Chapter 2 & 3 Review for Midterm
|
|
- Arlene Bond
- 5 years ago
- Views:
Transcription
1 Math Links 9 Chapter 2 & Review for Midterm Chapter 2 Highlights: When adding or subtracting fractions, work with parts of the whole that are of equal size (Equivalent fractions). We do this by finding the lowest common denominator or LCD = = ) + = 2) = When multiplying 2 proper fractions, you can multiply the numerators and multiply the denominators: = = = = To divide two fractions, you multiply the reciprocal of the second fraction: = = or or = You can compare fractions with the same denominator by comparing the numerators: 7 6 < because -7< A perfect square can be expressed as the product of two equal rational factors.6=.9 x.9 = x 2 2 The square root of a perfect square can be determined exactly.6 =. 9 = 9 Multiplying Integers: Dividing Integers: Rules: Rules: ) + + = + ) + + = + 2) + = 2) + = ) + = ) + = ) = + ) = + Chapter Highlights: A power is a short way to represent repeated multiplication Ie. 7 x 7 x 7 = 7 5 x 5 x 5 x 5= A power consists of a base and an exponent. The base represents the number you multiply repeatedly. The exponent represents the number of times you multiply the base Ie. (-) 5 (-) represents the base 5 represents the exponent (-) 5 represents the power Exponent Laws: To multiply powers with the same base, the base stays the same and we add the exponents. a m x a n = a m+n Example: 7 x 2 = 7+2 = x 5 = To divide powers with the same base, the base stays the same and we subtract the exponents.
2 a m a n = a m-n Example: = = = To simplify a power of a power, the base stays the same and we multiply the exponents. (a m ) n = a mn Example: ( ) 5 = x5 = 20 (6 8 ) = To simplify a power of a product, we distribute the exponent onto every factor of the base. (a x b) m = a m x b m Example: (5 x 6) = 5 x 6 ( x 9) = To simplify a power of a quotient, we distribute the exponent onto both the numerator and the denominator. n n a a = Example: n = = b b Any base raised to a power of 0 is equal to (as long as the base does not equal 0). a 0 =, a 0 Example: (-0) 0 = but -5 0 = Expressions with powers can have a numerical coefficient. Evaluate the power and then multiply by the coefficient. 7(-2) = 7 x (-8) = -7 2 = Evaluate expressions with powers using the proper order of operations **Remember** BEDMAS Brackets Exponents Divide and multiply in order from left to right Add and subtract in order from left to right Example: (- 2 ) = Chapter 2 Practice For # to 5, choose the best answer.. Four students were asked to write the numbers, 2, 0.7, 0.72, and 5 in ascending order. Which 7 student wrote the numbers in the correct order? A Albert : 0.7, 5 7, 2, 0.72, B Beth: 5 7, 0.7,, 2, 0.72 C Carmella: 0.7, 5 7, 0.72, 2, D Devin: 5 7, 0.7, 2, 0.72, 2. Which rational number is between.06 and.07 on a number line? A B 2 C 26 D Colin was asked to simplify the expression 6. His work is shown below. 8 6 Step = (6 ) Step 2 20 = 2 2 Step 7 = 2 2 Step 7 = 2 2 In which step did Colin make his first mistake? A Step B Step 2 C Step D Step
3 . Which rational number is not an example of a square number? A 96 B C 9 Complete the statements in #5 to 7. D A decimal number, to the nearest tenth, between 2 and 5 6 is. 6. The value of the expression.7.6 ( 2.) +.7 is. Short Answer 7. Determine the value of each of the following to the nearest tenth. a) 0.6 b) 6 8. Write the value of each expression in the form a b. 8 a) b) Between what two whole numbers does the square root of 2 lie? 0. Determine the number that has a square root of 2... Shavonne is wearing a flat, metal pendant in the shape of a square. The area of the pendant is 0 cm 2. Estimate the dimensions of the pendant. 2. The area of Mara s square pumpkin patch is 2.25 m 2. She has a square tomato garden with the same area. She wants to determine the dimensions of each garden. Mara s solution is shown below. A = s 2 2A = s 2 2(2.25) = s 2.5 = s 2.5 = s 2.2 = s What error did Mara make in her solution? Correct her solution and determine the dimensions of each garden. 5. John created a painting on a large piece of paper with a length of 2 m and a width of m. 8 a) Determine the area of the painting in lowest terms. Express your answer in the form b a c. b) John did not paint to the edges of the paper. He decides that he wants to crop the painting by cutting off m from each of the four sides of the paper. What are the new dimensions of the painting, written in the form a b?
