Geometry Pre-Unit 1 Intro: Area, Perimeter, Pythagorean Theorem, Square Roots, & Quadratics. P-1 Square Roots and SRF
|
|
- Mabel Jacobs
- 6 years ago
- Views:
Transcription
1 Geometry Pre-Unit 1 Intro: Area, Perimeter, Pythagorean Theorem, Square Roots, & Quadratics P-1 Square Roots and SRF Square number the product of a number multiplied by itself. 1 * 1 = 1 1 is a square number * = 4 4 is a square number 3 * 3 = 9 9 is a square number List the first twelve square numbers:,,,,,,,,,,, Square Root a number that when multiplied by itself is a square number. 4 is the square root of is the square root of is the square root of 34 5 is the square root of 65 What are the square roots of the following numbers? A) 5 B) 49 C) 81 D) 11 E) 144 F) 576 G) 900 The following symbol (radical) is used for square roots: Examples: When you see that symbol it means find the square root of the number. 1
2 Simplest Radical form a radical that is not a perfect square but has been reduced to remove all squares from the radicand. Simplest radical form is a way of breaking up a radicand into primes then square rooting. For each pair of primes in the final breakdown, place one digit in front of the radical as a product and the radicand in the root is multiplied back together in the final result Examples Multiplying Radicals - Multiply what is outside the radical together and multiply what is under the radical together. Examples
3 Like roots roots with the same radicand P- Adding and Subtracting like roots x and x can be added together to make x, 3y and 3y can be added together to make 6y and in the same way like roots can added together. Examples: 3
4 P-3 Pythagorean Theorem Pythagorean Theorem- The sides of a right triangle are related according by the equation: a + b = c This is significant because you can find the third side of a right triangle if given the other two sides. a and b are the short sides of the triangle called legs c is the long side called the hypotenuse *c is the side not adjacent to the right angle Example 1: Find the length of the hypotenuse of the right triangle given both legs. Leg = 8in Leg = 6in Example : Find the missing leg of the right triangle given the length of the hypotenuse and a leg. Hypotenuse = 17 Leg = 13in 4
5 Example 3: Find the length of the hypotenuse given the legs are 6 in. Step 1: Find the hypotenuse using the Pythagorean Theorem 5
6 P-4 Midpoint and Distance Formulas Midpoint formula: Distance Formula: Find the midpoint of A(-1, 7) and B(4, 13) is calculated using the midpoint formula: The distance between of A(-1, 7) and B(4, 13) is calculated using the distance formula: Class Activity: The following is a mathematical proof Given points: A(, 6) and B(18, 14) Find the midpoint C and prove that it bisects. 6
7 P-5 Perimeter Perimeter the sum of the lengths of the sides of a polygon (shape) The perimeter of the square at right would be: 1.5in + 1.5in +1.5in + 1.5in = 6in 1.5in The formula for perimeter of a square is P = 4s P stands for perimeter and S stands for side P = 4(1.5) = 6in What are the perimeters of the following squares? A) 3ft on a side B) seven halves inches on a side C).5 yd on a side D) m on a side The formula for perimeter of a rectangle is P = b + h h stands for height and b stands for base b The perimeter of the rectangle is.5 ft h P = (3.ft) + (.5ft) = = 11.4ft 3. ft What would be the perimeter of the following rectangles? Draw a picture first A) base = 3 in B) base = ft C) base = 5.6m height = 8 in height = 3.7 ft height = 3m Extension: The base of the Great Pyramid in Egypt is a square measuring 756ft per side. What is the perimeter of the base of the pyramid? 7
8 Equilateral Triangle A triangle with all side lengths congruent. What is the perimeter of the figure at right? P = 3(0.5) = 1.5ft 0.5ft What would be the perimeter of an equilateral triangle with: A) side length w B) side length C) side length 14km Isosceles Triangle A triangle with two congruent sides. The triangle at right is isosceles. The congruent sides are called legs. The non-congruent side is called the base. What would the perimeter be of an isosceles triangle with the following measurements? A) legs 4in, base 5in B) legs 1.5ft, base 1ft C) legs ft, base 5.4ft 8
