Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.


 Phoebe O’Neal’
 1 years ago
 Views:
Transcription
1 Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704: Statistical Analysis for Public Policy will be better prepared for the course. For some students, this Basic Math Refresher will be rudimentary. Other students may need to spend more time reviewing the material and working through problems. Students may take the test as many times as they need to. Each student must score better than 85% on each assessment. The Basic Math Refresher covers the following topics: I) Fractions and Decimals, II) Percents; III) Exponents and Radicals; IV) Order of Arithmetic Operations; V) Basic Algebra and VI) Basic Coordinate Geometry. It is recommended that students print off the Basic Math Refresher Tutorial to review before taking the assessment. I. Fractions and Decimals Fractions, decimals and percents are all numbers that represent a part of the whole. We often need to convert from fractions to decimals or percents or from decimals to percents or fractions. Example: Fraction Decimal Percent.20 20% Converting a fraction to a decimal Divide the numerator (the top number) by the denominator (the bottom number) in your calculator. Example: or Note that the final decimal in this example is expressed to three decimal places. When you round a decimal, you round up if the number following is 5, 6, 7, 8, or 9 (as we did here) and you round down if the number following is 0,, 2, 3, or 4 (as in ) Converting a decimal to a percent Move the decimal point two places to the right. What you are doing is multiplying the decimal by 00 and attaching a % sign. Example: = 28.6%
2 Converting a percent to a decimal Move the decimal point two places to the left. What you are doing is dividing the percentage by 00 and removing the % sign. Example: 0.8% =.08 Converting a percent to a fraction Put the number over 00 and reduce (i.e. simplify the fraction so that the top number and bottom number cannot be divided by the same number.) Example: 56% = Convert a decimal to a fraction Determine how many numbers follow the decimal place (i.e. the number of decimal places.) If there is one decimal place, place the number over 0 and reduce. If there are two decimal places, place the number over 00 and reduce. If there are three decimal places, place the number over 000 and reduce. And so on. Example: 0.06 = = Adding and subtracting fractions To add or subtract fractions, each fraction must have the same denominator (i.e. the same number in the bottom of the fraction.) If the denominators are different, you must find the lowest common denominator (LCD.) The LCD is the smallest number that is divisible by the denominator of each fraction. Once you determine the LCD, you multiply the top and the bottom by the number that will make the denominator of the fraction equal to the LCD. Then add the two numerators (i.e. numbers in the top) and put that sum over the LCD. Example: =? These fractions have different denominators (3 and 4.) The LCD is 2 because it is the smallest number into which both 3 and 4 are evenly divided. To make the denominator of the first fraction equal to 2, multiply the top and the bottom of the fraction by 4. To make the denominator of the second fraction equal to 2, multiply the top and the bottom of the fraction by 3: So, is the same as 2
3 Example: =? The LCD is 30. So, is the same as Multiplying and dividing fractions To multiply fractions, simply multiply across the top and across the bottom of the fractions. Example:? Since 2 x = 2 and 5 x 3 = 5, the answer is To divide fractions, take the reciprocal of the second fraction (i.e. flip the second fraction) and multiply it by the first. Example:? Flip the second fraction and change the divide symbol to a multiplication symbol x ? Then multiply the two fractions II. Percents Find one number as a percent of another Divide the first number by the second number. Move the decimal two places to the right and attach a % sign. Example: The number 5 is what percent of 48? Divide 5 by 48: 5 48 =.325 Move the decimal over two places to the right and add % sign: 3.25% So, 5 is 3.25% of 48 homes. Find a given percent of a number Convert the given percent to a decimal. Multiply the number by that decimal. Example: What is 62.% of 205? Convert 62.% into a decimal: 0.62 Multiply 205 by 0.62: 205 * 0.62 = So, is 62.% of