4 c) What is the area of the cropped painting, in the form a, expressed in lowest terms? b. Match each letter on the number line to one of the following rational numbers Which integers are between 6 and 9 2? 6. Evaluate. Show your work. 7 2 b) + c) d) f) + 2 g) h) Chapter Practice For # to 5, select the best answer.. In the equation ( 2) 5 = 2, which number represents the base of the power? A 2 B 2 C D 2 2. Which expression is equivalent to ( 2) ( 2) ( 2) ( 2) ( 2)? A 2 5 B 2 C ( 2) 5 D ( 2) 5. What is the product of 5 2 and 5? A 650 B 25 6 C 5 8 D 5 6
5 . Devin was asked to simplify the expression 0 2 ( 2 0 ) 2. His work is shown below. 0 2 ( 2 0 ) 2 = 0 6 ( ) 2 Step = 0 6 Step 2 = 0 2 Step = Step In which step did Devin make his first mistake? A Step B Step 2 C Step D Step 5. Two students were asked to write each product of powers as a single power. Their work is shown below. Danica 2 = ( ) ( ) = 5 Frank 2 = 2 = 6 Which of the following statements about their procedures is true? A Frank s procedure contains an error and Danica s does not. B Danica s procedure contains an error and Frank s does not. C Both Danica and Frank have no errors in their procedure. D Both Danica and Frank have errors in their procedure. Complete the statements in #6 and The value of + 0 is. 7. The expression 5 0 Short Answer written as a fraction in simplified form is. 8. Arrange the powers in order from smallest value to largest value. ( ) 2, (2), (), ( ) 5 9. Write each expression as repeated multiplication. a) 7 b) ( 6) 5 c) ( 5) 0. Write each expression as a power in simplified form. a) b) (2 2 + ) c) ( 2 ). Explain in words the difference between the powers and. 2. For every metre a scuba diver dives below the water surface of a lake, the light intensity is reduced by 5%. The percent of light intensity can be represented by the equation I = 00( 0.05) d, where I is the intensity of light, as a percent, and d is the depth of the dive, in metres. The intensity of light at the surface of the lake is 00%. Austin wanted to determine the light intensity at a depth of m. His solution is shown below. I = 00( 0.05) d I = 00( 0.05) I = 00( 0.05 )
6 I = 00( ) I 00 Austin realized that it is not possible for the light intensity to be approximately 00% at a depth of m. Explain where Austin made his mistake. a) Correct Austin s mistake and provide a detailed solution to determine the percent of light intensity at a depth of m. Give your answer to the nearest whole percent. b) What is the light intensity at a depth of 5 m? Give your answer to the nearest whole percent.. What is the volume of a cube with a side length of cm? Show your work... A colony of bacteria triples every hour. There are 0 bacteria now. How many will there be after each amount of time? Show your work. a) h b) h c) 2 h d) n h Solutions for Chapter 2 Practice:. A 2. B. A. D , a) 0.6 b) a) 9 5 b) 7 9. and Should be A, not 2A. s = 5. a) 9 2 m b) 7 8 m by 5 m c) 85 2 m. A B 2. C 0. D 7 E 0.9 F ,,, 2,, 0,, 2,, 6. b) c) d) 7 f) 7 2 g) 2 h) Solutions for Chapter Practice:. D 2. C. D. A 5. D (), ( ) 5, 2, ( ) 2 9. a) 8 b) ( ) ( 6) ( 6) ( 6) ( 6) ( 6) c) a) 6 b) 7 c) 2 2. means that a base of is multiplied times: =. means that a base of is multiplied times: = a) In the third line, Austin incorrectly distributed the exponent over subtraction to the bases of and You can only distribute an exponent over multiplication: (ab) x = a x b x. I = 00(0.95) ; I = 00( ); I 86. The light intensity is approximately 86%. b) When d = 5, I = 6%.. Volume = = 6 cm. a) 0 = 90 b) 0 = 80 c) 0 2 = d) 0 n 6 Extra Practice: P #5, 6 0 (o.l),,, 6-2, 25 P #6 6, 8-22
4.1 Estimating Roots Name: Date: Goal: to explore decimal representations of different roots of numbers. Main Ideas:
4.1 Estimating Roots Name: Goal: to explore decimal representations of different roots of numbers Finding a square root Finding a cube root Multiplication Estimating Main Ideas: Definitions: Radical: an
More informationMath 2 Variable Manipulation Part 2 Powers & Roots PROPERTIES OF EXPONENTS:
Math 2 Variable Manipulation Part 2 Powers & Roots PROPERTIES OF EXPONENTS: 1 EXPONENT REVIEW PROBLEMS: 2 1. 2x + x x + x + 5 =? 2. (x 2 + x) (x + 2) =?. The expression 8x (7x 6 x 5 ) is equivalent to?.