9 P-6 Circumference & Area Circumference the perimeter of a circle Area the number of square units that it would take to fill an object. Formula s: C = πr or C = dπ A = πr π is about 3.14 Radius half the length of the diameter (r) r = d Diameter the length across a circle through the center (d) A 4ft A 1ft The diameter is 4ft The radius is 1ft C = dπ C = πr A = πr C = 4π 1.56ft C = π 6.8ft A = π 3.14 ft Try these: Find the circumference and area of the circles below given the information: A) radius = 3m B) diameter = 7mi C) radius = in Compound Shapes A shape that contains more than one polygon. The perimeter of this shape is a combination of three sides of a rectangle and a semicircle. Use 3.14 for π Perimeter of the three sides: Perimeter of the semicircle: Sum of the perimeters: 1.3 ft ft 9
10 P-7 Area of Polygons Area the number of square units that it would take to fill an object. Rectangle: A = bh Square: A = s base = 14km side = 1.5cm A = (3)(14) = 4km height = 3km A = 1.5 =.5cm The area of the rectangle is 4km. The area of the square is 1.5cm. A) Rectangle: b = 4in, h =.5in B) Square s = 1.mi C) Rectangle: b = ft, h = 3.4ft Triangle: A = 0.5 bh h h h b b b Acute triangle Right triangle Obtuse triangle All angles less than 90 One angle exactly 90 One angle larger than 90 Height is inside Height is the edge of the right angle Height is outside the triangle 10
11 Examples: 3cm 3.1in 1.1ft 4cm 5in.8ft Parallelogram: A = bh b h h b NOTE: The base and height must meet at a perpendicular. 3 in 4ft 4in 5.1ft Trapezoid: A = 0.5h(b1+b) It does not matter which base you label as b1 or b h 11
12 .5 ft 8ft A = 6 ft 3 ft 34ft A = 48 ft Rhombus: A= 0.5(d1d) d=diagonal Kite A= 0.5(d1d) Solve for the Area of the rhombus if A) JL = 3cm and MK = 6cm B) JZ = 7, LZ = 7, MZ = 5, and KZ = 5 J K Z M L Solve for the Area of the kite if A) WA = 1ft and HT = 34ft B) HS = 4, TS = 16, WS = 5 and AS = 5ft H W S A T 1
13 If each side of the pentagon at right is congruent and the length of one side is 6m. The apothem is 3.4m. What is the Area of the regular polygon? Regular Polygon: P = Perimeter A = 0.5 ap a = apothem \ a) Find the Area of a regular octagon with the length one side is 10 cm and the apothem is 1.1 cm? b) Find the Area of a regular heptagon with the length one side is 4 cm and the apothem is 3.1 cm? 13
14 P-8 Using the Quadratic Formula Quadratic Formula If ax bx c a 0, 0, and b 4ac 0, then x b b 4ac Solve by factoring: a Use the quadratic formula to solve: x 6x 8 0 x 7x n 8n 0 3x x 3 0 Solve the quadratic by factoring, by taking the square root, completing the square, or the quadratic formula. n 4n
Chapter 7 Sect. 2. A pythagorean triple is a set of three nonzero whole numbers a, b, and c, that satisfy the equation a 2 + b 2 = c 2.
Chapter 7 Sect. 2 The well-known right triangle relationship called the Pythagorean Theorem is named for Pythagoras, a Greek mathematician who lived in the sixth century b.c. We now know that the Babylonians,
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 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 informationAlgebra I. Exponents and Polynomials. Name
Algebra I Exponents and Polynomials Name 1 2 UNIT SELF-TEST QUESTIONS The Unit Organizer #6 2 LAST UNIT /Experience NAME 4 BIGGER PICTURE DATE Operations with Numbers and Variables 1 CURRENT CURRENT UNIT
More informationUnit 4-Review. Part 1- Triangle Theorems and Rules
Unit 4-Review - Triangle Theorems and Rules Name of Theorem or relationship In words/ Symbols Diagrams/ Hints/ Techniques 1. Side angle relationship 2. Triangle inequality Theorem 3. Pythagorean Theorem
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 informationNew Rochelle High School Geometry Summer Assignment
NAME - New Rochelle High School Geometry Summer Assignment To all Geometry students, This assignment will help you refresh some of the necessary math skills you will need to be successful in Geometry and
More informationName Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement.
Chapter 6 Review Geometry Name Score Period Date Solve the proportion. 3 5 1. = m 1 3m 4 m = 2. 12 n = n 3 n = Find the geometric mean of the two numbers. Copy and complete the statement. 7 x 7? 3. 12
More informationGlossary. Glossary 981. Hawkes Learning Systems. All rights reserved.
