Pretest. Explain and use formulas for lateral area, surface area, and volume of solids.
|
|
- Nathan Sherman
- 5 years ago
- Views:
Transcription
1 Pretest Please complete the pretest for this standard on your own. Try to remember all you can from our first discussion of this topic. Explain and use formulas for lateral area, surface area, and volume of solids. MA.912.G.7.5 1
2 Surface Area and Volume Surface Area: What it takes to COVER something Volume: What it takes to FILL something Lateral Area & Surface Area Surface Area covers the ENTIRE object. Lateral Area does not include any of the BASES. (tops and boloms) Surface area will ALWAYS be GREATER than lateral area. 2
3 Use the reference sheet as a guide when solving area and volume problems!!! Use the reference sheet as a guide when solving area and volume problems!!! 3
4 Find the volume of the cone shown as a decimal rounded to the nearest tenth. A yd 3 B yd 3 C yd 3 D yd 3 V = 1 3 πr2 h V = 1 3 π ( 7 ) 2 ( 17) V = 1 3 π ( 49 )( 17) Since the radius is squared and the height is not, you need to be careful where you plug in your values in this formula. V = 1 ( )π Your answer may differ slightly if you use the approximaaon 3.14 rather than the pi key on your calculator. V yd 3 Volume 1. Find the surface area of the cylinder in terms of π. Since this problem asks for the surface area and not the lateral surface area, we will include the two bases. S.A. = 2πrh + 2πr 2 πr 2 is the area of a circle. Since there are two circular bases, we see this reflected in the S.A. formula S.A. = 2π ( 6) ( 19) + 2π ( 6) 2 S.A. = 228π + 72π S.A. = 300π in 2 4
5 2. Find the volume of the sphere shown. Give your answer rounded to the nearest cubic cenameter. V = 4 3 πr3 V = 4 3 π ( 7 ) 3 V = 4 ( )π V =1436 cm 3 Find both the lateral area and the surface area of the square pyramid at the right. S.A. = 1 2 P + B We are given the alatude and not the slant height so we need to apply the Pythagorean Theorem. Remember that the first leg is the alatude and the second leg is half of the base s edge. = ( 19) 2 + ( 20) 2 = 761 P = =152 B = =1444 Remember, that lateral area does not include any bases, so you can leave B out of the formula. Surface Area S.A. = 1 2 P + B S.A. = 1 ( ) yd 2 S.A. = 1 ( ) yd 2 5
6 Determine how changes in dimensions affect the surface area and volume of common geometric solids MA.912.G.7.7 Kendra has a compost box that has the shape of a cube. She wants to increase the size of the box by extending every edge of the box by half its original length. Afer the box is increased in size, which of the following statements is true? A. The volume of the new compost box is exactly 112.5% of the volume of the original box. B. The volume of the new compost box is exactly 150% of the volume of the original box. C. The volume of the new compost box is exactly 337.5% of the volume of the original box. D. The volume of the new compost box is exactly 450% of the volume of the original box. Since we do not know the length of the original edge, we can make our own. Let s say that the edge was 4 units. Then the new edge would be increased by half of that which is 2. The new edge would be 6 units. Old volume is 64 units 3. New volume is 216 units = 337.5% 64 Using a Concrete Example to Solve 6
7 A city is planning to replace one of its water storage tanks with a larger one. The city s old tank is a right circular cylinder with a radius of 12 feet and a volume of 10,000 cubic feet. The new tank is a right circular cylinder with a radius of 15 feet and the same height as the old tank. What is the maximum number of cubic feet of water the new storage tank will hold? Strategy: Make a table Comparing Volume Old Tank New Tank Formula Missing Dimensions r=12; V=10,000 r=15 h=? Vnew=? V = πr 2 h Strategy: Make a table Old Tank New Tank Formula Missing Dimensions r=12; V=10,000 ( ) 2 h = π π = h r=15 h=? Vnew=? V = πr 2 h Begin by using what you know about the old tank to find the height of both tanks. Now that we know the height and the radius of the new tank, we can calculate the volume. V = πr 2 h V = π 15! $ & " 144π % ( ) 2 # V =15, 625 ft 3 Comparing Volumes 7