More informationMATH 9 YEAR END REVIEW
Name: Block: MATH 9 YEAR END REVIEW Complete the following reviews in pencil. Use a separate piece of paper if you need more space. Please pay attention to whether you can use a calculator or not for each
More informationNAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4
Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as
More informationABE Math Review Package
P a g e ABE Math Review Package This material is intended as a review of skills you once learned and wish to review before your assessment. Before studying Algebra, you should be familiar with all of the
More informationSail into Summer with Math!
Sail into Summer with Math! For Students Entering Algebra 1 This summer math booklet was developed to provide students in kindergarten through the eighth grade an opportunity to review grade level math
More informationGrade 7. Critical concept: Integers. Curricular content. Examples and Strategies
Grade 7 Critical concept: Integers Curricular content Operations with integers Addition, subtraction, multiplication, division AND order of operations Examples and Strategies Always start with manipulatives.
More informationExam 2 Review Chapters 4-5
Math 365 Lecture Notes S. Nite 8/18/2012 Page 1 of 9 Integers and Number Theory Exam 2 Review Chapters 4-5 Divisibility Theorem 4-1 If d a, n I, then d (a n) Theorem 4-2 If d a, and d b, then d (a+b).
More information3.1 Solving Quadratic Equations by Factoring
3.1 Solving Quadratic Equations by Factoring A function of degree (meaning the highest exponent on the variable is ) is called a Quadratic Function. Quadratic functions are written as, for example, f(x)
More information8 th Grade Intensive Math
8 th Grade Intensive Math Ready Florida MAFS Student Edition August-September 2014 Lesson 1 Part 1: Introduction Properties of Integer Exponents Develop Skills and Strategies MAFS 8.EE.1.1 In the past,
More informationAdding and Subtracting Rational Expressions. Add and subtract rational expressions with the same denominator.
Chapter 7 Section 7. Objectives Adding and Subtracting Rational Expressions 1 3 Add and subtract rational expressions with the same denominator. Find a least common denominator. Add and subtract rational
More information6.1 Solving Quadratic Equations by Factoring
6.1 Solving Quadratic Equations by Factoring A function of degree 2 (meaning the highest exponent on the variable is 2), is called a Quadratic Function. Quadratic functions are written as, for example,
More informationChapter 3: Factors, Roots, and Powers
Chapter 3: Factors, Roots, and Powers Section 3.1 Chapter 3: Factors, Roots, and Powers Section 3.1: Factors and Multiples of Whole Numbers Terminology: Prime Numbers: Any natural number that has exactly
More informationExponents, Radicals, and Scientific Notation
General Exponent Rules: Exponents, Radicals, and Scientific Notation x m x n = x m+n Example 1: x 5 x = x 5+ = x 7 (x m ) n = x mn Example : (x 5 ) = x 5 = x 10 (x m y n ) p = x mp y np Example : (x) =
More informationBeginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions
1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations:
More informationNatural Whole Integer Rational Irrational Real. Sep 8 6:51 AM. Today we are starting our first non review unit REAL NUMBERS
Warm Up: 1. Prove that 0.14 can be written as a fraction 2. Mark a check in each column that idenfies the subset of the Real number system to which the number belongs. Natural Whole Integer Rational Irrational
More informationPowers and Exponents Mrs. Kornelsen
Powers and Exponents Mrs. Kornelsen Lesson One: Understanding Powers and Exponents We write 5 + 5 + 5 + 5 as 5 4 How do we write 8 + 8 + 8 + 8 + 8? How do you think we write 7 7 7? This is read as seven
More informationSome of the more common mathematical operations we use in statistics include: Operation Meaning Example
Introduction to Statistics for the Social Sciences c Colwell and Carter 206 APPENDIX H: BASIC MATH REVIEW If you are not using mathematics frequently it is quite normal to forget some of the basic principles.
