
Answer Key for the Review Packet for Eam # Professor Danielle Benedetto Math MaMin Problems. Show that of all rectangles with a given area, the one with the smallest perimeter is a square. Diagram: y
More informationTRAINING AND EQUIPMENT MANUAL 304 LADDER PRACTICES 304.006 EXTENSION LADDERS EFFECTIVE: OCTOBER 2007
TRAINING AND EQUIPMENT MANUAL 304 LADDER PRACTICES 304.006 EXTENSION LADDERS EFFECTIVE: OCTOBER 2007 The Department utilizes 10foot, 14foot, 24foot, and 35foot extension ladders. Extension ladders
More informationLand Survey (Land of Plenty) Classroom Activity
Land Survey (Land of Plenty) Classroom Activity The Classroom Activity introduces students to the context of a performance task, so they are not disadvantaged in demonstrating the skills the task intends
More information72 Factoring by GCF. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1
72 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Simplify. 1. 2(w + 1) 2. 3x(x 2 4) 2w + 2 3x 3 12x Find the GCF of each pair of monomials. 3. 4h 2 and 6h 2h 4. 13p and 26p
More informationIt s time to have some fun!
WAKE UP YOUR BRAINS It s time to have some fun! We have put together some great ways to have fun working with math, reviewing math skills, and exploring math in the world all around you! OUR goal is for
More informationWarmUp 1. 1. What is the least common multiple of 6, 8 and 10?
WarmUp 1 1. What is the least common multiple of 6, 8 and 10? 2. A 16page booklet is made from a stack of four sheets of paper that is folded in half and then joined along the common fold. The 16 pages
More informationIrrigation Water Management: Training Manual No. 2  Elements of Topographic Surveying
Table of Contents Irrigation Water Management: Training Manual No. 2  Elements of Topographic Surveying by C. Brouwer International Institute for Land Reclamation and Improvement and A. Goffeau J. Plusjé
More informationAmerican Diploma Project
Student Name: American Diploma Project ALGEBRA l EndofCourse Eam PRACTICE TEST General Directions Today you will be taking an ADP Algebra I EndofCourse Practice Test. To complete this test, you will
More informationCHAPTER 7 TRAVERSE Section I. SELECTION OF TRAVERSE DEFINITION
CHAPTER 7 TRAVERSE Section I. SELECTION OF TRAVERSE DEFINITION A traverse is a series of straight lines called traverse legs. The surveyor uses them to connect a series of selected points called traverse
More informationThe Dance Lesson. A good dance lesson should contain some or all of the following:
The Dance Lesson The Primary School Curriculum says: Dance in education involves the child in creating, performing and appreciating movement as a means of expression and communication. Dance differs from
More informationStar and convex regular polyhedra by Origami.
Star and convex regular polyhedra by Origami. Build polyhedra by Origami.] Marcel Morales Alice Morales 2009 E D I T I O N M O R A L E S Polyhedron by Origami I) Table of convex regular Polyhedra... 4
More information( ) ( ) Math 0310 Final Exam Review. # Problem Section Answer. 1. Factor completely: 2. 2. Factor completely: 3. Factor completely:
Math 00 Final Eam Review # Problem Section Answer. Factor completely: 6y+. ( y+ ). Factor completely: y+ + y+ ( ) ( ). ( + )( y+ ). Factor completely: a b 6ay + by. ( a b)( y). Factor completely: 6. (
More informationAlgebra II Unit 1: Foundations of Functions 20142015. 27 2.2 Linear Equations Day 1. HW: Linear Equations WS 1. 3 Quiz 2.1, 2.2, and 2.
Algebra II Unit 1: Foundations of Functions 20142015 Aug 25 School Starts Class rules, etc 26 2.1 Relations and Functions HW: Relations and functions WS 27 2.2 Linear Equations Day 1 HW: Linear Equations
More informationPolynomials. Polynomials
Preview of Algebra 1 Polynomials 1A Introduction to Polynomials 11 Polynomials LAB Model Polynomials 1 Simplifying Polynomials 1B Polynomial Operations LAB Model Polynomial Addition 13 Adding Polynomials
More informationMathematics as Reasoning Students will use reasoning skills to determine the best method for maximizing area.
Title: A Pen for Penny Brief Overview: This unit is a reinforcement of the concepts of area and perimeter of rectangles. Methods for maximizing area while perimeter remains the same are also included.