8 Rodney s dad wants him to paint a box that he was making. Rodney calculated that he needed 128 cubic inches of paint to cover the box. Later, Rodney s dad changed the size of the box by mulaplying each of its edges by ¾. How much paint does Rodney need to buy now? S.A. = 2bh + 2bw + 2hw Surface area is the sum of the areas of the sides. Since the area is squared, we need to square ¾. 2! 3$ # & " 4 % = 9 16 This means that the surface area of the box will be reduced by a factor of 9/ = 72 in3 16 Comparing Surface Area 1. A rectangular fish tank is 7 feet wide by 3 feet long and is filled to a depth of 3 feet. All of the water is poured into a second tank that is 6 feet wide by 2 feet long. What is the depth of the water in the new tank? Find the volume of the old tank. V = lwh V = 3 ( )( 7) ( 3) = 63 ft 3 The water in the new tank will have the same volume. Use it to determine the new depth (height). 63 = ( 2) ( 6)h 63 =12h h = = 21 4 ft 8
9 2. A rectangular prism with dimensions 2 in by 3 in by 6 in has the same volume as a right square pyramid that has a 6 in by 6 in base. What is the height of the pyramid? Volume of the rectangular prism: V = lwh V = 2 ( )( 3) ( 6) = 36 in 3 Volume of a right square pyramid: V = 1 3 Bh 36 = 1 ( )h 36 = 1 ( 3 36 )h 36 =12h h = 3 in 3. A firework explodes and is spreading from its center in a spherical palern. The sphere currently covers a surface area of 240 sq. meters. The diameter of the firework is expected to double in the next 30 seconds. What will be the new surface area of the sphere? S.A. = 4πr 2 S.A. = 4π ( 2r) 2 If the diameter doubles, so does the radius. S.A. = 4π 4r 2 So the surface area increases by a factor of = 960 square meters 9
Right Circular Cylinders A right circular cylinder is like a right prism except that its bases are congruent circles instead of congruent polygons.
Volume-Lateral Area-Total Area page #10 Right Circular Cylinders A right circular cylinder is like a right prism except that its bases are congruent circles instead of congruent polygons. base height base
More informationTurn Up the Volume and Let s Bend Light Beams Volume and Surface Area of a Prism
CH 12 Test Review Turn Up the Volume and Let s Bend Light Beams Volume and Surface Area of a Prism Vocabulary Write the term from the box that best completes each statement bases of a prism lateral faces
More informationKansas City Area Teachers of Mathematics 2015 KCATM Math Competition GEOMETRY GRADE 7
Kansas City Area Teachers of Mathematics 2015 KCATM Math Competition GEOMETRY GRADE 7 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may use calculators. Mark
More informationLESSON 2: TRIANGULAR PRISMS, CYLINDERS, AND SPHERES. Unit 9: Figures and Solids
LESSON 2: TRIANGULAR PRISMS, CYLINDERS, AND SPHERES Unit 9: Figures and Solids base parallel two The sum of the area of the lateral faces (al sides except for the bases) The sum of all the area (lateral
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 information( ) ) in 2 ( ) ) in 3
Chapter 1 Test Review Question Answers 1. Find the total surface area and volume of a cube in which the diagonal measures yards. x + x ) = ) x = x x A T.S. = bh) = ) ) = 1 yd V = BH = bh)h = ) ) ) = yd.
More informationI.G.C.S.E. Volume & Surface Area. You can access the solutions from the end of each question
I.G.C.S.E. Volume & Surface Area Index: Please click on the question number you want Question 1 Question Question Question 4 Question 5 Question 6 Question 7 Question 8 You can access the solutions from
More informationSurface Areas of Prisms and Cylinders. Find the lateral area and surface area of each prism. Round to the nearest tenth if necessary.
12-2 Skills Practice Surface Areas of Prisms and Cylinders Find the lateral area and surface area of each prism. Round to the nearest tenth if necessary. 12 yd 6 m 12 yd 10 yd 8 m 12 m 3. 4. 6 in. 8 in.