4 Find the percent change Calculate the difference between the first and second numbers. Divide that difference by the first number. Convert the resulting decimal to a percent. Example: Calculate the percent increase from 50 to 205. Find the difference: = 55 Divide difference by starting value: = Convert decimal to percentage: 36.7% So, the percent increase is 36.7%. III. Exponents and Radicals Positive Exponents Exponents (or powers) indicate that a number is multiplied by itself a certain number of times. In other words, exponents are just a short hand way of writing out a number multiplied by itself. For example, if we see 5 2 (said five squared and sometimes written as 5^2), it is the same thing as 5 * 5. The number that is to be multiplied by itself is called the base. How many times the number is to be multiplied by itself is called the exponent or the power. Be very careful when a negative number is raised to a power. Be sure to keep track of the sign. A negative number multiplied by itself an even number of times will give a positive number result. A negative number multiplied by itself an odd number of times will give a negative number. For example, (2) 2 is equal to (2)*(2) = 4. (try it!) Note that the exponent is even and the resulting answer is positive. However, (2) 3 is equal to (2)*(2)*(2) = 8. (try it!) Note that the exponent in this case is odd and the resulting answer is negative. Some calculators have a ^ key that allows you to enter in an expression with an exponent directly. In other words, you can key in 3^2= to get 9. See below. 4
5 If your calculator does not have a ^ key, then you need to type in the multiplication expression i.e. for 3 2 you need to type 3 * 3. Example: Find = * = Example: Find (3.5) 5 (3.5) 5 = (3.5)*(3.5)*(3.5)*(3.5)*(3.5) = Negative Exponents Exponents can also be negative. Negative exponents are treated differently. We will not be using negative exponents in the class. Radicals Radicals (or roots) are sort of the opposite of positive exponents. The radical is the symbol placed over a number. The most common radical is the square root,. The square root is the number you need to multiply by itself twice to get the number that is under the radical. For example, the square root of 4, or 4, is equal to 2 (or 2) because when you multiply 2 (or 2) by itself two times, you get 4. 5
6 There are other higher order roots, such as the cube root,, or the fourth root,. In these cases, the root is the number that is multiplied by itself 3 or 4 times to get the number under the radical. For example, the cube root of 8, 8, is 2 because 2*2*2 or 2 3 equals 8. Your calculator should have a square root button. On some calculators, you need to hit the square root button first and then the number. On other calculators, you hit the buttons in reverse order. Note: Your calculator will only show you the positive square root. Graphing calculators will have options for calculating higher order roots. Example: Find 25 Since 5*5 = 25, 5 is a square root of 25. (5 is also a square root of 25.) IV. Order of Arithmetic Operations When performing a series of arithmetic operations (i.e. addition, subtraction, division, multiplication, exponents), you must perform those operations in a particular order. There is a mnemonic to help you remember the order  PEMDAS: P E M D A S Parentheses Exponents Multiplication Division Addition Subtraction If you have a series of operations, do what s in parentheses first, then apply exponents, then do any multiplication or division, and finally do any adding or subtracting. Example: 432 2? Do what s in parentheses first (find LCD): 2 So now we have 43 2 =? Now apply exponents: 2 8 So now we have 43 8 =? 6
7 Now do multiplication: 3 So now we have 4 8 Now do addition and subtraction (find LCD): 4 So our answer is. 8 is the same as V. Basic Algebra An algebraic expression is a combination of numbers and variables connected by some mathematical operation, like addition, subtraction, multiplication or division. A variable is a letter (we often use x and y) that represents or is a holding place for a number. In statistical analysis, we will define variables and sometimes will use algebraic equations to relate two (or more) variables. Examples of algebraic expressions: 2x + y, 5d, 0r Evaluating an Algebraic Expression To evaluate an algebraic expression, replace the variable with the given number. Example: Evaluate 2x + 5 when x = 0. Substitute 0 in for x: 2(0) + 5 Solve: 2*0 + 5 = 25 (Note: 2 * 0 is the same as 2(0).) Equations An equation is two expressions set equal to each other. For example, = 4 is an equation. Equations can include variables (such as x and y). So, for another example, 3x 5 = 0 is an equation (though it is only true for one value of x.) The solution to an equation is the number, such that when you replace the variable, makes the equation true (i.e. the left side equals the right side.) Example: Determine if any of these values of x is a solution to the following equation: 3x 5 = 0 a) x = 5 b) x = 5 Substitute in the value for x (x = 5) and solve: 3(5) 5 =? 5 5 = 0 So, x = 5 is a solution because the left hand side equals 0 and the right hand side equals 0. Now try x = 5: 3(5) 5 =? 5 5 = 20 χ x = 5 is not a solution because the left hand side equals 20 and the right hand side equals 0. 7
