The document outlines the critical path to success in a course. It states that students should always arrive on time, prepared with materials like notebooks, pencils, and pens. It also emphasizes asking questions when confused and getting extra help from the teacher if falling behind. The document discusses forgetting curves and reviewing notes daily.
Verify the following trigonometric identities:
1. sin^2(θ) + cos^2(θ) = 1
2. tan^2(θ) + 1 = sec^2(θ)
3. cot^2(θ) + 1 = csc^2(θ)
Show the steps for transforming the left-hand side into the right-hand side for each identity.
The document provides information and examples about linear equations and functions. It discusses determining if equations are linear based on their standard form, graphing linear equations, identifying x- and y-intercepts, determining if a relation is a function, and solving equations that contain only an x-variable. Examples include graphing the equation y=-3x/4, finding the x-intercept of 2x-2=-4, and graphing the function 5x+2=7.
The document discusses various counting principles including the fundamental counting principle, permutations, combinations, and probabilities. It provides examples of how to use these principles to calculate the number of possible outcomes in situations like choosing options, arranging objects in order, and selecting objects without regard to order.
1) Rational numbers are numbers that can be written as a quotient of two integers, such as a/b where b does not equal 0. They include integers as well as fractions and terminating or repeating decimals.
2) The document provides examples of rational numbers and asks students to determine if examples are rational numbers and to plot them on a number line.
3) Students are given practice locating rational numbers on a number line, such as -5/3, and asked to plot multiple rational numbers on a single number line.
Algebra II builds on concepts from Algebra I and introduces new topics. It includes solving equations, finding slopes of lines, and absolute value expressions. New topics covered are arithmetic and geometric series, conics, counting principles, and logarithms. Algebra II requires skills from Algebra I and geometry. It aims to take students to an intermediate level in algebra.
Rational numbers can be used to solve equations that cannot be solved using only natural numbers, whole numbers, or integers. Rational numbers are numbers that can be expressed as fractions p/q where p and q are integers and q is not equal to 0. Rational numbers are closed under addition, subtraction, and multiplication, but not division. They are commutative for addition and multiplication, but not for subtraction or division. Addition is associative for rational numbers, but subtraction is not.
This document covers functions, including evaluating functions at given inputs, domains and ranges of functions, and sequences. It defines arithmetic and geometric sequences, providing examples of writing equations for each type of sequence and generating additional terms. Students are asked to evaluate functions, write equations for sequences, and find subsequent terms of given arithmetic and geometric sequences.
CBSE Class 10 Mathematics Real Numbers Topic
Real Numbers Topics discussed in this document:
Introduction
Rational numbers
Fundamental theorem of Arithmetic
Decimal representation of Rational numbers
Terminating decimal
Non-terminating repeating decimals
Irrational numbers
Surd
General form of a surd
Operations on surds
· Addition and subtraction
· Multiplication of surds
More Topics under Class 10th Real Numbers (CBSE):
Real numbers
Laws of
logarithms
Common and natural logarithms
Visit Edvie.com for more topics
Verify the following trigonometric identities:
1. sin^2(θ) + cos^2(θ) = 1
2. tan^2(θ) + 1 = sec^2(θ)
3. cot^2(θ) + 1 = csc^2(θ)
Show the steps for transforming the left-hand side into the right-hand side for each identity.
The document provides information and examples about linear equations and functions. It discusses determining if equations are linear based on their standard form, graphing linear equations, identifying x- and y-intercepts, determining if a relation is a function, and solving equations that contain only an x-variable. Examples include graphing the equation y=-3x/4, finding the x-intercept of 2x-2=-4, and graphing the function 5x+2=7.
The document discusses various counting principles including the fundamental counting principle, permutations, combinations, and probabilities. It provides examples of how to use these principles to calculate the number of possible outcomes in situations like choosing options, arranging objects in order, and selecting objects without regard to order.
1) Rational numbers are numbers that can be written as a quotient of two integers, such as a/b where b does not equal 0. They include integers as well as fractions and terminating or repeating decimals.
2) The document provides examples of rational numbers and asks students to determine if examples are rational numbers and to plot them on a number line.
3) Students are given practice locating rational numbers on a number line, such as -5/3, and asked to plot multiple rational numbers on a single number line.
Algebra II builds on concepts from Algebra I and introduces new topics. It includes solving equations, finding slopes of lines, and absolute value expressions. New topics covered are arithmetic and geometric series, conics, counting principles, and logarithms. Algebra II requires skills from Algebra I and geometry. It aims to take students to an intermediate level in algebra.
Rational numbers can be used to solve equations that cannot be solved using only natural numbers, whole numbers, or integers. Rational numbers are numbers that can be expressed as fractions p/q where p and q are integers and q is not equal to 0. Rational numbers are closed under addition, subtraction, and multiplication, but not division. They are commutative for addition and multiplication, but not for subtraction or division. Addition is associative for rational numbers, but subtraction is not.
This document covers functions, including evaluating functions at given inputs, domains and ranges of functions, and sequences. It defines arithmetic and geometric sequences, providing examples of writing equations for each type of sequence and generating additional terms. Students are asked to evaluate functions, write equations for sequences, and find subsequent terms of given arithmetic and geometric sequences.
