Math 10  Unit 3 Final Review  Numbers


 Donna Dixon
 5 years ago
 Views:
Transcription
1 Class: Date: Math 10  Unit Final Review  Numbers Multiple Choice Identify the choice that best answers the question. 1. Write the prime factorization of 60. a b. 2 6 c d Write the prime factorization of 116. a b c d Determine the greatest common factor of 6 and 88. a. 77 b. 616 c. 7 d. 8. Determine the greatest common factor of 280 and 60. a. 9 b. 6 c. 220 d. 0. Determine the greatest common factor of 8, 210, and 6. a. 1 b c. 21 d Determine the least common multiple of 10 and 22. a. 2 b. c. 220 d Determine the least common multiple of 78 and 102. a. 126 b. 6 c. 262 d Determine the least common multiple of 8, 72, and 108. a. 2 b. 216 c d A developer wants to subdivide a rectangular plot of land measuring 600 m by 70 m into congruent square lots. What is the side length of the largest possible square? a. 7 m b. 0 m c. 10 m d. 0 m 10. What is the side length of the smallest square that could be tiled using a 6cm by 1cm tile? Assume the tiles cannot be cut. a. 10 cm b. 90 cm c. 0 cm d. cm 11. One neighbour cuts his lawn every 8 days. Another neighbour cuts her lawn every 10 days. Suppose both neighbours cut their lawns today. How many days will pass before both neighbours cut their lawns on the same day again? a. 80 days b. 60 days c. 2 days d. 0 days 12. What is the side length of the largest square that could be used to tile a rectangle that measures 6 ft. by ft.? Assume the squares cannot be cut. a. 6 ft. b. 2 ft. c. 102 ft. d. ft. 1. There are 16 male students and 20 female students in a Grade 10 math class. The teacher wants to divide the class into groups with the same number of males and the same number of females in each group. What is the greatest number of groups the teacher can make? a. 12 b. c. 8 d. 16 1
2 1. A fruit grower wants to plant 6 apple seedlings and 108 pear seedlings in rows. Each row is to have the same number of each type of seedling. What is the greatest number of rows the grower can plant? a. 8 b. 16 c. d List the first multiples of 2. a., 6, 8, 10 c. 2,, 6, 8 b. 2,,, d. 1, 2,, Which numbers in the list below are multiples of 1? 70, 2, 6,, 1, 29, 9 a. 2,, 6, 70 c. 2, 6, 70 b. 29, 1,, 70 d. 9, 2, List all the factors of. a. 1,, 11, c., 11 b. 1, d., 18. Which numbers in the list below are factors of 7? 2,,,, 6, 8, 9, 10 a. c., b. d. 2,,, 19. Find all the factors of that are prime. a., 11 c. 1, b. 1,, 11, d., 20. Complete this statement: A prime number has exactly factors. a. 0 c. b. 2 d Find all the common multiples of and 18 that are less than 100. a. 1, 2,, 18 c. 6, 72 b. 72 d Find all the common factors of 27 and 6. a. 1, 9 c. 1,, 9 b. 9 d. 1, 2. Determine the square root of without using your calculator. a. 100 b. 6 c. 00 d Determine the cube root of 2 87 without using your calculator. a. 122 b c d. 2. A cube has volume 1 62 cm. What is the surface area of the cube? a cm 2 b. 70 cm 2 c. 2 cm 2 d cm 2 2
3 26. Determine the side length of this square. a. 6 cm b. 1.8 cm c cm d. 1 cm 27. Determine the edge length of this cube. a cm b. cm c cm d. 7 cm 28. A cube has surface area 70 square feet. What is its volume? a. 62 cubic feet c. 18 cubic feet b. 2 cubic feet d cubic feet 29. How many perfect square whole numbers are between 000 and 6000? a. 6 b. 8 c. 1 d How many perfect cube whole numbers are between 6000 and 800? a. b. 2 c. 1 d A rectangular prism with a square base has height 12 ft. The volume of the prism is 68 cubic feet. Determine the side length of the base of the prism to the nearest foot. a. 289 ft. b. 72 ft. c. 2 ft. d. 17 ft. 2. A cube with volume 729 m is to be painted. Each can of paint covers 2 m 2. How many cans of paint are needed to paint the cube? a. 16 b. 2 c. 1 d. 1. An aquarium approximates a cube with surface area 101 square feet. Water was poured into the empty aquarium at a rate of 6 cubic feet per minute. To the nearest minute, how long did it take to fill the aquarium? a. 2 h 8 min b. 6 h 6 min c. 6 h min d. 2 h 9 min. Use prime factorization to determine which of the following numbers is not both a perfect square and a perfect cube. a. 1 1 b. 12 c d. 1 62