A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Addends The numbers being added in an addition problem Addition principle
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 informationGeometry Honors Summer Packet
Geometry Honors Summer Packet Hello Student, First off, welcome to Geometry Honors! In the fall, we will embark on an eciting mission together to eplore the area (no pun intended) of geometry. This packet
More informationClasswork 8.1. Perform the indicated operation and simplify each as much as possible. 1) 24 2) ) 54w y 11) wy 6) 5 9.
- 7 - Classwork 8.1 Name Perform the indicated operation and simplify each as much as possible. 1) 4 7) 16+ 5 49 ) 5 4 8) 11 6 81 ) 5 4x 9) 9 x + 49x 4) 75w 10) 6 5 54w y 5) 80wy 11) 15 6 6) 5 9 1) 15x
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 informationresources Symbols < is less than > is greater than is less than or equal to is greater than or equal to = is equal to is not equal to
Symbols < is less than > is greater than is less than or equal to is greater than or equal to resources = is equal to is not equal to is approximately equal to similar a absolute value: = ; - = (x, y)
More informationGeometry Unit 8 - Notes Perimeter and Area
Geometry Unit 8 - Notes Perimeter and Area Syllabus Objective: 8. - The student will formulate strategies for finding the perimeter or area of various geometric figures. Review terms: ) area ) perimeter
More informationGeometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems
Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary
More information221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM
Math Refresher Session 3 1 Area, Perimeter, and Volume Problems Area, Perimeter, and Volume 301. Formula Problems. Here, you are given certain data about one or more geometric figures, and you are asked
More informationAlgebra 1B. Unit 9. Algebraic Roots and Radicals. Student Reading Guide. and. Practice Problems
Name: Date: Period: Algebra 1B Unit 9 Algebraic Roots and Radicals Student Reading Guide and Practice Problems Contents Page Number Lesson 1: Simplifying Non-Perfect Square Radicands 2 Lesson 2: Radical
More informationUsing Isosceles and Equilateral Triangles
Geometry Unit 4: Intro to Triangles Name Day 2: Isosceles, Equilateral, and Sum of Triangles Notes Block Date Today, we will understand isosceles and equilateral triangles And you will be able to find
More informationGlossary. Glossary Hawkes Learning Systems. All rights reserved.
A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Acute triangle A triangle in which all three angles are acute Addends The
More information17. The length of a diagonal of a square is 16 inches. What is its perimeter? a. 8 2 in. b in. c in. d in. e in.
Geometry 2 nd Semester Final Review Name: 1. Pentagon FGHIJ pentagon. 2. Find the scale factor of FGHIJ to KLMNO. 3. Find x. 4. Find y. 5. Find z. 6. Find the scale factor of ABCD to EFGD. 7. Find the
More information02)
GRE / GMATmath,! abscissa, scalene, intercept, markup, such that, break even. abscissa. (4, 2) 4abscissa, 2ordinate absolute value acre add adjacent angles altitude ; angle () acute angle (90 ) right angle
More informationInteger (positive or negative whole numbers or zero) arithmetic
Integer (positive or negative whole numbers or zero) arithmetic The number line helps to visualize the process. The exercises below include the answers but see if you agree with them and if not try to
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 informationYear 1 - What I Should Know by Heart
Year 1 - What I Should Know by Heart Count in 1 s forward and backwards from 0 to 150, beginning from any number. Count in multiples of 2, 5 and 10 up to 100. Recognise odd and even numbers. Know 1 st,
More informationGeometry Summer Assignment
2018-2019 Geometry Summer Assignment You must show all work to earn full credit. This assignment will be due Friday, August 24, 2018. It will be worth 50 points. All of these skills are necessary to be
More informationAlgebra I Part B. Help Pages & Who Knows
Algebra I Part B & Who Knows 83 Vocabulary General Absolute Value the distance between a number,, and zero on a number line; written as. Eample: 5 = 5 reads The absolute value of 5 is 5. -7 = 7 reads The
More informationVirginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning
BUI L T F O VIR R G INIA 2014 2015 Virginia -Specific Learning Pathways Grades 6-Algebra I: Standards of Learning Table of Contents Grade 6...3 Grade 7...6 Grade 8...9 Algebra I... 11 Grade 6 Virginia
More informationSkills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson.1 Name Date Get Radical or (Be)! Radicals and the Pythagorean Theorem Vocabulary Write the term that best completes each statement. 1. An expression that includes
More informationName: Class: Date: 5. If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28. a. True b.