More informationFORM 3 MATHEMATICS SCHEME C TIME: 30 minutes Non Calculator Paper INSTRUCTIONS TO CANDIDATES
DIRECTORATE FOR QUALITY AND STANDARDS IN EDUCATION Department for Curriculum Management and elearning Educational Assessment Unit Annual Examinations for Secondary Schools 2011 C FORM 3 MATHEMATICS SCHEME
More informationCOORDINATE GEOMETRY Mathematics 1 MM1G1a,b,c,d,e
Student Learning Map Unit 6 COORDINATE GEOMETRY Mathematics 1 MM1G1a,b,c,d,e Key Learning(s): Unit Essential Question(s): 1. Algebraic formulas can be used to find measures of distance on the coordinate
More informationSOLUTIONS TO HANDBOOK PROBLEMS
SOLUTIONS TO HNDBOOK PROBLEMS The solutions provided here are only possible solutions. It is very likely that you or your students will come up with additional and perhaps more elegant solutions. Happy
More informationSection 1.1. Introduction to R n
The Calculus of Functions of Several Variables Section. Introduction to R n Calculus is the study of functional relationships and how related quantities change with each other. In your first exposure to
More informationGraphing and Solving Nonlinear Inequalities
APPENDIX LESSON 1 Graphing and Solving Nonlinear Inequalities New Concepts A quadratic inequality in two variables can be written in four different forms y < a + b + c y a + b + c y > a + b + c y a + b
More informationApplied Mathematics. Level 7. Worldwide Interactive Network, Inc. 1000 Waterford Place, Kingston, TN 37763 888.717.9461
Applied Mathematics Level 7 Worldwide Interactive Network, Inc. 1000 Waterford Place, Kingston, TN 37763 888.717.9461 2008 Worldwide Interactive Network, Inc. All rights reserved. Copyright 1998 by Worldwide
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationKeystone National High School Placement Exam Math Level 1. Find the seventh term in the following sequence: 2, 6, 18, 54
1. Find the seventh term in the following sequence: 2, 6, 18, 54 2. Write a numerical expression for the verbal phrase. sixteen minus twelve divided by six Answer: b) 1458 Answer: d) 16 12 6 3. Evaluate
More informationChapter 3B  Vectors. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 3B  Vectors A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Vectors Surveyors use accurate measures of magnitudes and directions to
More informationSolving Simultaneous Equations and Matrices
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
More informationPossible Stage Two Mathematics Test Topics
Possible Stage Two Mathematics Test Topics The Stage Two Mathematics Test questions are designed to be answerable by a good problemsolver with a strong mathematics background. It is based mainly on material
More informationIn this section, you will develop a method to change a quadratic equation written as a sum into its product form (also called its factored form).
CHAPTER 8 In Chapter 4, you used a web to organize the connections you found between each of the different representations of lines. These connections enabled you to use any representation (such as a graph,
More information4 Trigonometry. 4.1 Squares and Triangles. Exercises. Worked Example 1. Solution
4 Trigonometr MEP Pupil Tet 4 4.1 Squares and Triangles triangle is a geometric shape with three sides and three angles. Some of the different tpes of triangles are described in this Unit. square is a
More informationChapter 4: The Concept of Area
Chapter 4: The Concept of Area Defining Area The area of a shape or object can be defined in everyday words as the amount of stuff needed to cover the shape. Common uses of the concept of area are finding
More informationWe start with the basic operations on polynomials, that is adding, subtracting, and multiplying.
R. Polnomials In this section we want to review all that we know about polnomials. We start with the basic operations on polnomials, that is adding, subtracting, and multipling. Recall, to add subtract
More informationPreAlgebra Exam Review Review for Part 2: You may use a calculator to solve these problems.