4 . Find the area of this square. a. 20 square units c. 10 square units b. 2 square units d. square units 6. Find the side length of this square. a. 9 units c. 1 unit b. 28 units d. 7 units 7. Find 6 2. a. 2 b. 12 c. 6 d. 6 Ê 8ˆ 8. Find Ë Á 9 16 a b. 8 9 c. 6 9 d Find a b. 7 9 c d Find 0.0. a. 0.2 b c. 8 d Identify the index of 2 7. a. 2 7 b. c. 7 d Identify the index of 7. a. b. 7 c. d.. Identify the radicand of 8 6. a. b. 8 c. 6 d. 8
5 . Identify the radicand of a. 9 b c. d. 10. Evaluate 16 without a calculator. a. 2 b. 2.6 c. 16 d Evaluate 6 without a calculator. a. b. impossible c d. 7. Evaluate a. 26 without a calculator. 62 b. 2 c d Write an equivalent form of 9 as a cube root. a. 661 b. 729 c d Write an equivalent form of as a square root. 9 a b. 6 c d Determine which of these roots lies between and without using your calculator. 28, 172, 17, 118 a. 118 b. 17 c. 28 d Estimate the value of 0 to one decimal place. a. 0. b.. c. 0.9 d Which of these numbers is rational? 169, 8, 16, 8.1 a. 8 b. 8.1 c. 16. Which of these numbers is irrational? 8, 216, 9 16, 68 a. 68 b. 8 c. 216 d. d Order these numbers from greatest to least by estimating each root: 99 a. 170, 99 b. 00, 00, 18, 1, 18, 1, 170, 99 c. 00 d. 00, 170, 00, 18, 1, 170, 99, 18, 1, 170, 18, 1, 99
6 . Order these numbers from least to greatest by estimating each root: 7 a. 7 b. 0, 100, 1, 0, 1, 17, 7, 100, 17 c. 100 d. 17, 7 6. Determine which of these numbers is the least by estimating each root. 1, 0 a. 100, 100, 7, 17 b. 0, 0, 1, 17, 7, 1, 100, 17, 0, 100, 1, 0 c. 1 d Between which two consecutive integers on a number line would you locate 18? Don t use your calculator! a. 2 and b. and c. 2 and d. 1 and 2 8. Which of these numbers is an integer, but not a whole number? 9, 0, 1, a. 0 b. 9 c. d Which of these numbers is a natural number? 9, 0, 1, 1.8 a. 9 b. 0 c. 1.8 d Which of these numbers is a whole number, but not a natural number? 0,, 1, 8.1 a. 8.1 b. 1 c. 0 d. 61. For which number will the fifth root be irrational? 62, 7776, , 2 a b. 2 c d To which set(s) of numbers does 2 belong? a. II and III only b. III only c. I, II and III only d. IV only 6. Write 108 in simplest form. a. 12 b. 6 c. 6 d Write 67 in simplest form. a. 7 b. 1 c. 22 d Write 200 in simplest form. a. 2 0 b c d
7 66. Write 80 a Write 120 a Write 187 a Write 0 a. in simplest form. b in simplest form. b. 10 in simplest form. b. 1 in simplest form. b. 81 c c c c. 9 d. d. 2 2 d. 2 d. 70. Write 6 as an entire radical. a. 0 b. 10 c. 180 d Write 2 as an entire radical. a. 6 b. 12 c. 18 d Write a Write 9 a Write 2 a. 8 as an entire radical. b. 1 as an entire radical. b. 202 as an entire radical. b. 18 c. 6 c. 22 c. 162 d. 192 d. 6 d Write 98 in simplest form. a. 7 1 b. 7 2 c. 2 7 d Write 172 a Write 160 a in simplest form. b. 7 in simplest form. b. 10 c. 1 7 c d. 7 d Write 7 1 as an entire radical. a. 960 b. 98 c. 686 d Write 16 a Write 12 a. 192 as an entire radical. b as an entire radical. b. 20 c. 20 c d. 2 d
8 81. A square has an area of 12 square inches. Determine the side length of the square as a radical in simplest form. a. in. b. 2 6 in. c. 2 in. d. 2 in. 82. A cube has a volume of 7290 cm. Determine the edge length of the cube as a radical in simplest form. a cm b cm c cm d Order these numbers from greatest to least: 2 0,, 2 7,, 2 1 a. 2 1, 2 7,,, 2 0 c., 2 0,, 2 1, 2 7 b., 2 0, 2 1, 2 7, d.,, 2 0, 2 1, Between which 2 consecutive whole numbers is 207? a. 206 and 208 b. 1 and 2 c. 1 and 1 d. 196 and What is the greatest whole number less than 9? a. 10 b. 7 c. 6 d. 86. What is the least whole number greater than 7? a. 6 b. 7 c. 1 d Estimate the value of 1 to the nearest tenth. a. b..1 c. d Find the approximate side length of a square with area 1 cm 2. Give your answer to the nearest tenth. a..6 cm b..9 cm c. 7.8 cm d. 1. cm cm Short Answer 89. Write the prime factorization of Determine the greatest common factor of 7 and Determine the least common multiple of 0 and A builder wants to cover a wall measuring 9 ft. by 1 ft. with square pieces of plywood. a) What is the side length of the largest square that could be used to cover the wall? Assume the squares cannot be cut. b) How many square pieces of plywood would be needed? 