Indicate whether the statement is true or false. 1. If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square. 2. If M and N are midpoints of sides and of, then. 3. The
More information~ 1 ~ Geometry 2 nd Semester Review Find the value for the variable for each of the following situations
Geometry nd Semester Review 018 Find the value for the variable for each of the following situations. 7. 400 m 1. 7 8. y. 8.9 cm 0 0 9.. 19 6 60 1 11 10. 45 4. 58 5 11. 5. 11 6. 18 1 slide 4.1 meters long
More informationGeometry Cumulative Review
Geometry Cumulative Review Name 1. Find a pattern for the sequence. Use the pattern to show the next term. 1, 3, 9, 27,... A. 81 B. 45 C. 41 D. 36 2. If EG = 42, find the value of y. A. 5 B. C. 6 D. 7
More informationArea Formulas. Linear
Math Vocabulary and Formulas Approximate Area Arithmetic Sequences Average Rate of Change Axis of Symmetry Base Behavior of the Graph Bell Curve Bi-annually(with Compound Interest) Binomials Boundary Lines
More informationBasic Math. Curriculum (358 topics additional topics)
Basic Math This course covers the topics outlined below and is available for use with integrated, interactive ebooks. You can customize the scope and sequence of this course to meet your curricular needs.
More informationReteaching , or 37.5% 360. Geometric Probability. Name Date Class
Name ate lass Reteaching Geometric Probability INV 6 You have calculated probabilities of events that occur when coins are tossed and number cubes are rolled. Now you will learn about geometric probability.
More informationMath Glossary. Version September 1, Next release: On or before September 30, for the latest version.
Math Glossary Version 0.1.1 September 1, 2003 Next release: On or before September 30, 2003. E-mail edu@ezlink.com for the latest version. Copyright 2003 by Brad Jolly All Rights Reserved Types of Numbers
More informationAnswer Explanations for: ACT June 2012, Form 70C
Answer Explanations for: ACT June 2012, Form 70C Mathematics 1) C) A mean is a regular average and can be found using the following formula: (average of set) = (sum of items in set)/(number of items in
More information8 Right Triangle Trigonometry
www.ck12.org CHAPTER 8 Right Triangle Trigonometry Chapter Outline 8.1 THE PYTHAGOREAN THEOREM 8.2 CONVERSE OF THE PYTHAGOREAN THEOREM 8.3 USING SIMILAR RIGHT TRIANGLES 8.4 SPECIAL RIGHT TRIANGLES 8.5
More information9-12 Mathematics Vertical Alignment ( )
Algebra I Algebra II Geometry Pre- Calculus U1: translate between words and algebra -add and subtract real numbers -multiply and divide real numbers -evaluate containing exponents -evaluate containing
More informationPre-Algebra (7) B Mathematics
Course Overview Students will develop skills in using variables, evaluating algebraic expressions by the use of the order of operations, solving equations and inequalities, graphing linear equations, functions
More informationCorrelation of 2012 Texas Essential Knowledge and Skills (TEKS) for Algebra I and Geometry to Moving with Math SUMS Moving with Math SUMS Algebra 1
Correlation of 2012 Texas Essential Knowledge and Skills (TEKS) for Algebra I and Geometry to Moving with Math SUMS Moving with Math SUMS Algebra 1 ALGEBRA I A.1 Mathematical process standards. The student
More informationUNIT 6. BELL WORK: Draw 3 different sized circles, 1 must be at LEAST 15cm across! Cut out each circle. The Circle
UNIT 6 BELL WORK: Draw 3 different sized circles, 1 must be at LEAST 15cm across! Cut out each circle The Circle 1 Questions How are perimeter and area related? How are the areas of polygons and circles
More informationThanks for downloading this product from Time Flies!
Thanks for downloading this product from Time Flies! I hope you enjoy using this product. Follow me at my TpT store! My Store: https://www.teacherspayteachers.com/store/time-flies 2018 Time Flies. All
More informationRight Triangles
30 60 90 Right Triangles The 30-60 -90 triangle is another special triangle. Like the 45-45 -90 triangle, properties of the 30-60 -90 triangle can be used to find missing measures of a triangle if the
More informationAlgebra II/Geometry Curriculum Guide Dunmore School District Dunmore, PA
Algebra II/Geometry Dunmore School District Dunmore, PA Algebra II/Geometry Prerequisite: Successful completion of Algebra 1 Part 2 K Algebra II/Geometry is intended for students who have successfully
More informationPrep for the CSU ELM
Prep for the CSU ELM This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular
More informationGrade Demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts.