PreAlgebra Exam Review Review for Part 2: You may use a calculator to solve these problems. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More informationDOE FUNDAMENTALS HANDBOOK MATHEMATICS Volume 2 of 2
DOEHDBK1014/292 JUNE 1992 DOE FUNDAMENTALS HANDBOOK MATHEMATICS Volume 2 of 2 U.S. Department of Energy Washington, D.C. 20585 FSC6910 Distribution Statement A. Approved for public release; distribution
More informationSolutions to old Exam 1 problems
Solutions to old Exam 1 problems Hi students! I am putting this old version of my review for the first midterm review, place and time to be announced. Check for updates on the web site as to which sections
More informationFSCJ PERT. Florida State College at Jacksonville. assessment. and Certification Centers
FSCJ Florida State College at Jacksonville Assessment and Certification Centers PERT Postsecondary Education Readiness Test Study Guide for Mathematics Note: Pages through are a basic review. Pages forward
More informationTRIGONOMETRY FOR ANIMATION
TRIGONOMETRY FOR ANIMATION What is Trigonometry? Trigonometry is basically the study of triangles and the relationship of their sides and angles. For example, if you take any triangle and make one of the
More information85 Using the Distributive Property. Use the Distributive Property to factor each polynomial. 1. 21b 15a SOLUTION:
Use the Distributive Property to factor each polynomial. 1. 1b 15a The greatest common factor in each term is 3.. 14c + c The greatest common factor in each term is c. 3. 10g h + 9gh g h The greatest common
More informationALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form
ALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form Goal Graph quadratic functions. VOCABULARY Quadratic function A function that can be written in the standard form y = ax 2 + bx+ c where a 0 Parabola
More informationFree PreAlgebra Lesson 8 page 1
Free PreAlgebra Lesson 8 page 1 Lesson 8 Factor Pairs Measuring more accurately requires breaking our inches into fractions of an inch, little parts smaller than a whole inch. You can think ahead and
More informationUnit 1  Radian and Degree Measure Classwork
Unit 1  Radian and Degree Measure Classwork Definitions to know: Trigonometry triangle measurement Initial side, terminal side  starting and ending Position of the ray Standard position origin if the
More information83 Dot Products and Vector Projections
83 Dot Products and Vector Projections Find the dot product of u and v Then determine if u and v are orthogonal 1u =, u and v are not orthogonal 2u = 3u =, u and v are not orthogonal 6u = 11i + 7j; v
More informationWarning! Construction Zone: Building Solids from Nets
Brief Overview: Warning! Construction Zone: Building Solids from Nets In this unit the students will be examining and defining attributes of solids and their nets. The students will be expected to have
More information1. What data might a car leave behind at the scene of an accident?
Bellwork 21015 It takes 8,460 bolts to assemble an automobile, and one nut to scatter it all over the road. Author Unknown 1. What data might a car leave behind at the scene of an accident? 1 5 9 ACCIDENT
More informationMath BINGO MOST POPULAR. Do you have the lucky card? B I N G O
MOST POPULAR Math BINGO Do you have the lucky card? Your club members will love this MATHCOUNTS reboot of a classic game. With the perfect mix of luck and skill, this is a game that can be enjoyed by students
More informationBlue Pelican Alg II First Semester
Blue Pelican Alg II First Semester Teacher Version 1.01 Copyright 2009 by Charles E. Cook; Refugio, Tx (All rights reserved) Alg II Syllabus (First Semester) Unit 1: Solving linear equations and inequalities
More informationNatural Disaster Recovery and Quadrilaterals
Natural Disaster Recovery and Quadrilaterals I. UNIT OVERVIEW & PURPOSE: In this unit, students will apply their knowledge of quadrilaterals to solve mathematics problems concerning a tornado that struck
More informationEXERCISE INSTRUCTIONS 1
EXERCISE INSTRUCTIONS 1 Contents ANKLE TOUCHES... 4 BACK EXTENSIONS... 4 BACK REVERSE FLYES... 4 BALL ROLL... 4 BASKETBALL SQUATS... 4 BEAR CRAWL... 4 BICEP CURL (Resistance Band)... 4 BOXING JABS... 5
More informationLesson 1: Multiplying and Factoring Polynomial Expressions
Lesson 1: Multiplying and Factoring Polynomial Expressions Student Outcomes Students use the distributive property to multiply a monomial by a polynomial and understand that factoring reverses the multiplication
More informationIOWA EndofCourse Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa.
IOWA EndofCourse Assessment Programs Released Items Copyright 2010 by The University of Iowa. ALGEBRA I 1 Sally works as a car salesperson and earns a monthly salary of $2,000. She also earns $500 for
More informationTopic: Special Products and Factors Subtopic: Rules on finding factors of polynomials
Quarter I: Special Products and Factors and Quadratic Equations Topic: Special Products and Factors Subtopic: Rules on finding factors of polynomials Time Frame: 20 days Time Frame: 3 days Content Standard:
More informationSurfa Surf ce ace Area Area What You Will Learn
Surface Area A skyline is a view of the outline of buildings or mountains shown on the horizon. You can see skylines during the day or at night, all over the world. Many cities have beautiful skylines.