9. Bill and Betty do chores at home. Bill mows the lawn every 8 days, and Betty bathes the dog every 1 days. Suppose Bill and Betty do their chores today. How many days will pass before they both do their chores on the same day again? 9. Determine the cube root of
9 9. A cube has volume 9261 cubic inches. Determine the area of one face of the cube. 96. Determine the square root of Which of these numbers is not a perfect square: 16, 17, 6, or 6? 98. Which of these numbers is a perfect square: 0, 9, 60, or 8? 99. Evaluate Evaluate Estimate the value of to one decimal place Between which 2 consecutive integers on a number line would you locate 220? 10. Which of these numbers are rational numbers, but not integers?.12,,, 7, 2., 8, 0, 1 2, Which of these numbers are irrational? 102, 72, 12, 6.1, 6, 12.8, 196, Determine the side length of a square with area 72 cm 2. Write your answer to the nearest tenth of a centimetre Determine the edge length of a cube with volume cm. Write your answer to the nearest tenth of a centimetre Write 169 in simplest form Write 8 19 as an entire radical Write in simplest form Which of these numbers is the greatest? 7, 9 2, 11 2, 1 90,
10 Problem 111. A rectangle is divided into 2 smaller rectangles. The area of the rectangle on the left is 209 square inches, and the area of the rectangle on the right is 19 square inches. Determine the greatest possible measure of the side that the two rectangles share A cube has surface area 266 m 2. What is its volume? 11. Use factoring to determine whether 91 is a perfect square, a perfect cube, or neither. 11. Germaine wants to paint a cube with volume 27 m. Each tub of paint covers 79 m 2. How many tubs of paint does Germaine need to paint the cube? 11. Find the number whose square root is 1. Explain your strategy The factors of 180 are listed in ascending order. 180: 1, 2,,,, 6, 9, 10, 12, 1, 18, 20, 0, 6,, 60, 90, 180 Is 180 a perfect square? How do you know? 117. A square gymnasium floor has area 81 m 2. Find the perimeter of the gymnasium floor Is the cube root of 20 rational or irrational? Use 2 different strategies to justify your answer Order these numbers from least to greatest: 8, 1, 1, 2, In isosceles ABC, what is the length of BC? Write your answer as a mixed radical. 10
11 Math 10  Unit Final Review  Numbers Answer Section MULTIPLE CHOICE 1. C 2. B. D. D. D 6. D 7. A 8. A 9. C 10. C 11. D 12. B 1. B 1. C 1. C 16. D 17. A 18. C 19. A 20. B 21. C 22. C 2. C 2. D 2. B 26. A 27. B 28. D 29. D 0. B 1. D 2. A. B. B. B 6. D 7. C 8. D 9. B 1
12 0. A 1. B 2. B. B. B. A 6. A 7. A 8. B 9. D 0. C 1. B 2. D. B. C. B 6. B 7. A 8. B 9. A 60. C 61. D 62. A 6. B 6. B 6. B 66. B 67. B 68. B 69. A 70. C 71. C 72. A 7. A 7. C 7. B 76. D 77. A 78. C 79. B 80. D 81. D 82. B 8. B 8. C 2
13 8. C 86. B 87. D 88. A SHORT ANSWER , or a) ft. b) days square inches and , 7, 2., and , 6, and cm cm PROBLEM 111. The area of a rectangle is the product of its dimensions. List the factors of 209 and 19. The factors represent possible lengths of a side of each rectangle. Check to see which factors of 209 are also factors of 19. The greatest common factor will be the greatest possible measure of the side that the two rectangles share. The factors of 209 are: 1, 11, 19, 209 The factors of 19 are: 1, 11, 29, 19 The greatest common factor of 209 and 19 is 11. Τhe greatest possible measure of the side that the two rectangles share is 11 in.