8 General Solutions to a Linear Equation Sometimes you will be given a linear equation and will need to solve for x (i.e. find a value for x that makes the equation true.) To solve linear equations, remember the following properties:  If you add or subtract a value from both sides of an equation, then the equation is still true. For example: If you have the equation 2x = 4 and add 5 to both sides (like this: 2x + 5 = 4 + 5) then the equation is still true.  If you multiply or divide on both sides of an equation by the same number (except 0), then the equation remains true. For example: If you have the equation 2x = 4 and divide both sides by 2 (like this: 2x 2 = 4 2 or x = 2) then the equation will still be true. You use these properties to solve a linear equation. Example: Solve the following equation for x: x + 5 = 2 Subtract 5 from both sides: x = 2 5 x = 7 So, x = 7 is the solution to this linear equation (i.e. 7 is the value for x that makes the equation true.) Example: Solve the following equation for x: 3x 4 = 8 Add 4 to both sides: 3x = x = 2 Divide both sides by 3 (to get x alone): 3x 3 = 2 3 x = 4 Remember: if you divide by a fraction (e.g. ), it is the same thing as multiplying by the reciprocal or inverse of the fraction (e.g., or 2) VI. Basic Coordinate Geometry Points on a coordinate plane A coordinate plane is often very useful for writing linear equations with two variables. The coordinate plane is formed by a horizontal axis (xaxis) and a vertical axis (yaxis). The two axes intersect at a point called the origin. Points are plotted on a coordinate plane using a set of ordered pairs (x,y.) The first number in the ordered pair indicates how many spaces to move along the xaxis and the second number in the ordered pair indicates how many spaces to move along the yaxis. 8
9 yaxis (,2) origin xaxis Example: Write the coordinates of the point shown on the coordinate plane. Because the point is located 4 units right along the xaxis, the xvalue of the point is 4. Because the point is located unit up along the yaxis, the yvalue of the point is. Therefore, the x, y coordinates of the point are (4,.) Note: points along the xaxis to the left of the origin are negative and points along the yaxis below the origin are negative. 9
This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the
More informationAlgebra 1A and 1B Summer Packet
Algebra 1A and 1B Summer Packet Name: Calculators are not allowed on the summer math packet. This packet is due the first week of school and will be counted as a grade. You will also be tested over the
More informationAlgebra 1 Chapter 3 Vocabulary. equivalent  Equations with the same solutions as the original equation are called.
Chapter 3 Vocabulary equivalent  Equations with the same solutions as the original equation are called. formula  An algebraic equation that relates two or more reallife quantities. unit rate  A rate
More informationPractice Math Placement Exam
Practice Math Placement Exam The following are problems like those on the Mansfield University Math Placement Exam. You must pass this test or take MA 0090 before taking any mathematics courses. 1. What
More informationTYPES OF NUMBERS. Example 2. Example 1. Problems. Answers
TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime
More informationAccuplacer Arithmetic Study Guide
Testing Center Student Success Center Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
More informationThe integer is the base number and the exponent (or power). The exponent tells how many times the base number is multiplied by itself.
Exponents An integer is multiplied by itself one or more times. The integer is the base number and the exponent (or power). The exponent tells how many times the base number is multiplied by itself. Example:
More informationFractions and Linear Equations
Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps
More informationChapter 15 Radical Expressions and Equations Notes
Chapter 15 Radical Expressions and Equations Notes 15.1 Introduction to Radical Expressions The symbol is called the square root and is defined as follows: a = c only if c = a Sample Problem: Simplify
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 informationMBA Jump Start Program
MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Online Appendix: Basic Mathematical Concepts 2 1 The Number Spectrum Generally we depict numbers increasing from left to right
More informationEXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS
To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires
More informationSelfDirected Course: Transitional Math Module 2: Fractions
Lesson #1: Comparing Fractions Comparing fractions means finding out which fraction is larger or smaller than the other. To compare fractions, use the following inequality and equal signs:  greater than
More informationMyMathLab ecourse for Developmental Mathematics
MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and
More informationAlgebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.
Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear
More informationALGEBRA 1/ALGEBRA 1 HONORS
ALGEBRA 1/ALGEBRA 1 HONORS CREDIT HOURS: 1.0 COURSE LENGTH: 2 Semesters COURSE DESCRIPTION The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical
More informationA coordinate system is formed by the intersection of two number lines, the horizontal axis and the vertical axis. Consider the number line.
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. An exponent indicates the number the base is to be multiplied by. The exponent indicates the
More informationSTUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS
STUDY GUIDE FOR SOME BASIC INTERMEDIATE ALGEBRA SKILLS The intermediate algebra skills illustrated here will be used extensively and regularly throughout the semester Thus, mastering these skills is an
More informationIntegration Unit 5 Quadratic Toolbox 1: Working with Square Roots. Using your examples above, answer the following:
Integration Unit 5 Quadratic Toolbox 1: Working with Square Roots Name Period Objective 1: Understanding Square roots Defining a SQUARE ROOT: Square roots are like a division problem but both factors must
More informationMATH 65 NOTEBOOK CERTIFICATIONS
MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (1,3), (3,3), (2,3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the xcomponent of a point in the form (x,y). Range refers to the set of possible values of the ycomponent of a point in
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More information3.1. RATIONAL EXPRESSIONS
3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers
More informationThe xintercepts of the graph are the xvalues for the points where the graph intersects the xaxis. A parabola may have one, two, or no xintercepts.
Chapter 101 Identify Quadratics and their graphs A parabola is the graph of a quadratic function. A quadratic function is a function that can be written in the form, f(x) = ax 2 + bx + c, a 0 or y = ax
More information2.3. Finding polynomial functions. An Introduction:
2.3. Finding polynomial functions. An Introduction: As is usually the case when learning a new concept in mathematics, the new concept is the reverse of the previous one. Remember how you first learned
More informationModuMath Algebra Lessons
ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations
More informationascending order decimal denominator descending order Numbers listed from largest to smallest equivalent fraction greater than or equal to SOL 7.
SOL 7.1 ascending order Numbers listed in order from smallest to largest decimal The numbers in the base 10 number system, having one or more places to the right of a decimal point denominator The bottom
More informationMath 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4)
Chapter 2: Functions and Linear Functions 1. Know the definition of a relation. Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4) 2. Know the definition of a function. 3. What
More informationNumber Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
More informationAlgebra I Credit Recovery
Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,
More informationSummer Mathematics Packet Say Hello to Algebra 2. For Students Entering Algebra 2
Summer Math Packet Student Name: Say Hello to Algebra 2 For Students Entering Algebra 2 This summer math booklet was developed to provide students in middle school an opportunity to review grade level
More informationWord Problems. Simplifying Word Problems
Word Problems This sheet is designed as a review aid. If you have not previously studied this concept, or if after reviewing the contents you still don t pass, you should enroll in the appropriate math
More informationSection P.9 Notes Page 1 P.9 Linear Inequalities and Absolute Value Inequalities
Section P.9 Notes Page P.9 Linear Inequalities and Absolute Value Inequalities Sometimes the answer to certain math problems is not just a single answer. Sometimes a range of answers might be the answer.
More informationIntroduction to the Practice Exams
Introduction to the Practice Eams The math placement eam determines what math course you will start with at North Hennepin Community College. The placement eam starts with a 1 question elementary algebra
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 informationARITHMETIC. Overview. Testing Tips
ARITHMETIC Overview The Arithmetic section of ACCUPLACER contains 17 multiple choice questions that measure your ability to complete basic arithmetic operations and to solve problems that test fundamental
More informationMATH0910 Review Concepts (Haugen)
Unit 1 Whole Numbers and Fractions MATH0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,
More information1.1 Solving a Linear Equation ax + b = 0
1.1 Solving a Linear Equation ax + b = 0 To solve an equation ax + b = 0 : (i) move b to the other side (subtract b from both sides) (ii) divide both sides by a Example: Solve x = 0 (i) x = 0 x = (ii)
More informationProject 4: Simplifying Expressions with Radicals
Project 4: Simplifying Expressions with Radicals Defintion A radical, which we symbolize with the sign, is just the opposite of an exponent. In this class, the only radical we will focus on is square roots,
More informationSection R.2. Fractions
Section R.2 Fractions Learning objectives Fraction properties of 0 and 1 Writing equivalent fractions Writing fractions in simplest form Multiplying and dividing fractions Adding and subtracting fractions
More informationAssociative Property The property that states that the way addends are grouped or factors are grouped does not change the sum or the product.