More informationWE OFTEN BELIEVE artists
Analyzing the Residential Landscape WE OFTEN BELIEVE artists have the liberty to create anything they want. That is sometimes true, but many artists are hired to do particular types of work. Landscape
More informationIntroduction Assignment
PRECALCULUS 11 Introduction Assignment Welcome to PREC 11! This assignment will help you review some topics from a previous math course and introduce you to some of the topics that you ll be studying
More informationUnit 5 Area. What Is Area?
Trainer/Instructor Notes: Area What Is Area? Unit 5 Area What Is Area? Overview: Objective: Participants determine the area of a rectangle by counting the number of square units needed to cover the region.
More informationCardiac Rehab Program: Stretching Exercises
Cardiac Rehab Program: Stretching Exercises Walk around the room, step side to side, ride a bike or walk on a treadmill for at least 5 minutes to warm up before doing these stretches. Stretch warm muscles
More informationJust want the standards alone? You can find the standards alone at www.corestandards.org. 7 th Grade Mathematics Unpacked Content February, 2012
7 th Grade Mathematics Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 201213 School Year. This document is designed to help North Carolina
More information4.3 Least Squares Approximations
18 Chapter. Orthogonality.3 Least Squares Approximations It often happens that Ax D b has no solution. The usual reason is: too many equations. The matrix has more rows than columns. There are more equations
More informationSPECIAL PRODUCTS AND FACTORS
CHAPTER 442 11 CHAPTER TABLE OF CONTENTS 111 Factors and Factoring 112 Common Monomial Factors 113 The Square of a Monomial 114 Multiplying the Sum and the Difference of Two Terms 115 Factoring the
More informationJUST THE MATHS UNIT NUMBER 8.5. VECTORS 5 (Vector equations of straight lines) A.J.Hobson
JUST THE MATHS UNIT NUMBER 8.5 VECTORS 5 (Vector equations of straight lines) by A.J.Hobson 8.5.1 Introduction 8.5. The straight line passing through a given point and parallel to a given vector 8.5.3
More informationWhy are Word Problems so Darned Hard? Alan H. Schoenfeld University of California Berkeley, CA, USA Alans@Berkeley.edu
Why are Word Problems so Darned Hard? Alan H. Schoenfeld University of California Berkeley, CA, USA Alans@Berkeley.edu Preface: Why middle school math is important My friend complains to a hospital doctor
More informationA.3. Polynomials and Factoring. Polynomials. What you should learn. Definition of a Polynomial in x. Why you should learn it
Appendi A.3 Polynomials and Factoring A23 A.3 Polynomials and Factoring What you should learn Write polynomials in standard form. Add,subtract,and multiply polynomials. Use special products to multiply
More informationPreparing for the Washington State Criminal Justice Training Commission Physical Ability Test
Preparing for the Washington State Criminal Justice Training Commission Physical Ability Test Whereas many training routines can be used to improve performance in the Physical Ability Test (PAT), participants
More information4/27/2010 ALGEBRA 1 CHAPTER 8 FACTORING. PAR Activities Cara Boening
4/27/2010 ALGEBRA 1 CHAPTER 8 FACTORING PAR Activities Cara Boening Table of Contents Preparation Strategies... 3 Scavenger Hunt... 4 Graphic Organizer Chapter 8.... 6 Word Inventory... 8 TEASE... 12 Anticipation
More informationFACTORING OUT COMMON FACTORS
278 (6 2) Chapter 6 Factoring 6.1 FACTORING OUT COMMON FACTORS In this section Prime Factorization of Integers Greatest Common Factor Finding the Greatest Common Factor for Monomials Factoring Out the
More informationGeoGebra. 10 lessons. Gerrit Stols
GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter
More informationExample SECTION 131. XAXIS  the horizontal number line. YAXIS  the vertical number line ORIGIN  the point where the xaxis and yaxis cross
CHAPTER 13 SECTION 131 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants XAXIS  the horizontal
More informationThe following table lists metric prefixes that come up frequently in physics. Learning these prefixes will help you in the various exercises.
Chapter 0 Solutions Circles Learning Goal: To calculate the circumference or area of a circle Every day, we see circles in compact disks, coins, and wheels, just to name a few examples Circles are also
More information