14 112. To calculate the volume, first determine the edge length of the cube. The surface area of a cube is the sum of the areas of its 6 congruent square faces. So, the area, A, of one face is: A = A = 1 The edge length, e, of the cube is the square root of the area of one square face. e = 1 e = 21 So, the volume, V, of the cube is the cube of its edge length. V = 21 V = 9261 The volume of the cube is 9261 m. 11. Write 91 as a product of its prime factors. 91 = Since 91 is the product of three equalfactors, it is a perfect cube. It is not possible to rearrange the factors in 2 equalgroups, so 91 is not a perfect square. 11. To calculate how many tubs of paint are needed, first determine the surface area of the cube. The edge length, e, of a cube is equal to the cube root of its volume. e = 27 e = 1 The surface area, SA, of a cube is the sum of the areas of its 6 congruent square faces. SA = 6(1 1) SA = 6(196) SA = 1176 Calculate how many tubs of paint are needed: = Germaine needs 1 tubs of paint to paint the cube. 11. To find the number whose square root is 1, find the square of 1. The square of 1 is: 1 2 = 1 1 = 169 The number whose square root is 1 is 169.
15 116. Any perfect square can be written as the product of two equal factors, and this factor is listed only once in the list of factors. So, a perfect square has an odd number of factors. 180 has 18 factors. 18 is an even number. So, 180 is not a perfect square Find the side length of the gymnasium floor: Find a number which, when multiplied by itself, gives = 81 So, the gymnasium floor has side length 9 m. Perimeter is the distance around the gymnasium floor. A square has equal sides, so the perimeter of the floor is: 9 m + 9 m + 9 m + 9 m = 6 m The perimeter of the gymnasium floor is 6 m is not a perfect cube, so the cube root of 20 is irrational. 20 = does not appear to terminate or repeat. So, the cube root of 20 is likely irrational is between the perfect squares 6 and 9, so 8 is between 6 and 7. Use a calculator: 8 =Ö is between the perfect cubes 12 and 729, so 1 Use a calculator: 1 Write 1 as: 1 =. =Ö 8 is between 8 and 9. 2 is between the perfect squares 1 and, so 2 is between 1 and 2. Use a calculator: 2 =Ö is between the perfect cubes 12 and 216, so 128 Use a calculator: 128 =Ö From least to greatest: 2, 1, 128, 8, 1 is between and 6.
16 120. Use the Pythagorean Theorem in ABD to determine BD = 2 + BD 2 BD 2 = BD 2 = 7 BD = 7 BD = BD = 1 2 BC So, BC = 2 BD Ê ˆ BC = 2 Ë Á = 10 The length of BC is 10 ft. 6
Lesson 3.1 Factors and Multiples of Whole Numbers Exercises (pages 140 141)
Lesson 3.1 Factors and Multiples of Whole Numbers Exercises (pages 140 141) A 3. Multiply each number by 1, 2, 3, 4, 5, and 6. a) 6 1 = 6 6 2 = 12 6 3 = 18 6 4 = 24 6 5 = 30 6 6 = 36 So, the first 6 multiples
More informationSQUARESQUARE ROOT AND CUBECUBE ROOT
UNIT 3 SQUAREQUARE AND CUBEUBE (A) Main Concepts and Results A natural number is called a perfect square if it is the square of some natural number. i.e., if m = n 2, then m is a perfect square where m
More informationVOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.
Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:
More informationSquare Roots and the Pythagorean Theorem
4.8 Square Roots and the Pythagorean Theorem 4.8 OBJECTIVES 1. Find the square root of a perfect square 2. Use the Pythagorean theorem to find the length of a missing side of a right triangle 3. Approximate
More information2nd Semester Geometry Final Exam Review
Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular
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 informationSURFACE AREA AND VOLUME
SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationArea and Perimeter. Name: Class: Date: Short Answer
Name: Class: Date: ID: A Area and Perimeter Short Answer 1. The squares on this grid are 1 centimeter long and 1 centimeter wide. Outline two different figures with an area of 12 square centimeters and
More informationCharacteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
More informationFactors and Products
CHAPTER 3 Factors and Products What You ll Learn use different strategies to find factors and multiples of whole numbers identify prime factors and write the prime factorization of a number find square
More informationPerimeter, Area, and Volume
Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all
More informationQuick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More informationPizza! Pizza! Assessment
Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the
More informationArea of Parallelograms, Triangles, and Trapezoids (pages 314 318)
Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base
More informationArea of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in
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 informationGeometry: Classifying, Identifying, and Constructing Triangles
Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral
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 informationAdvanced GMAT Math Questions
Advanced GMAT Math Questions Version Quantitative Fractions and Ratios 1. The current ratio of boys to girls at a certain school is to 5. If 1 additional boys were added to the school, the new ratio of
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 informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More informationMath Mammoth EndoftheYear Test, Grade 6, Answer Key
Math Mammoth EndoftheYear Test, Grade 6, Answer Key Instructions to the teacher: In order to continue with the Math Mammoth Grade 7 Complete Worktext, I recommend that the student score a minimum of
More informationGrade 5 Work Sta on Perimeter, Area, Volume
Grade 5 Work Sta on Perimeter, Area, Volume #ThankATeacher #TeacherDay #TeacherApprecia onweek 6. 12. Folder tab label: RC 3 TEKS 5(4)(H) Perimeter, Area, and Volume Cover: Reporting Category 3 Geometry
More informationCopy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any.
Algebra 2  Chapter Prerequisites Vocabulary Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. P1 p. 1 1. counting(natural) numbers  {1,2,3,4,...}
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 informationOpenEnded ProblemSolving Projections
MATHEMATICS OpenEnded ProblemSolving Projections Organized by TEKS Categories TEKSING TOWARD STAAR 2014 GRADE 7 PROJECTION MASTERS for PROBLEMSOLVING OVERVIEW The Projection Masters for ProblemSolving
More informationFind the Square Root
verview Math Concepts Materials Students who understand the basic concept of square roots learn how to evaluate expressions and equations that have expressions and equations TI30XS MultiView rational
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationTeacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 91.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
More informationSolids. Objective A: Volume of a Solids
Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular
More informationSolving Geometric Applications
1.8 Solving Geometric Applications 1.8 OBJECTIVES 1. Find a perimeter 2. Solve applications that involve perimeter 3. Find the area of a rectangular figure 4. Apply area formulas 5. Apply volume formulas
More informationMATH 100 PRACTICE FINAL EXAM
MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number
More informationFilling and Wrapping: Homework Examples from ACE
Filling and Wrapping: Homework Examples from ACE Investigation 1: Building Smart Boxes: Rectangular Prisms, ACE #3 Investigation 2: Polygonal Prisms, ACE #12 Investigation 3: Area and Circumference of
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 informationIrrational Numbers. A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers.
Irrational Numbers A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers. Definition: Rational Number A rational number is a number that
More informationSect 6.7  Solving Equations Using the Zero Product Rule
Sect 6.7  Solving Equations Using the Zero Product Rule 116 Concept #1: Definition of a Quadratic Equation A quadratic equation is an equation that can be written in the form ax 2 + bx + c = 0 (referred
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationAPPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS
APPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS Now that we are starting to feel comfortable with the factoring process, the question becomes what do we use factoring to do? There are a variety of classic
More informationApplications of the Pythagorean Theorem
9.5 Applications of the Pythagorean Theorem 9.5 OBJECTIVE 1. Apply the Pythagorean theorem in solving problems Perhaps the most famous theorem in all of mathematics is the Pythagorean theorem. The theorem
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 information10 7, 8. 2. 6x + 30x + 36 SOLUTION: 89 Perfect Squares. The first term is not a perfect square. So, 6x + 30x + 36 is not a perfect square trinomial.