More informationUnit 5 Test Review: Modeling with Geometry Honors
Name: ate: 1. What is the volume, in cubic centimeters, of a cube whose edge measures 2 centimeters? 5. A right circular cylinder has a base whose area is 12π. If the height of the cylinder is 6, the volume
More informationAnswer Keys for Calvert Math
Answer Keys for Calvert Math Lessons CMAKF- Contents Math Textbook... Math Workbook... Math Manual... Answer Keys Math Textbook Lessons Math Textbook Answer Key Lessons. Area and Circumference of Circles
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 informationSection 0 5: Evaluating Algebraic Expressions
Section 0 5: Evaluating Algebraic Expressions Algebraic Expressions An algebraic expression is any expression that combines numbers and letters with a set of operations on those numbers and letters. An
More informationSection Volume, Mass, and Temperature
Section 11.5 - Volume, Mass, and Temperature Surface Area is the number of square units covering a three dimensional figure; Volume describes how much space a three-dimensional figure contains. The unit
More informationClasswork. Opening Exercises 1 2. Note: Figures not drawn to scale. 1. Determine the volume for each figure below.
Classwork Opening Exercises 1 2 Note: Figures not drawn to scale. 1. Determine the volume for each figure below. a. Write an expression that shows volume in terms of the area of the base,, and the height
More informationFebruary 29 th March 4 th
February 29 th March 4 th Unit 7: Introduction to Functions Jump Start Table A: Bags of candy ( ) Cost ( ) 1 2 3 4 5 6 7 8 $1.25 $2.50 $3.75 $5.00 $6.25 $7.50 $8.75 $10.00 Table B: Number of seconds (
More informationMesa Public Schools. Q3 practice test. Assessment Summary: Powered by SchoolCity Inc. Page 1 of 44
Mesa Public Schools Assessment Summary: Q3 practice test Powered by SchoolCity Inc. www.schoolcity.com Page 1 of 44 Assessment Summary: Q3 practice test Year: 2016-2017 Subject: Math Total Items: 43 Total
More informationGrade 11 Mathematics Practice Test
Grade Mathematics Practice Test Nebraska Department of Education 204 Directions: On the following pages are multiple-choice questions for the Grade Practice Test, a practice opportunity for the Nebraska
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 informationHigh School HS Geometry 1819 GSE Geometry Unit 5 Full Touchstone
High School HS Geometry 1819 GSE Geometry Unit 5 Full Touchstone ID: 294579 Standard: GSE G-MG.1 1. A fish tank is in the shape of a rectangular prism. The dimensions of the tank are 18 inches by 17 inches
More informationGeometry Final Exam Review
1. In the figures find the missing parts. Geometry Final Eam Review 2. In the figures find the missing parts. 3. Tom is trying to put a divider diagonally to separate his animals and his play area. If
More informationMay 05, surface area and volume of spheres ink.notebook. Page 171. Page Surface Area and Volume of Spheres.
12.6 surface area and volume of spheres ink.notebook Page 171 Page 172 12.6 Surface Area and Volume of Spheres Page 173 Page 174 Page 175 1 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards
More informationMENSURATION. Mensuration is the measurement of lines, areas, and volumes. Before, you start this pack, you need to know the following facts.
MENSURATION Mensuration is the measurement of lines, areas, and volumes. Before, you start this pack, you need to know the following facts. When you see kilo, it indicates 000 in length, mass and capacity.
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 informationUsing the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles
Math 154 Chapter 9.6: Applications of Radical Equations Objectives: Finding legs of right triangles Finding hypotenuse of right triangles Solve application problems involving right triangles Pythagorean
More information1. Use. What are the vertices of A.,, B.,, C.,, D.,,
1. Use. What are the vertices of A.,, B.,, C.,, D.,, 2. Given, how are the distances to the origin from each image point related to the distance to the origin from each corresponding preimage point? A.
More informationPlease allow yourself one to two hours to complete the following sections of the packet. College Integrated Geometry Honors Integrated Geometry
Incoming Integrated Geometry Summer Work Dear Incoming Integrated Geometry Students, To better prepare for your high school mathematics entry process, summer work is assigned to ensure an easier transition
More informationImportant: You must show your work on a separate sheet of paper. 1. There are 2 red balls and 5 green balls. Write the ratio of red to green balls.