Unit 1 Number Theory 1 a B Find the prime factorization of numbers (Lesson 1.9) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 1b BD Rename numbers written in exponential
More informationPre Algebra and Introductory Algebra
Pre Algebra and Introductory Algebra This course covers the topics outlined below and is available for use with integrated, interactive ebooks. You can customize the scope and sequence of this course to
More informationGeometry Final Exam Review
Name: Date: Period: Geometry Final Exam Review 1. Fill in the flow chart below with the properties that belong to each polygon. 2. Find the measure of each numbered angle: 3. Find the value of x 4. Calculate
More informationContent Guidelines Overview
Content Guidelines Overview The Pearson Video Challenge is open to all students, but all video submissions must relate to set of predetermined curriculum areas and topics. In the following pages the selected
More informationCircle Theorems. Angles at the circumference are equal. The angle in a semi-circle is x The angle at the centre. Cyclic Quadrilateral
The angle in a semi-circle is 90 0 Angles at the circumference are equal. A B They must come from the same arc. Look out for a diameter. 2x Cyclic Quadrilateral Opposite angles add up to 180 0 A They must
More informationSect Formulas and Applications of Geometry:
72 Sect 2.6 - Formulas and Applications of Geometry: Concept # Solving Literal Equations for a particular variable. Now, we will examine solving formulas for a particular variable. Sometimes it is useful
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MGF 1106 Exam #3 Review Sheet Chapters 8-9 Fill in the missing value. 1) 816 mm = cm 2) 54.96 m = km 3) 492 L = ml 4) 800 mg = kg 5) 25 kg = mg Arrange the quantities in order from smallest to largest.
More informationAppendices. Appendix A.1: Factoring Polynomials. Techniques for Factoring Trinomials Factorability Test for Trinomials:
APPENDICES Appendices Appendi A.1: Factoring Polynomials Techniques for Factoring Trinomials Techniques for Factoring Trinomials Factorability Test for Trinomials: Eample: Solution: 696 APPENDIX A.1 Factoring
More informationCorrelation of Manitoba Curriculum to Pearson Foundations and Pre-calculus Mathematics 10
Measurement General Outcome: Develop spatial sense and proportional reasoning. 10I.M.1. Solve problems that involve linear measurement, using: SI and imperial units of measure estimation strategies measurement
More informationMath Contest, Fall 2017 BC EXAM , z =
Math Contest, Fall 017 BC EXAM 1. List x, y, z in order from smallest to largest fraction: x = 111110 111111, y = 1 3, z = 333331 333334 Consider 1 x = 1 111111, 1 y = thus 1 x > 1 z > 1 y, and so x
More informationApplications Using Factoring Polynomials
Applications Using Factoring Polynomials This section will discuss applications involving the area of a rectangle, consecutive integers, and right triangles. Recall the steps that will help to translate
More information1 st Preparatory. Part (1)
Part (1) (1) omplete: 1) The square is a rectangle in which. 2) in a parallelogram in which m ( ) = 60, then m ( ) =. 3) The sum of measures of the angles of the quadrilateral equals. 4) The ray drawn
More informationKCATM Geometry Group Test
KCATM Geometry Group Test Group name Choose the best answer from A, B, C, or D 1. A pole-vaulter uses a 15-foot-long pole. She grips the pole so that the segment below her left hand is twice the length
More informationFor math conventions used on the GRE, refer to this link:
GRE Review ISU Student Success Center Quantitative Workshop One Quantitative Section: Overview Your test will include either two or three 35-minute quantitative sections. There will be 20 questions in
More informationAnswer Key. 7.1 Tangent Ratio. Chapter 7 Trigonometry. CK-12 Geometry Honors Concepts 1. Answers
7.1 Tangent Ratio 1. Right triangles with 40 angles have two pairs of congruent angles and therefore are similar. This means that the ratio of the opposite leg to adjacent leg is constant for all 40 right
More informationCalifornia 5 th Grade Standards / Excel Math Correlation by Lesson Number
(Activity) L1 L2 L3 Excel Math Objective Recognizing numbers less than a million given in words or place value; recognizing addition and subtraction fact families; subtracting 2 threedigit numbers with
More informationFinal Exam - Math 201
Name: Final Exam - Math 201 Instructions: There are 14 problems on this exam, all with an equal weight of 20 points. Work any of the problems you like in any order you prefer. Indicate the 10 you wish
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 informationIntegrated Mathematics II
Integrated Mathematics II This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet
More information8-2 The Pythagorean Theorem and Its Converse. Find x. 27. SOLUTION: The triangle with the side lengths 9, 12, and x form a right triangle.