Squares Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it. 1.5x + 60x + 36 SOLUTION: The first term is a perfect square. 5x = (5x) The last term is a perfect
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 informationArea is a measure of how much space is occupied by a figure. 1cm 1cm
Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number
More information7.2 Quadratic Equations
476 CHAPTER 7 Graphs, Equations, and Inequalities 7. Quadratic Equations Now Work the Are You Prepared? problems on page 48. OBJECTIVES 1 Solve Quadratic Equations by Factoring (p. 476) Solve Quadratic
More informationShow that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.
Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional
More informationFactor Polynomials Completely
9.8 Factor Polynomials Completely Before You factored polynomials. Now You will factor polynomials completely. Why? So you can model the height of a projectile, as in Ex. 71. Key Vocabulary factor by grouping
More informationMATHCOUNTS TOOLBOX Facts, Formulas and Tricks
MATHCOUNTS TOOLBOX Facts, Formulas and Tricks MATHCOUNTS Coaching Kit 40 I. PRIME NUMBERS from 1 through 100 (1 is not prime!) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 II.
More informationIllinois State Standards Alignments Grades Three through Eleven
Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other
More information1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?
Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is
More informationPOLYNOMIAL FUNCTIONS
POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a
More informationMath 0306 Final Exam Review
Math 006 Final Exam Review Problem Section Answers Whole Numbers 1. According to the 1990 census, the population of Nebraska is 1,8,8, the population of Nevada is 1,01,8, the population of New Hampshire
More informationGAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book
GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18
More informationSolving Quadratic Equations
9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation
More informationPowerScore Test Preparation (800) 5451750
Question 1 Test 1, Second QR Section (version 2) Two triangles QA: x QB: y Geometry: Triangles Answer: Quantity A is greater 1. The astute student might recognize the 0:60:90 and 45:45:90 triangle right
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 informationSandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.
Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.
More informationArea, Perimeter, Volume and Pythagorean Theorem Assessment
Area, Perimeter, Volume and Pythagorean Theorem Assessment Name: 1. Find the perimeter of a right triangle with legs measuring 10 inches and 24 inches a. 34 inches b. 60 inches c. 120 inches d. 240 inches
More informationBasic Lesson: Pythagorean Theorem
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
More informationFinding Volume of Rectangular Prisms
MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of threedimensional composite shapes.
More informationAnswer Key For The California Mathematics Standards Grade 7
Introduction: Summary of Goals GRADE SEVEN By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use
More informationCSU Fresno Problem Solving Session. Geometry, 17 March 2012
CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfdprep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 27, 2015 1:15 to 4:15 p.m.
INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tuesday, January 27, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession
More informationMultiplication and Division Properties of Radicals. b 1. 2. a Division property of radicals. 1 n ab 1ab2 1 n a 1 n b 1 n 1 n a 1 n b
488 Chapter 7 Radicals and Complex Numbers Objectives 1. Multiplication and Division Properties of Radicals 2. Simplifying Radicals by Using the Multiplication Property of Radicals 3. Simplifying Radicals
More information8 th Grade Task 2 Rugs
8 th Grade Task 2 Rugs Student Task Core Idea 4 Geometry and Measurement Find perimeters of shapes. Use Pythagorean theorem to find side lengths. Apply appropriate techniques, tools and formulas to determine
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationWhat You ll Learn. Why It s Important
These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why
More informationHow To Solve Factoring Problems
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 information86 Radical Expressions and Rational Exponents. Warm Up Lesson Presentation Lesson Quiz
86 Radical Expressions and Rational Exponents Warm Up Lesson Presentation Lesson Quiz Holt Algebra ALgebra2 2 Warm Up Simplify each expression. 1. 7 3 7 2 16,807 2. 11 8 11 6 121 3. (3 2 ) 3 729 4. 5.