Math Department Math Summer Packet: Incoming 8 th -Graders, 2018-2019 Student Name: Period: Math Teacher: Important: You must show your work on a separate sheet of paper. Remember: It is important to arrive
More informationMCAS Review - Measurement Session 4A
lass: ate: I: MS Review - Measurement Session 4 Multiple hoice Identify the choice that best completes the statement or answers the question. 1 circle has an area of 16π square centimeters. What is the
More informationLesson 14.1 Skills Practice
Lesson 14.1 Skills Practice Name Date Drum Roll, Please! Volume of a Cylinder Vocabulary Explain why the term describes each given figure. 1. cylinder 2. right circular cylinder Chapter 14 Skills Practice
More informationMathematics Conversions/Formula. S.A. 2 r. cylinder. V cone S.A. 4. sphere
Mathematics 1201 Midterm Review 2015 Unit I: Measurement Conversions/Formula 1 ft. = 12 in. 1 in. = 2.5 cm 2 S.A. 2r 2rh cylinder V pyramid 1 (area of base)(height) 1 yd. = ft. 1 mi. = 1.6 km 2 S.A. cone
More informationMATH LESSON 24 EXAMPLE SOLUTIONS OCTOBER 27, 2017
MATH 16020 LESSON 24 EXAMPLE SOLUTIONS OCTOBER 27, 2017 Example 1. We are tasked with constructing a rectangular box with a volume of 64 cubic feet. The material for the top costs 8 dollars per square
More informationh h h b b Where B is the area of the base and h is the height. . Multiply this by the height to get 20(81 ) 1620 The base is a circle of area (9)
Area and Volume Area Formulas: A bh 1 A bh A r C r h b b b h h h b b b r Volume: Prisms and Cylinders. V Bh Where B is the area of the base and h is the height. 10ft 9in 4ft 5ft 0in The base can be any
More informationLESSON 11 PRACTICE PROBLEMS
LESSON 11 PRACTICE PROBLEMS 1. a. Determine the volume of each of the figures shown below. Round your answers to the nearest integer and include appropriate units of b. Determine the volume of each of
More informationDividing in Scientific Notation Name (page 778)
LESSON 111 Dividing in Scientific Notation Name (page 778) To divide powers of 10, subtract the exponents. 10 7 10 4 = 10 7 4 = 10 3 To divide numbers in scientific notation: 1. Divide the decimal or whole
More informationMathematics 10C. UNIT ONE Measurement. Unit. Student Workbook. Lesson 1: Metric and Imperial Approximate Completion Time: 3 Days
Mathematics 10C Student Workbook Unit 1 0 1 2 Lesson 1: Metric and Imperial Approximate Completion Time: 3 Days Lesson 2: Surface Area and Volume Approximate Completion Time: 2 Days hypotenuse adjacent
More information1201 Common Mathematics Assessment - June 2013 Answer Sheet. Name
1201 Common Mathematics Assessment - June 2013 Answer Sheet Name Mathematics Teacher: 1. A B C D 2. A B C D 3. A B C D 4. A B C D 5. A B C D 6. A B C D 7. A B C D 8. A B C D 9. A B C D 10. A B C D 11.
More informationKansas City Area Teachers of Mathematics 2013 KCATM Math Competition GEOMETRY GRADES 7-8
Kansas City Area Teachers of Mathematics 2013 KCATM Math Competition GEOMETRY GRADES 7-8 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may use calculators.
More informationEx 1: If a linear function satisfies the conditions of h( 3) = 1 and h(3) = 2, find h(x).
In lesson 1, the definition of a linear function was given. A linear function is a function of the form f(x) = ax + b, where a is the slope of the line and (0, b) is the y-intercept. A linear function
More informationDays 3 & 4 Notes: Related Rates
AP Calculus Unit 4 Applications of the Derivative Part 1 Days 3 & 4 Notes: Related Rates Implicitly differentiate the following formulas with respect to time. State what each rate in the differential equation
More informationThe GED math test gives you a page of math formulas that
Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding
More informationFind the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides.
Mth101 Chapter 8 HW Name Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 1) 1) Rectangle 6 in. 12 in. 12 in.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) dc. D) dr dt = 2πdC dt
MAC 3 Chapter Review Materials (Part III) Topics Include Related Rates, Differentials, and Linear Approximations MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers
More informationMA 40S APPLIED UNIT F: DESIGN AND MEASUREMENT CLASS NOTES
1 MA 40S APPLIED UNIT F: DESIGN AND MEASUREMENT CLASS NOTES 1. Introduction. In Grade 1 Applied you learn some powerful mathematics. But it remains necessary to re-enforce the most basic practical type
More informationGeometry Final Exam REVIEW
Name: Class: _ Date: _ Geometry Final Exam 09-10 - REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the perimeter and area of the parallelogram.