addend A number that is added to another in an addition problem. 2 + 3 = 5 The addends are 2 and 3. area The number of square units needed to cover a surface. area = 9 square units array An arrangement
More informationSection 3.2. Graphing linear equations
Section 3.2 Graphing linear equations Learning objectives Graph a linear equation by finding and plotting ordered pair solutions Graph a linear equation and use the equation to make predictions Vocabulary:
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 Help and Additional Practice Websites
Name: Math Help and Additional Practice Websites http://www.coolmath.com www.aplusmath.com/ http://www.mathplayground.com/games.html http://www.ixl.com/math/grade7 http://www.softschools.com/grades/6th_and_7th.jsp
More informationy x x 2 Squares, square roots, cubes and cube roots TOPIC 2 4 x 2 2ndF 2ndF Oral activity Discuss squares, square roots, cubes and cube roots
TOPIC Squares, square roots, cubes and cube roots By the end of this topic, you should be able to: ü Find squares, square roots, cubes and cube roots of positive whole numbers, decimals and common fractions
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 informationExam 2 Review. 3. How to tell if an equation is linear? An equation is linear if it can be written, through simplification, in the form.
Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? To solve an equation is to find the solution set, that is, to find the set of all elements in the domain of the
More informationUnit 7: Radical Functions & Rational Exponents
Date Period Unit 7: Radical Functions & Rational Exponents DAY 0 TOPIC Roots and Radical Expressions Multiplying and Dividing Radical Expressions Binomial Radical Expressions Rational Exponents 4 Solving
More informationBrunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year.
Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year. Goal The goal of the summer math program is to help students
More informationAlgebra 1: Topic 1 Notes
Algebra 1: Topic 1 Notes Review: Order of Operations Please Parentheses Excuse Exponents My Multiplication Dear Division Aunt Addition Sally Subtraction Table of Contents 1. Order of Operations & Evaluating
More informationPREPARATION FOR MATH TESTING at CityLab Academy
PREPARATION FOR MATH TESTING at CityLab Academy compiled by Gloria Vachino, M.S. Refresh your math skills with a MATH REVIEW and find out if you are ready for the math entrance test by taking a PRETEST
More informationHigh School Mathematics Algebra
High School Mathematics Algebra This course is designed to give students the foundation of understanding algebra at a moderate pace. Essential material will be covered to prepare the students for Geometry.
More informationThis is a square root. The number under the radical is 9. (An asterisk * means multiply.)
Page of Review of Radical Expressions and Equations Skills involving radicals can be divided into the following groups: Evaluate square roots or higher order roots. Simplify radical expressions. Rationalize
More informationDomain Essential Question Common Core Standards Resources
Middle School Math 20162017 Domain Essential Question Common Core Standards First Ratios and Proportional Relationships How can you use mathematics to describe change and model real world solutions? How
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationHFCC Math Lab Arithmetic  4. Addition, Subtraction, Multiplication and Division of Mixed Numbers
HFCC Math Lab Arithmetic  Addition, Subtraction, Multiplication and Division of Mixed Numbers Part I: Addition and Subtraction of Mixed Numbers There are two ways of adding and subtracting mixed numbers.
More informationAlgebra Course KUD. Green Highlight  Incorporate notation in class, with understanding that not tested on
Algebra Course KUD Yellow Highlight Need to address in Seminar Green Highlight  Incorporate notation in class, with understanding that not tested on Blue Highlight Be sure to teach in class Postive and
More informationMATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationSummer Math Packet. Number Sense & Math Skills For Students Entering PreAlgebra. No Calculators!!
Summer Math Packet Number Sense & Math Skills For Students Entering PreAlgebra No Calculators!! Within the first few days of your PreAlgebra course you will be assessed on the prerequisite skills outlined
More informationGraphing Linear Equations in Two Variables
Math 123 Section 3.2  Graphing Linear Equations Using Intercepts  Page 1 Graphing Linear Equations in Two Variables I. Graphing Lines A. The graph of a line is just the set of solution points of the
More information2. Simplify. College Algebra Student SelfAssessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses
College Algebra Student SelfAssessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2
More information1.3 Algebraic Expressions
1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,
More informationClick on the links below to jump directly to the relevant section
Click on the links below to jump directly to the relevant section What is algebra? Operations with algebraic terms Mathematical properties of real numbers Order of operations What is Algebra? Algebra is
More informationOrdered Pairs. Graphing Lines and Linear Inequalities, Solving System of Linear Equations. Cartesian Coordinates System.