More informationChapter 4  Decimals
Chapter 4  Decimals $34.99 decimal notation ex. The cost of an object. ex. The balance of your bank account ex The amount owed ex. The tax on a purchase. Just like Whole Numbers Place Value  1.23456789
More information12) 13) 14) (5x)2/3. 16) x5/8 x3/8. 19) (r1/7 s1/7) 2
DMA 080 WORKSHEET # (8.8.2) Name Find the square root. Assume that all variables represent positive real numbers. ) 6 2) 8 / 2) 9x8 ) 00 ) 8 27 2/ Use a calculator to approximate the square root to decimal
More informationVocabulary Cards and Word Walls Revised: June 29, 2011
Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,
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 informationMcDougal Littell California:
McDougal Littell California: PreAlgebra Algebra 1 correlated to the California Math Content s Grades 7 8 McDougal Littell California PreAlgebra Components: Pupil Edition (PE), Teacher s Edition (TE),
More informationGeometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
More informationPennsylvania System of School Assessment
Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read
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 informationChapter 4: Area, Perimeter, and Volume. Geometry Assessments
Chapter 4: Area, Perimeter, and Volume Geometry Assessments Area, Perimeter, and Volume Introduction The performance tasks in this chapter focus on applying the properties of triangles and polygons to
More informationcalled and explain why it cannot be factored with algebra tiles? and explain why it cannot be factored with algebra tiles?
Factoring Reporting Category Topic Expressions and Operations Factoring polynomials Primary SOL A.2c The student will perform operations on polynomials, including factoring completely first and seconddegree
More information2. Complete the table to identify the effect tripling the radius of a cylinder s base has on its volume. Cylinder Height (cm) h
Name: Period: Date: K. Williams ID: A 8th Grade Chapter 14 TEST REVIEW 1. Determine the volume of the cylinder. Use 3.14 for. 2. Complete the table to identify the effect tripling the radius of a cylinder
More informationInv 1 5. Draw 2 different shapes, each with an area of 15 square units and perimeter of 16 units.
Covering and Surrounding: Homework Examples from ACE Investigation 1: Questions 5, 8, 21 Investigation 2: Questions 6, 7, 11, 27 Investigation 3: Questions 6, 8, 11 Investigation 5: Questions 15, 26 ACE
More informationExpression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds
Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative
More informationGeometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
More informationSTUDENT NAME: GRADE 9 MATHEMATICS
STUDENT NAME: GRADE 9 MATHEMATICS Administered January 2010 Name: Class: Date: 9th Grade TAKS Mathematics Test 1. Olga plans to take a trip from her house in San Marcos, Texas, to a friend s house in Zapata,
More informationMath Review. for the Quantitative Reasoning Measure of the GRE revised General Test
Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important
More informationCalculating Area, Perimeter and Volume
Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly
More informationYOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!
DETAILED SOLUTIONS AND CONCEPTS  SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST
More informationof surface, 569571, 576577, 578581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationArea of Parallelograms (pages 546 549)
A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular
More informationCourse 2 Summer Packet For students entering 8th grade in the fall
Course 2 Summer Packet For students entering 8th grade in the fall The summer packet is comprised of important topics upcoming eighth graders should know upon entering math in the fall. Please use your
More informationGeorgia Department of Education Georgia Standards of Excellence Framework GSE Grade 6 Mathematics Unit 5
**Volume and Cubes Back to Task Table In this problembased task, students will examine the mathematical relationship between the volume of a rectangular prism in cubic units and the number of unit cubes
More informationNMC Sample Problems: Grade 5
NMC Sample Problems: Grade 5 1. What is the value of 5 6 3 4 + 2 3 1 2? 1 3 (a) (b) (c) (d) 1 5 1 4 4 4 12 12 2. What is the value of 23, 456 + 15, 743 3, 894 expressed to the nearest thousand? (a) 34,
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 22, 2013 9:15 a.m. to 12:15 p.m.
INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tuesday, January 22, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationGrade 7/8 Math Circles Fall 2012 Factors and Primes
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 2012 Factors and Primes Factors Definition: A factor of a number is a whole
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 informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
More informationGeometry EOC Practice Test #2
Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply
More informationMATH STUDENT BOOK. 6th Grade Unit 8
MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF
More informationALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only
ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The
More information