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 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 informationCP Geometry Final Exam Review Packet
CP Geometry Final Exam Review Packet 016-017 This packet reviews the basic concepts that you learned in each of the units taught this semester that will be assessed on the final exam. You should complete
More informationSection MWF 12 1pm SR 117
Math 1431 Section 12485 MWF 12 1pm SR 117 Dr. Melahat Almus almus@math.uh.edu http://www.math.uh.edu/~almus COURSE WEBSITE: http://www.math.uh.edu/~almus/1431_sp16.html Visit my website regularly for announcements
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 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 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 informationLesson 4.1 (Part 1): Roots & Pythagorean Theorem
Lesson 4.1 (Part 1): Roots & Pythagorean Theorem Objectives Students will understand how roots are used to undo powers. how the Pythagorean theorem is used in applications. Students will be able to use
More informationContents. Formulas and Geometry. Additional Practice. Answers to Check Your Work. Section D
Contents Section D Lichens 34 Circles and Solids 38 Pyramids 40 Summary 42 Check Your Work 42 Additional Practice Answers to Check Your Work Contents v D Lichens Many formulas are used in geometry. In
More informationCONNECTED RATE OF CHANGE PACK
C4 CONNECTED RATE OF CHANGE PACK 1. A vase with a circular cross-section is shown in. Water is flowing into the vase. When the depth of the water is h cm, the volume of water V cm 3 is given by V = 4 πh(h
More informationFinal Exam Review Packet
Final Exam Review Packet Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to scale. 6 8 a.
More informationXAVIER JR. HIGH. Grade 8 MATHEMATICS Things to Know Booklet. Mrs. J. Bennett or Mr. Sheppard (circle) NAME: Class:
P a g e 1 XAVIER JR. HIGH NAME: Class: Teacher: Mrs. J. Bennett or Mr. Sheppard (circle) Grade 8 MATHEMATICS Things to Know Booklet Unit 1: Powers Unit 2: Integers Unit 3: Fractions Unit Unit 4: Prisms
More informationMEA 502 Work Sheet Period Name. CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 402 Use geometric formulas when all necessary
MEA 502 Work Sheet Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 402 Use geometric formulas when all necessary attain mastery at this level information is given MEA 502 Level 2
More informationImplicit Differentiation
Week 6. Implicit Differentiation Let s say we want to differentiate the equation of a circle: y 2 + x 2 =9 Using the techniques we know so far, we need to write the equation as a function of one variable
More informationNational 5 Course Notes. Scientific Notation (or Standard Form) This is a different way of writing very large and very small numbers in the form:-
National 5 Course Notes Scientific Notation (or Standard Form) This is a different way of writing very large and very small numbers in the form:- a x 10 n where a is between 1 and 10 and n is an integer
More informationLarge & Small Numbers
Large & Small Numbers Scientists frequently work with very large or small numbers. Astronomers work with galaxies that contain billions of stars at great distances from us. On the other hand, biologists
More informationKg hg dag g dg cg mg. Km hm dam m dm cm mm
Metric System Conversions Mass (g = gram) 0 0 0 0 0 0 Kg hg dag g dg cg mg 0 0 0 0 0 0 Distance or Length ( m = metre) 0 0 0 0 0 0 Km hm dam m dm cm mm 0 0 0 0 0 0 Area (m = square metre) 00 00 00 00 00
More information4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 1 1. Write the slope-intercept form of an equation of a. Write a definition of slope. 7 line with a slope of, and a y-intercept of 3. 11 3. You want
More information2.6 Related Rates. The Derivative as a Rate of Change. = ft related rates 175
2.6 related rates 175 2.6 Related Rates Throughout the next several tions we ll look at a variety of applications of derivatives. Probably no single application will be of interest or use to everyone,