More informationMultiplication and Division
UNIT 3 Multiplication and Division Skaters work as a pair to put on quite a show. Multiplication and division work as a pair to solve many types of problems. 82 UNIT 3 MULTIPLICATION AND DIVISION Isaac
More informationLinear Equations & Inequalities Definitions
Linear Equations & Inequalities Definitions Constants - a term that is only a number Example: 3; -6; -10.5 Coefficients - the number in front of a term Example: -3x 2, -3 is the coefficient Variable -
More information6.4. The Quadratic Formula. LEARN ABOUT the Math. Selecting a strategy to solve a quadratic equation. 2x 2 + 4x - 10 = 0
6.4 The Quadratic Formula YOU WILL NEED graphing calculator GOAL Understand the development of the quadratic formula, and use the quadratic formula to solve quadratic equations. LEARN ABOUT the Math Devlin
More informationChapter 2 INTEGERS. There will be NO CALCULATORS used for this unit!
Chapter 2 INTEGERS There will be NO CALCULATORS used for this unit! 2.2 What are integers? 1. Positives 2. Negatives 3. 0 4. Whole Numbers They are not 1. Not Fractions 2. Not Decimals What Do You Know?!
More information27 = 3 Example: 1 = 1
Radicals: Definition: A number r is a square root of another number a if r = a. is a square root of 9 since = 9 is also a square root of 9, since ) = 9 Notice that each positive number a has two square
More informationUnit 9 Study Sheet Rational Expressions and Types of Equations
Algebraic Fractions: Unit 9 Study Sheet Rational Expressions and Types of Equations Simplifying Algebraic Fractions: To simplify an algebraic fraction means to reduce it to lowest terms. This is done by
More informationPRE-ALGEBRA SUMMARY WHOLE NUMBERS
PRE-ALGEBRA SUMMARY WHOLE NUMBERS Introduction to Whole Numbers and Place Value Digits Digits are the basic symbols of the system 0,,,, 4,, 6, 7, 8, and 9 are digits Place Value The value of a digit in
More informationNumbers and Operations Review
C H A P T E R 5 Numbers and Operations Review This chapter reviews key concepts of numbers and operations that you need to know for the SAT. Throughout the chapter are sample questions in the style of
More informationMini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models
Mini Lecture. Introduction to Algebra: Variables and Mathematical Models. Evaluate algebraic expressions.. Translate English phrases into algebraic expressions.. Determine whether a number is a solution
More informationName: Math 9. Comparing & Ordering Rational Numbers. integers (positive or negative numbers, no decimals) and b 0
Page 1 Ch.2- Rational Numbers 2.1 Name: Math 9 What is a rational number? Comparing & Ordering Rational Numbers A number that can be expressed as a b (a fraction), where a and b are integers (positive
More informationReview Unit 2. Multiple Choice Identify the choice that best completes the statement or answers the question.
Review Unit 2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the index of. a. b. 3 c. 7 d. 2 2. Identify the radicand of. a. 4 b. c. 6 d. 8 3.
More informationRadical Expressions, Equations, and Functions
Radical Expressions, Equations, and Functions 0 Real-World Application An observation deck near the top of the Sears Tower in Chicago is 353 ft high. How far can a tourist see to the horizon from this
More informationEquations and Inequalities
Equations and Inequalities 2 Figure 1 CHAPTER OUTLINE 2.1 The Rectangular Coordinate Systems and Graphs 2.2 Linear Equations in One Variable 2.3 Models and Applications 2.4 Complex Numbers 2.5 Quadratic
More informationHSED Math Course Outcome Summary
Wisconsin Technical College System HSED 5.09 - Math Course Outcome Summary Course Information Description Learners will apply math concepts in real-world context including financial literacy consumer applications.
More information5.1. Integer Exponents and Scientific Notation. Objectives. Use the product rule for exponents. Define 0 and negative exponents.
Chapter 5 Section 5. Integer Exponents and Scientific Notation Objectives 2 4 5 6 Use the product rule for exponents. Define 0 and negative exponents. Use the quotient rule for exponents. Use the power
More informationAlgebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , )
Algebra I+ Pacing Guide Days Units Notes Chapter 1 (1.1-1.4, 1.6-1.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order
More informationMath 20-1 Functions and Equations Multiple Choice Questions
Math 0-1 Functions and Equations Multiple Choice Questions 1 7 18 simplifies to: A. 9 B. 10 C. 90 D. 4 ( x)(4 x) simplifies to: A. 1 x B. 1x 1 4 C. 1x D. 1 x 18 4 simplifies to: 6 A. 9 B. 4 C. D. 7 4 The
More informationMEP Practice Book ES6
6 Number System 6.5 Estimating Answers 1. Express each of the following correct to significant figures: 96.6 16.5 1.90 5 (d) 0.00 681 (e) 50.9 (f) 0.000 60 8 (g) 0.00 71 (h) 5.98 (i) 6.98. Write each of
More informationSection September 6, If n = 3, 4, 5,..., the polynomial is called a cubic, quartic, quintic, etc.