Ordered Pairs Graphing Lines and Linear Inequalities, Solving System of Linear Equations Peter Lo All equations in two variables, such as y = mx + c, is satisfied only if we find a value of x and a value
More informationx button, the number 13, close
Calculator Skills: Know the difference between the negative button (by the decimal point) and the subtraction button (above the plus sign). Know that your calculator automatically does order of operations,
More information1.6 The Order of Operations
1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative
More informationAble Enrichment Centre  Prep Level Curriculum
Able Enrichment Centre  Prep Level Curriculum Unit 1: Number Systems Number Line Converting expanded form into standard form or vice versa. Define: Prime Number, Natural Number, Integer, Rational Number,
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 informationDevelopmental Math Course Outcomes and Objectives
Developmental Math Course Outcomes and Objectives I. Math 0910 Basic Arithmetic/PreAlgebra Upon satisfactory completion of this course, the student should be able to perform the following outcomes and
More informationAlgebra Cheat Sheets
Sheets Algebra Cheat Sheets provide you with a tool for teaching your students notetaking, problemsolving, and organizational skills in the context of algebra lessons. These sheets teach the concepts
More informationWelcome to Basic Math Skills!
Basic Math Skills Welcome to Basic Math Skills! Most students find the math sections to be the most difficult. Basic Math Skills was designed to give you a refresher on the basics of math. There are lots
More informationChapter 4 Fractions and Mixed Numbers
Chapter 4 Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers Parts of a Fraction Whole numbers are used to count whole things. To refer to a part of a whole, fractions are used.
More informationYear 8  Maths Autumn Term
Year 8  Maths Autumn Term Whole Numbers and Decimals Order, add and subtract negative numbers. Recognise and use multiples and factors. Use divisibility tests. Recognise prime numbers. Find square numbers
More informationA Quick Algebra Review
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals
More informationCourse Title: Honors Algebra Course Level: Honors Textbook: Algebra 1 Publisher: McDougall Littell
Course Title: Honors Algebra Course Level: Honors Textbook: Algebra Publisher: McDougall Littell The following is a list of key topics studied in Honors Algebra. Identify and use the properties of operations
More informationOrder of Operations  PEMDAS. Rules for Multiplying or Dividing Positive/Negative Numbers
Order of Operations  PEMDAS *When evaluating an expression, follow this order to complete the simplification: Parenthesis ( ) EX. (52)+3=6 (5 minus 2 must be done before adding 3 because it is in parenthesis.)
More informationVariable. 1.1 Order of Operations. August 17, evaluating expressions ink.notebook. Standards. letter or symbol used to represent a number
1.1 evaluating expressions ink.notebook page 8 Unit 1 Basic Equations and Inequalities 1.1 Order of Operations page 9 Square Cube Variable Variable Expression Exponent page 10 page 11 1 Lesson Objectives
More informationMath. MCC5.OA.1 Use parentheses, brackets, or braces in. these symbols. 11/5/2012 1
MCC5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 11/5/2012 1 MCC5.OA.2 Write simple expressions that record calculations with numbers,
More informationALGEBRA I A PLUS COURSE OUTLINE
ALGEBRA I A PLUS COURSE OUTLINE OVERVIEW: 1. Operations with Real Numbers 2. Equation Solving 3. Word Problems 4. Inequalities 5. Graphs of Functions 6. Linear Functions 7. Scatterplots and Lines of Best
More informationMathematical Procedures
CHAPTER 6 Mathematical Procedures 168 CHAPTER 6 Mathematical Procedures The multidisciplinary approach to medicine has incorporated a wide variety of mathematical procedures from the fields of physics,
More informationNorwalk La Mirada Unified School District. Algebra Scope and Sequence of Instruction
1 Algebra Scope and Sequence of Instruction Instructional Suggestions: Instructional strategies at this level should include connections back to prior learning activities from K7. Students must demonstrate
More informationMSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions
MSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions The goal of this workshop is to familiarize you with similarities and differences in both the graphing and expression of polynomial
More informationOrder of Operations More Essential Practice
Order of Operations More Essential Practice We will be simplifying expressions using the order of operations in this section. Automatic Skill: Order of operations needs to become an automatic skill. Failure
More informationACCUPLACER. Testing & Study Guide. Prepared by the Admissions Office Staff and General Education Faculty Draft: January 2011
ACCUPLACER Testing & Study Guide Prepared by the Admissions Office Staff and General Education Faculty Draft: January 2011 Thank you to Johnston Community College staff for giving permission to revise
More informationMATH LEVEL 1 ARITHMETIC (ACCUPLACER)
MATH LEVEL ARITHMETIC (ACCUPLACER) 7 Questions This test measures your ability to perform basic arithmetic operations and to solve problems that involve fundamental arithmetic concepts. There are 7 questions
More informationGRADE 5 SKILL VOCABULARY MATHEMATICAL PRACTICES Evaluate numerical expressions with parentheses, brackets, and/or braces.