More informationwith dt. with 2. If x = u, find an equation relating du dt
MATH 2250 Royal Section 3.10: Related Rates EXPANDED VERSION In this section, we consider two (or more) dependent variables that depend on a third variable (the independent variable). Usually, the independent
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 informationOptimization Problems. By Tuesday J. Johnson
Optimization Problems By Tuesday J. Johnson 1 Suggested Review Topics Algebra skills reviews suggested: None Trigonometric skills reviews suggested: None 2 Applications of Differentiation Optimization
More informationModeling with Volume
1.2 Modeling with Essential Question How can you use the mass and volume of an object to describe the density of the object? Finding Densities Work with a partner. Approximate the volume of each object
More information3x 2 + 3y 2 +18x + 6y 60 = 0. 1) C(3,1), r = 30
1. Find the center and radius of the circle with the following equation: x 2 + y 2 +18x + 6y 60 = 0. 1) C(,1), r = 0 2) C(,1), r = 0 ) C(, 1), r = 0 4) C(, 1), r = 0 5) C(9,), r = 110 6) C(9,), r =110
More informationALGEBRA I AND GEOMETRY SUMMER ASSIGNMENT
NAME: This packet has been designed to help you review various mathematical topics that are necessary for your success in Algebra I and/or Geometry next year, as well as PSAT/SAT/ACT. Complete all problems
More informationGeometry Honors Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Geometry Honors Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the conclusion of the following conditional? A number is divisible
More informationLesson 9: Examples of Functions from Geometry
Lesson 9: Examples of Functions from Geometry Classwork Exercises As you complete Exercises 1 4, record the information in the table below. Side length (s) Area (A) Expression that describes area of border
More informationChapter 1 Symmetry and Surface Area REMEMBER TO SHOW ALL WORK! P.G. 2-38
Name: Class: Chapter 1 Symmetry and Surface Area REMEMBER TO SHOW ALL WORK! P.G. 2-38 John says to rotate a rectangle 90 you have to move the rectangle ¼ clockwise. Brianna says to rotate a rectangle 90
More informationMath-2A. Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms
Math-A Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms Describe the idea of area. Area attempts to answer the question how big is it? The area
More informationMATH 1371 Fall 2010 Sec 043, 045 Jered Bright (Hard) Mock Test for Midterm 2
1. A container in the shape of a paraboloid (a parabola revolved around an axis going through the vertex of the parabola and the directrix, so every horizontal slice, or cross section, is a circle.) is
More informationFINAL REVIEW MATH 6 STUDENT NAME MATH TEACHER
FINAL REVIEW MATH 6 STUDENT NAME MATH TEACHER ** As you go through this review packet, be sure to show all work as you have done throughout the school year. Remember- NO WORK NO CREDIT ** REAL NUMBERS,
More informationEnglish Measurement Relationships
Math 30 Prealgebra Sec 10.1: Using Unit Fractions with U.S. and Metric Units Defn A unit fraction is a fraction that shows the relationship between units and is equal to 1. Ex English Measurement Relationships
More informationDefinitions Term Description Examples Mixed radical the product of a monomial and a radical
Chapter 5 Radical Expressions and Equations 5.1 Working With Radicals KEY IDEAS Definitions Term Description Examples Mixed radical the product of a monomial and a radical index radical sign -8 45 coefficient
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 informationChapter 1. Solving Algebraic Equations for a Variable
www.ck1.org CHAPTER 1 Solving Algebraic Equations for a Variable Here you ll learn how to isolate the variable in an equation or formula. Problem: You are planning a trip to Spain in the summer. In the
More informationSemester Final Exam Review
Semester Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the volume of the right triangular prism shown? 9 yd 21 yd a. b. c.