Find x. 27. The triangle with the side lengths 9, 12, and x form a right triangle. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
More informationBig Ideas: determine an approximate value of a radical expression using a variety of methods. REVIEW Radicals
Big Ideas: determine an approximate value of a radical expression using a variety of methods. REVIEW N.RN. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
More informationCourse Readiness and Skills Review Handbook (Topics 1-10, 17) (240 topics, due. on 09/11/2015) Course Readiness (55 topics)
Course Name: Gr. 8 Fall 2015 Course Code: C6HNH-TEK9E ALEKS Course: Middle School Math Course 3 Instructor: Mr. Fernando Course Dates: Begin: 08/31/2015 End: 06/17/2016 Course Content: 642 Topics (637
More informationChapter 10. Right Triangles
Chapter 10 Right Triangles If we looked at enough right triangles and experimented a little, we might eventually begin to notice some relationships developing. For instance, if I were to construct squares
More informationCorrelation of WNCP Curriculum to Pearson Foundations and Pre-calculus Mathematics 10
Measurement General Outcome: Develop spatial sense and proportional reasoning. 1. Solve problems that involve linear measurement, using: SI and imperial units of measure estimation strategies measurement
More informationKansas City Area Teachers of Mathematics 2018 KCATM Math Competition. GEOMETRY and MEASUREMENT GRADE 7-8
Kansas City Area Teachers of Mathematics 2018 KCATM Math Competition INSTRUCTIONS GEOMETRY and MEASUREMENT GRADE 7-8 Do not open this booklet until instructed to do so. Time limit: 20 minutes Mark your
More informationPractice Test Student Answer Document
Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
More informationPreliminary chapter: Review of previous coursework. Objectives
Preliminary chapter: Review of previous coursework Objectives By the end of this chapter the student should be able to recall, from Books 1 and 2 of New General Mathematics, the facts and methods that
More informationCommon Core Edition Table of Contents
Common Core Edition Table of Contents ALGEBRA 1 Chapter 1 Foundations for Algebra 1-1 Variables and Expressions 1-2 Order of Operations and Evaluating Expressions 1-3 Real Numbers and the Number Line 1-4
More informationSummer Packet Pre-AP Algebra
Name: (5/11/17) Summer Packet Pre-AP Algebra 1-2018-19 To receive credit all work must be shown. There will be a test the first week back from summer on this packet. Any work done on additional paper must
More informationOBJECTIVES UNIT 1. Lesson 1.0
OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint
More informationDue to the detail of some problems, print the contests using a normal or high quality setting.
General Contest Guidelines: Keep the contests secure. Discussion about contest questions is not permitted prior to giving the contest. Due to the detail of some problems, print the contests using a normal
More informationGeometry: Hutschenreuter Semester II. Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH!
Geometry: Hutschenreuter Semester II Review B Name Period Date Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH! 1. A parallelogram has a diagonal of 41 cm and side
More informationCN#5 Objectives 5/11/ I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed.
CN#5 Objectives I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed. When the dimensions of a figure are changed proportionally, the figure will
More informationMCA/GRAD Formula Review Packet
MCA/GRAD Formula Review Packet 1 2 3 4 5 6 The MCA-II / BHS 2 Math Plan GRAD Page 1 of 16 Portions Copyright 2005 by Claude Paradis 8 9 10 12 11 13 14 15 16 1 18 19 20 21 The MCA-II / BHS 2 Math Plan GRAD
More information10.5 Areas of Circles and Sectors
10.5. Areas of Circles and Sectors www.ck12.org 10.5 Areas of Circles and Sectors Learning Objectives Find the area of circles, sectors, and segments. Review Queue Find the area of the shaded region in
More informationLevel 1: Simplifying (Reducing) Radicals: 1 1 = 1 = 2 2 = 4 = 3 3 = 9 = 4 4 = 16 = 5 5 = 25 = 6 6 = 36 = 7 7 = 49 =
Name Period Date Unit 5:Special Right Triangles and TrigonometryNotes Packet #1 Section 7.2/7.3: Radicals, Pythagorean Theorem, Special Right Triangles (PA) CRS NCP 24-27 Work with squares and square roots
More information1.) Determine whether the following numbers could be the sides of a right triangle. Show your work.