Common Core Math Curriculum Grade 5 ESSENTIAL DOMAINS AND QUESTIONS CLUSTERS Operations and Algebraic Thinking 5.0A What can affect the relationship between numbers? round decimals? compare decimals? What
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 informationGRAPHING LINEAR EQUATIONS IN TWO VARIABLES
GRAPHING LINEAR EQUATIONS IN TWO VARIABLES The graphs of linear equations in two variables are straight lines. Linear equations may be written in several forms: SlopeIntercept Form: y = mx+ b In an equation
More informationLAKE ELSINORE UNIFIED SCHOOL DISTRICT
LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1Semester 2 Grade Level: 1012 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:
More informationAlgorithm set of steps used to solve a mathematical computation. Area The number of square units that covers a shape or figure
Fifth Grade CCSS Math Vocabulary Word List *Terms with an asterisk are meant for teacher knowledge only students need to learn the concept but not necessarily the term. Addend Any number being added Algorithm
More information1.5. section. Arithmetic Expressions
15 Exponential Expression and the Order of Operations (19) 9 83. 1 5 1 6 1 84. 3 30 5 1 4 1 7 0 85. 3 4 1 15 1 0 86. 1 1 4 4 Use a calculator to perform the indicated operation. Round answers to three
More informationSystems of Linear Equations: Elimination by Addition
OpenStaxCNX module: m21986 1 Systems of Linear Equations: Elimination by Addition Wade Ellis Denny Burzynski This work is produced by OpenStaxCNX and licensed under the Creative Commons Attribution License
More informationEquations and Inequalities
Rational Equations Overview of Objectives, students should be able to: 1. Solve rational equations with variables in the denominators.. Recognize identities, conditional equations, and inconsistent equations.
More informationSolutions of Linear Equations in One Variable
2. Solutions of Linear Equations in One Variable 2. OBJECTIVES. Identify a linear equation 2. Combine like terms to solve an equation We begin this chapter by considering one of the most important tools
More informationFUNCTIONS. Introduction to Functions. Overview of Objectives, students should be able to:
FUNCTIONS Introduction to Functions Overview of Objectives, students should be able to: 1. Find the domain and range of a relation 2. Determine whether a relation is a function 3. Evaluate a function 4.
More informationNotes for EER #4 Graph transformations (vertical & horizontal shifts, vertical stretching & compression, and reflections) of basic functions.
Notes for EER #4 Graph transformations (vertical & horizontal shifts, vertical stretching & compression, and reflections) of basic functions. Basic Functions In several sections you will be applying shifts
More informationStudent Lesson: Absolute Value Functions
TEKS: a(5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete,
More informationContents. Number. Algebra. Exam board specification map Introduction Topic checker Topic checker answers. iv vi x xv
Contents Exam board specification map Introduction Topic checker Topic checker answers iv vi x xv Number The decimal number system Fraction calculations Fractions, decimals and percentages Powers and roots
More informationUnit 1 Equations, Inequalities, Functions
Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1100 Overview: This unit models realworld situations by using one and twovariable linear equations. This unit will further expand upon pervious
More information