More informationArea and Volume 2. Circles. Trapeziums. and Measures. Geometry. Key Point. Key Point. Key Point
Geometry and Measures Area and Volume 2 You must be able to: Recall and use the formulae for the circumference and area of a circle Recall and use the formula for the area of a trapezium Recall and use
More informationUnit 8: Designs Applied Math 30. Unit 8: Designs
8-1: Reviewing Perimeter, Area, Surface Area and Volume Perimeter: - the length (one-dimensional) around an object. Area: - the amount of space (two-dimensional) a flat-object occupies. Surface Area: -
More informationBeginning Algebra MATH 100B. Math Study Center BYU-Idaho
Beginning Algebra MATH 100B Math Study Center BYU-Idaho Preface This math book has been created by the BYU-Idaho Math Study Center for the college student who needs an introduction to Algebra. This book
More information8 th grade practice test. Objective 1.1a
8 th grade practice test Objective 1.1a 1. Stacey earns $15 each week plus $.50 for each customer on her paper route. She wants to earn at least $25 each week. What equation can she use to find x the number
More informationMath 131. Related Rates Larson Section 2.6
Math 131. Related Rates Larson Section 2.6 There are many natural situations when there are related variables that are changing with respect to time. For example, a spherical balloon is being inflated
More informationCircle - Circumference
Name : Score : Circle - Circumference Example : Circumference of a circle = 2πr or πd 8.53 m Diameter (d) = 8.53 m πd = 3.14 x 8.53 26.78 m Find the circumference of each circle. Round the answer to two
More informationMt. Douglas Secondary
Foundations of Math Section.5 Volume of Similar Figures 47.5 Volume of Similar Figures The cubes shown below are similar. The corresponding sides are in a ratio of :. What is the ratio of the volumes?
More informationSAT Subject Test Practice Test II: Math Level I Time 60 minutes, 50 Questions
SAT Subject Test Practice Test II: Math Level I Time 60 minutes, 50 Questions All questions in the Math Level 1 and Math Level Tests are multiple-choice questions in which you are asked to choose the BEST
More informationRelated Rates STEP 1 STEP 2:
Related Rates You can use derivative analysis to determine how two related quantities also have rates of change which are related together. I ll lead off with this example. 3 Ex) A spherical ball is being
More informationC Expressions and Equations, Lesson 5, Transforming Formulas (r. 2018) LEARNING OBJECTIVES. Overview of Lesson
C Expressions and Equations, Lesson 5, Transforming Formulas (r. 2018) EXPRESSIONS AND EQUATIONS Transforming Formulas Common Core Standard A-CED.A.4 Rearrange formulas to highlight a quantity of interest,
More informationKansas City Area Teachers of Mathematics 2016 KCATM Math Competition
Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition GEOMETRY AND MEASUREMENT TEST GRADE 5 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 15 minutes You may
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1332 Chapter 10 Review Name Solve the problem. 1) The hour hand of a clock moves from 12 to 4 oʹclock. Through how many degrees does it move? 1) Find the measure of the angle in which? appears. 2)
More informationNumber Sense Practice Questions - Part 1 007
This practice test includes typical math questions encountered in the first 40 of 80 questions in MathLeague's Number Sense tests based on the 2017-2018 competition season. In competition the Number Sense
More informationMeasurement in Two Systems
Booklet Mark: 10 9 8 7 6 RE-Submit Measurement in Two Systems This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg.
More informationChapter 8 Solids. Pyramids. This is a square pyramid. Draw this figure and write names of edges. Height and Slant Height.
Chapter 8 Solids Pyramids This is a square pyramid. Draw this figure and write names of edges. Height and Slant Height Right angles of Square Pyramid. Write 1 problem of page 193 Answer: Area of square
More informationCustomary Units of Measurement
Customary Units of Measurement What would it be like to have no system of measurement? If we are to measure something, we need a unit of measure. standard unit of measure: one that people have agreed to
More informationGeometric Formulas (page 474) Name
LESSON 91 Geometric Formulas (page 474) Name Figure Perimeter Area Square P = 4s A = s 2 Rectangle P = 2I + 2w A = Iw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1_ 2 bh Teacher Note:
More informationNumber Sense Practice Questions - Part 1 009
This practice test includes typical math questions encountered in the first 40 of 80 questions in MathLeague's Number Sense tests based on the 2017-2018 competition season. In competition the Number Sense
More informationCHAPTER 0: Preliminary Topics
(Exercises for Chapter 0: Preliminary Topics) E.0.1 CHAPTER 0: Preliminary Topics (A) means refer to Part A, (B) means refer to Part B, etc. (Calculator) means use a calculator. Otherwise, do not use a
More informationOptimal Cone. 1 Grade Levels and Time. 2 Objectives and Topics. 3 Introduction. 4 Procedure and Discussion. Grades:11-12
1 Grade Levels and Time Optimal Cone Grades:11-12 Time: This lesson will take two 50-minute class periods. 2 Objectives and Topics Objectives: Topics: The students should be able to formulate the volume
More information