Section 2.1-2.2 September 6, 2017 1 Polynomials Definition. A polynomial is an expression of the form a n x n + a n 1 x n 1 + + a 1 x + a 0 where each a 0, a 1,, a n are real numbers, a n 0, and n is a
More informationAlgebra 1 Unit 6 Notes
Algebra 1 Unit 6 Notes Name: Day Date Assignment (Due the next class meeting) Monday Tuesday Wednesday Thursday Friday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday
More informationAlgebra I Unit Report Summary
Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02
More informationMaths Scheme of Work. Class: Year 10. Term: autumn 1: 32 lessons (24 hours) Number of lessons
Maths Scheme of Work Class: Year 10 Term: autumn 1: 32 lessons (24 hours) Number of lessons Topic and Learning objectives Work to be covered Method of differentiation and SMSC 11 OCR 1 Number Operations
More informationChapter 4: Exponents and Radicals
Math 0C Name: Chapter 4: Exponents and Radicals 4. Square Roots and Cube Roots Review. Evaluate the following. a. 8 b. 36 Outcome: Demonstrate an understanding of factors of whole numbers by determining
More informationRemember, you may not use a calculator when you take the assessment test.
Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.
More informationA constant is a value that is always the same. (This means that the value is constant / unchanging). o
Math 8 Unit 7 Algebra and Graphing Relations Solving Equations Using Models We will be using algebra tiles to help us solve equations. We will practice showing work appropriately symbolically and pictorially
More informationChapter 1: Fundamentals of Algebra Lecture notes Math 1010
Section 1.1: The Real Number System Definition of set and subset A set is a collection of objects and its objects are called members. If all the members of a set A are also members of a set B, then A is
More informationDay 3: Section P-6 Rational Expressions; Section P-7 Equations. Rational Expressions
1 Day : Section P-6 Rational Epressions; Section P-7 Equations Rational Epressions A rational epression (Fractions) is the quotient of two polynomials. The set of real numbers for which an algebraic epression
More information7.2 Rational Exponents
Section 7.2 Rational Exponents 49 7.2 Rational Exponents S Understand the Meaning of a /n. 2 Understand the Meaning of a m/n. 3 Understand the Meaning of a -m/n. 4 Use Rules for Exponents to Simplify Expressions
More informationChapter 5: Exponents and Polynomials
Chapter 5: Exponents and Polynomials 5.1 Multiplication with Exponents and Scientific Notation 5.2 Division with Exponents 5.3 Operations with Monomials 5.4 Addition and Subtraction of Polynomials 5.5
More informationClass 8: Numbers Exercise 3B
Class : Numbers Exercise B 1. Compare the following pairs of rational numbers: 1 1 i First take the LCM of. LCM = 96 Therefore: 1 = 96 Hence we see that < 6 96 96 1 1 1 1 = 6 96 1 or we can say that
More informationDivisibility, Factors, and Multiples
Divisibility, Factors, and Multiples An Integer is said to have divisibility with another non-zero Integer if it can divide into the number and have a remainder of zero. Remember: Zero divided by any number
More informationLesson 3.4 Exercises, pages
Lesson 3. Exercises, pages 17 A. Identify the values of a, b, and c to make each quadratic equation match the general form ax + bx + c = 0. a) x + 9x - = 0 b) x - 11x = 0 Compare each equation to ax bx
More informationUnit Essential Questions. What are the different representations of exponents? Where do exponents fit into the real number system?