4Unit 2 review Version 1 Name: Date: 1.) Determine whether the following numbers could be the sides of a right triangle. Show your work. a. 7, 25, 19 b. 17, 15, 8 2.) What is the approximate length of
More informationCourse 2 Benchmark Test Third Quarter
Course 2 Benchmark Test Third Quarter 1. Suppose the length of each side of a square is increased by 5 feet. If the perimeter of the square is now 56 feet, what were the original side lengths of the square?
More information0609ge. Geometry Regents Exam AB DE, A D, and B E.
0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible
More information2009 Math Olympics Level II Solutions
Saginaw Valley State University 009 Math Olympics Level II Solutions 1. f (x) is a degree three monic polynomial (leading coefficient is 1) such that f (0) 3, f (1) 5 and f () 11. What is f (5)? (a) 7
More informationHistogram, cumulative frequency, frequency, 676 Horizontal number line, 6 Hypotenuse, 263, 301, 307
INDEX A Abscissa, 76 Absolute value, 6 7, 55 Absolute value function, 382 386 transformations of, reflection, 386 scaling, 386 translation, 385 386 Accuracy, 31 Acute angle, 249 Acute triangle, 263 Addition,
More informationBIG Ideas. Assessment Teacher Resources Standards
Course Name: Unit: Introductory Time Line: 2 weeks Students will be able to simplify expressions. 1. Real Life Problems Solve problems using the four-step plan. Identify and use problemsolving strategies.
More informationMath 6 Extended Prince William County Schools Pacing Guide (Crosswalk)
Math 6 Extended Prince William County Schools Pacing Guide 2017-2018 (Crosswalk) Teacher focus groups have assigned a given number of days to each unit based on their experiences and knowledge of the curriculum.
More informationName Geometry Common Core Regents Review Packet - 3. Topic 1 : Equation of a circle
Name Geometry Common Core Regents Review Packet - 3 Topic 1 : Equation of a circle Equation with center (0,0) and radius r Equation with center (h,k) and radius r ( ) ( ) 1. The endpoints of a diameter
More informationWITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5
May 06 VIRGINIA MATHEMATICS STANDARDS OF LEARNING CORRELATED TO MOVING WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5 NUMBER AND NUMBER SENSE 5.1 The student will a. read, write, and identify the place values
More informationThe Theorem of Pythagoras
CONDENSED LESSON 9.1 The Theorem of Pythagoras In this lesson you will Learn about the Pythagorean Theorem, which states the relationship between the lengths of the legs and the length of the hypotenuse
More informationSolve problems involving proportions Describe the effect of scale factor
Strand: Ratios and Proportional Relationships (RP) 7th Grade Topic: Describe relationships of similar polygons Solve problems involving proportions Describe the effect of scale factor Compare or contrast
More informationGeometry. Midterm Review
Geometry Midterm Review Class: Date: Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 A plumber knows that if you shut off the water
More informationReview Topics. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review Topics MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. On the real number line, label the points with the given coordinates. 1) 11,- 11 1)
More informationPA Core Standards For Mathematics 2.2 Algebraic Concepts PreK-12
Addition and Represent addition and subtraction with CC.2.2.PREK.A.1 Subtraction objects, fingers, mental images, and drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
More informationAlaska Mathematics Standards Vocabulary Word List Grade 4
1 add addend additive comparison area area model common factor common multiple compatible numbers compose composite number counting number decompose difference digit divide dividend divisible divisor equal
More informationPRACTICE TEST 1 Math Level IC
SOLID VOLUME OTHER REFERENCE DATA Right circular cone L = cl V = volume L = lateral area r = radius c = circumference of base h = height l = slant height Sphere S = 4 r 2 V = volume r = radius S = surface
More information2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.
2009 FGCU Mathematics Competition. Geometry Individual Test 1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex. Which postulate/theorem
More informationSkill: determine an approximate value of a radical expression using a variety of methods.
Skill: determine an approximate value of a radical expression using a variety of methods. N.RN.A. Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational
More information