Unit Essential Questions What are the different representations of exponents? Where do exponents fit into the real number system? How can exponents be used to depict real-world situations? REAL NUMBERS
More informationMath Precalculus I University of Hawai i at Mānoa Spring
Math 135 - Precalculus I University of Hawai i at Mānoa Spring - 2013 Created for Math 135, Spring 2008 by Lukasz Grabarek and Michael Joyce Send comments and corrections to lukasz@math.hawaii.edu Contents
More informationRevision Mathematics
Essential Mathematics & Statistics for Science by Dr G Currell & Dr A A Dowman Revision Mathematics To navigate through these notes - use the Bookmarks on the left-hand menu. Contents: Page Number Line
More informationRadical Expressions and Graphs 8.1 Find roots of numbers. squaring square Objectives root cube roots fourth roots
8. Radical Expressions and Graphs Objectives Find roots of numbers. Find roots of numbers. The opposite (or inverse) of squaring a number is taking its square root. Find principal roots. Graph functions
More informationArithmetic. Integers: Any positive or negative whole number including zero
Arithmetic Integers: Any positive or negative whole number including zero Rules of integer calculations: Adding Same signs add and keep sign Different signs subtract absolute values and keep the sign of
More informationSection 1.3 Review of Complex Numbers
1 Section 1. Review of Complex Numbers Objective 1: Imaginary and Complex Numbers In Science and Engineering, such quantities like the 5 occur all the time. So, we need to develop a number system that
More informationSect Definitions of a 0 and a n
5 Sect 5. - Definitions of a 0 and a n Concept # Definition of a 0. Let s examine the quotient rule when the powers are equal. Simplify: Ex. 5 5 There are two ways to view this problem. First, any non-zero
More informationArithmetic with Whole Numbers and Money Variables and Evaluation (page 6)
LESSON Name 1 Arithmetic with Whole Numbers and Money Variables and Evaluation (page 6) Counting numbers or natural numbers are the numbers we use to count: {1, 2, 3, 4, 5, ) Whole numbers are the counting
More informationChapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers
Fry Texas A&M University! Fall 2016! Math 150 Notes! Section 1A! Page 1 Chapter 1A -- Real Numbers Math Symbols: iff or Example: Let A = {2, 4, 6, 8, 10, 12, 14, 16,...} and let B = {3, 6, 9, 12, 15, 18,
More informationSummer Math Packet for Students Entering 6th Grade. Please have your student complete this packet and return it to school on Tuesday, September 4.
Summer Math Packet for Students Entering 6th Grade Please have your student complete this packet and return it to school on Tuesday, September. Work on your packet gradually. Complete one to two pages
More informationNote: In this section, the "undoing" or "reversing" of the squaring process will be introduced. What are the square roots of 16?
Section 8.1 Video Guide Introduction to Square Roots Objectives: 1. Evaluate Square Roots 2. Determine Whether a Square Root is Rational, Irrational, or Not a Real Number 3. Find Square Roots of Variable
More informationMath 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2
Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 April 11, 2016 Chapter 10 Section 1: Addition and Subtraction of Polynomials A monomial is
More information24 = 5x. 4.8 = x. December 13, 2017
Learning Target Extend learning about solving equations with integer coefficients to equations that involve fractions and decimals. Learn how to change fractional and decimal coefficients and constants
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 informationDecimals Topic 1: Place value
Topic : Place value QUESTION Write the following decimal numbers in expanded form. Hund- reds Tens U nits. Tenths Hundreths Thousandths a. 8 b. 6 c 8. 7 d. 8 9 e 7. 0 0 f 0 9. 0 6 QUESTION Write the following
More informationChapter 7 Rational Expressions, Equations, and Functions
Chapter 7 Rational Expressions, Equations, and Functions Section 7.1: Simplifying, Multiplying, and Dividing Rational Expressions and Functions Section 7.2: Adding and Subtracting Rational Expressions
More informationMath Lecture 3 Notes
Math 1010 - Lecture 3 Notes Dylan Zwick Fall 2009 1 Operations with Real Numbers In our last lecture we covered some basic operations with real numbers like addition, subtraction and multiplication. This
More informationWhat Fun! It's Practice with Scientific Notation!
What Fun! It's Practice with Scientific Notation! Review of Scientific Notation Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction. The number 100,000,000
More informationSect Complex Numbers
161 Sect 10.8 - Complex Numbers Concept #1 Imaginary Numbers In the beginning of this chapter, we saw that the was undefined in the real numbers since there is no real number whose square is equal to a
More informationA group of figures, representing a number, is called a numeral. Numbers are divided into the following types.
1. Number System Quantitative Aptitude deals mainly with the different topics in Arithmetic, which is the science which deals with the relations of numbers to one another. It includes all the methods that
More information12.2 Simplifying Radical Expressions
x n a a m 1 1 1 1 Locker LESSON 1. Simplifying Radical Expressions Texas Math Standards The student is expected to: A.7.G Rewrite radical expressions that contain variables to equivalent forms. Mathematical
More informationSail into Summer with Math!
Sail into Summer with Math! For Students Entering Investigations into Mathematics This summer math booklet was developed to provide students in kindergarten through the eighth grade an opportunity to review
More informationQ 1 Find the square root of 729. 6. Squares and Square Roots Q 2 Fill in the blank using the given pattern. 7 2 = 49 67 2 = 4489 667 2 = 444889 6667 2 = Q 3 Without adding find the sum of 1 + 3 + 5 + 7
More informationName Period Date MATHLINKS GRADE 8 STUDENT PACKET 11 EXPONENTS AND ROOTS
Name Period Date 8-11 STUDENT PACKET MATHLINKS GRADE 8 STUDENT PACKET 11 EXPONENTS AND ROOTS 11.1 Squares and Square Roots Use numbers and pictures to understand the inverse relationship between squaring
More informationPart 1 - Pre-Algebra Summary Page 1 of 22 1/19/12
Part 1 - Pre-Algebra Summary Page 1 of 1/19/1 Table of Contents 1. Numbers... 1.1. NAMES FOR NUMBERS... 1.. PLACE VALUES... 3 1.3. INEQUALITIES... 4 1.4. ROUNDING... 4 1.5. DIVISIBILITY TESTS... 5 1.6.
More informationDecimal Addition: Remember to line up the decimals before adding. Bring the decimal straight down in your answer.
Summer Packet th into 6 th grade Name Addition Find the sum of the two numbers in each problem. Show all work.. 62 2. 20. 726 + + 2 + 26 + 6 6 Decimal Addition: Remember to line up the decimals before
More informationIntegers. number AnD AlgebrA NuMber ANd place value
2 2A Adding and subtracting integers 2B Multiplying integers 2C Dividing integers 2D Combined operations on integers WhAT Do You know? Integers 1 List what you know about positive and negative integers.
More informationSchool of Distance Education MATHEMATICAL TOOLS FOR ECONOMICS - I I SEMESTER COMPLEMENTARYCOURSE BA ECONOMICS. (CUCBCSS Admission)
MATHEMATICAL TOOLS FOR ECONOMICS - I I SEMESTER COMPLEMENTARYCOURSE BA ECONOMICS (CUCBCSS - 014 Admission) UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION Calicut university P.O, Malappuram Kerala,
More informationChapter 1 Indices & Standard Form
Chapter 1 Indices & Standard Form Section 1.1 Simplifying Only like (same letters go together; same powers and same letter go together) terms can be grouped together. Example: a 2 + 3ab + 4a 2 5ab + 10
More informationMath 9 Midterm Review
Class: Date: Math 9 Midterm Review Short Answer 1. Which graphs represent a linear relation? 2. Which expressions have negative values? È i) ( 4) 3 3 ÎÍ Ê ii) 4 3 ˆ 3 È iii) ( 4) 3 3 ÎÍ È iv) ( 4) 3 3
More informationContents. 2 Lesson. Common Core State Standards. Lesson 1 Irrational Numbers Lesson 2 Square Roots and Cube Roots... 14
Contents Common Core State Standards Lesson 1 Irrational Numbers.... 4 Lesson 2 Square Roots and Cube Roots... 14 Lesson 3 Scientific Notation... 24 Lesson 4 Comparing Proportional Relationships... 34
More informationFoundations of Mathematics and Pre-Calculus 10. Sample Questions for Algebra and Number. Teacher Version
Foundations of Mathematics and Pre-Calculus 0 Sample Questions for Algebra and Number Teacher Version Instructions. You may require a protractor and a ruler (metric and imperial) for paper versions of
More informationRAVEN S CORE MATHEMATICS GRADE 8
RAVEN S CORE MATHEMATICS GRADE 8 MODIFIED PROGRAM (Designed for the Western Provinces and the Territories) STUDENT GUIDE AND RESOURCE BOOK The Key to Student Success One of a series of publications by
More informationUNIT 4: RATIONAL AND RADICAL EXPRESSIONS. 4.1 Product Rule. Objective. Vocabulary. o Scientific Notation. o Base
UNIT 4: RATIONAL AND RADICAL EXPRESSIONS M1 5.8, M2 10.1-4, M3 5.4-5, 6.5,8 4.1 Product Rule Objective I will be able to multiply powers when they have the same base, including simplifying algebraic expressions
More informationName Date Class California Standards Prep for 4.0. Variables and Expressions
California Standards Prep for 4.0 To translate words into algebraic expressions, find words like these that tell you the operation. add subtract multiply divide sum difference product quotient more less
More informationGrade 8 Please show all work. Do not use a calculator! Please refer to reference section and examples.
Grade 8 Please show all work. Do not use a calculator! Please refer to reference section and examples. Name Date due: Tuesday September 4, 2018 June 2018 Dear Middle School Parents, After the positive
More informationSTUDY GUIDE Math 20. To accompany Intermediate Algebra for College Students By Robert Blitzer, Third Edition
STUDY GUIDE Math 0 To the students: To accompany Intermediate Algebra for College Students By Robert Blitzer, Third Edition When you study Algebra, the material is presented to you in a logical sequence.
More informationNever leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!!
1 ICM Unit 0 Algebra Rules Lesson 1 Rules of Exponents RULE EXAMPLE EXPLANANTION a m a n = a m+n A) x x 6 = B) x 4 y 8 x 3 yz = When multiplying with like bases, keep the base and add the exponents. a
More informationAlg. 1 Radical Notes
Alg. 1 Radical Notes Evaluating Square Roots and Cube Roots (Day 1) Objective: SWBAT find the square root and cube roots of monomials Perfect Squares: Perfect Cubes: 1 =11 1 = 11 =1111 11 1 =111 1 1 =
More informationNUMBER. Here are the first 20 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.
NUMBER Types of Number Prime Numbers A prime number is a number which can only be divided by 1 or itself. The smallest prime number is 2. 2 can only be divided by 2 or 1. Here are the first 20 prime numbers:
More informationA number that can be written as, where p and q are integers and q Number.
RATIONAL NUMBERS 1.1 Definition of Rational Numbers: What are rational numbers? A number that can be written as, where p and q are integers and q Number. 0, is known as Rational Example:, 12, -18 etc.
More informationAn equation is a statement that states that two expressions are equal. For example:
Section 0.1: Linear Equations Solving linear equation in one variable: An equation is a statement that states that two expressions are equal. For example: (1) 513 (2) 16 (3) 4252 (4) 64153 To solve the
More informationMini Lecture 9.1 Finding Roots
Mini Lecture 9. Finding Roots. Find square roots.. Evaluate models containing square roots.. Use a calculator to find decimal approimations for irrational square roots. 4. Find higher roots. Evaluat. a.
More informationMath Precalculus I University of Hawai i at Mānoa Spring
Math 135 - Precalculus I University of Hawai i at Mānoa Spring - 2014 Created for Math 135, Spring 2008 by Lukasz Grabarek and Michael Joyce Send comments and corrections to lukasz@math.hawaii.edu Contents
More informationOHS Algebra 1 Summer Packet
OHS Algebra 1 Summer Packet Good Luck to: Date Started: (please print student name here) 8 th Grade Math Teacher s Name: Complete each of the following exercises in this formative assessment. To receive
More informationSection 3-4: Least Common Multiple and Greatest Common Factor
Section -: Fraction Terminology Identify the following as proper fractions, improper fractions, or mixed numbers:, proper fraction;,, improper fractions;, mixed number. Write the following in decimal notation:,,.
More information3. Student will read teacher's notes and examples for each concept. 4. Student will complete skills practice questions for each concept.
Welcome to 8 th Grade, 8th Grade Summer Math Assignment: 1. Student will complete all 25 assignments on Buzz Math 2. Student will complete Pretest. 3. Student will read teacher's notes and examples for
More informationRational Numbers. An Introduction to the Unit & Math 8 Review. Math 9 Mrs. Feldes
Rational Numbers An Introduction to the Unit & Math 8 Review Math 9 Mrs. Feldes In this Unit, we will: Compare & order numbers using a variety of strategies. Strategies include: drawing pictures & number
More informationMATHS QUEST 8 for the Australian Curriculum
MATHS QUEST 8 for the Australian Curriculum 2 2A Adding and subtracting integers 2B Multiplying integers 2C Dividing integers 2D Combined operations on integers WHAT DO YOU KNOW? Integers 1 List what you
More informationSOLUTIONS FOR PROBLEMS 1-30
. Answer: 5 Evaluate x x + 9 for x SOLUTIONS FOR PROBLEMS - 0 When substituting x in x be sure to do the exponent before the multiplication by to get (). + 9 5 + When multiplying ( ) so that ( 7) ( ).
More information