CBSE Class 10 Mathematics Real Numbers Topic
Real Numbers Topics discussed in this document:
Introduction
Rational numbers
Fundamental theorem of Arithmetic
Decimal representation of Rational numbers
Terminating decimal
Non-terminating repeating decimals
Irrational numbers
Surd
General form of a surd
Operations on surds
· Addition and subtraction
· Multiplication of surds
More Topics under Class 10th Real Numbers (CBSE):
Real numbers
Laws of
logarithms
Common and natural logarithms
Visit Edvie.com for more topics
The document discusses operations with integers such as addition, subtraction, multiplication, and division. It explains that the minus sign can indicate a negative number, the opposite of an expression, or subtraction. It provides examples of using counters or blocks to model integer addition and subtraction by putting on and taking off quantities. Patterns are noticed, such as opposites adding to zero. Multiplication of integers results in positive or negative numbers depending on the signs of the factors. Division is related to the inverse operation of multiplication.
1) Rational numbers are numbers that can be written as a quotient of two integers, such as a/b where b does not equal 0. They include integers as well as fractions and repeating decimals.
2) The document provides examples of determining if numbers are rational and plotting them on a number line. It also gives examples of quotients that result in rational numbers and representing them on a number line.
3) Exercises are provided to have the reader locate and plot various rational numbers on a single number line.
This document contains a 50 question multiple choice math test covering topics like coordinate geometry, linear equations, functions, and logic. The questions require students to identify properties of linear equations and functions, determine if statements are true or false, identify parts of logical arguments, and choose answers involving math concepts like slope, solutions to inequalities, and properties of shapes. Scripture is included between questions.
The document discusses multiplication of integers. It explains that there are three ways to write multiplication and defines the rules for multiplying positive and negative numbers. A positive number multiplied by a positive number is positive, a negative number multiplied by a negative number is positive, and a positive number multiplied by a negative number or a negative number multiplied by a positive number is negative. It provides examples of multiplying integers and evaluating expressions with integers using order of operations.
The document discusses properties of real numbers. It defines real numbers and distinguishes between rational and irrational numbers. Rational numbers can be expressed as ratios of integers, while irrational numbers have non-terminating, non-repeating decimals. It also outlines relationships between subsets of real numbers and properties that real number operations satisfy, such as commutativity, associativity, identities, inverses, and distribution.
This document discusses different types of real numbers including natural numbers, integers, rational numbers, irrational numbers, and real numbers. It defines each type of number and provides examples. It also defines the absolute value or modulus of a real number, listing properties such as the modulus being non-negative and greater than or equal to both the number and its opposite. Formulas are given for the absolute value of products and sums of real numbers.
The document contains notes about Khan Academy assignments being due, exam grades being posted, and notebooks being collected on different days of the week. It also includes examples of writing inequalities, graphing linear inequalities, and solving word problems involving inequalities describing the number of coins a person could have with less than $5.
This document is a worksheet about parallel and perpendicular lines. It contains questions about determining the slope of lines from their equations, identifying whether pairs of lines are parallel, perpendicular, or neither, and properties of parallel and perpendicular lines. The questions cover finding the slope and identifying relationships between lines from their equations in slope-intercept form, standard form, and word problems.
1) Students will complete a two-part writing assignment on polynomial functions.
2) In part one, students must factor a polynomial, find all its roots, sketch its graph, and explain its end behavior and behavior at roots using formal algebra.
3) In part two, students must construct a polynomial in standard form given its roots, explaining the theorems used to find remaining roots and showing calculation steps.
The document discusses the distributive property in algebra. It provides definitions of key terms like term, coefficient, and like terms. It gives examples of using the distributive property to simplify expressions and solve problems involving perimeter. The distributive property allows multiplying a number by the sum of two other numbers, distributing the number factor across the addition.
The document discusses various methods for solving inequalities, including:
- Properties for adding, subtracting, multiplying, and dividing terms within an inequality
- Using set-builder and interval notation to describe the solution set of an inequality
- Graphical representations using open and closed circles to indicate whether a number is or isn't part of the solution set
The document provides examples of applying these different techniques to solve specific inequalities.
The document describes how to solve simultaneous equations using non-graphical methods. It involves numbering the equations, eliminating one of the unknowns by combining the equations, solving for the eliminated unknown, and then substituting back into one of the original equations to solve for the other unknown. Several examples are provided showing the steps of eliminating an unknown through addition or changing coefficients to match, then solving for the unknowns.
This document provides information about geometric sequences including their key properties and formulas. It defines a geometric sequence as one where the ratio between consecutive terms is constant, known as the common ratio. Formulas given include the recursive formula an = an-1r and explicit formula an = a1rn-1. Examples are provided for identifying geometric sequences and using the formulas to find missing terms. Additional notes state that arithmetic sequences have linear graphs while geometric sequences have exponential graphs.
This document contains NCERT solutions for Class 8 Maths Chapter 1 on Rational Numbers. It includes solutions to 11 questions from Exercise 1.1 that involve finding additive and multiplicative inverses of rational numbers, identifying properties used in multiplication, determining if a number is its own reciprocal, and filling in blanks about rational numbers and their reciprocals. The questions cover key concepts about rational numbers such as their properties and operations involving addition, subtraction, multiplication and division.
Roman numerals are used in SAT math and reading questions to represent answer choices. Each roman numeral should be considered a separate true/false statement. The correct answer will be the roman numeral choices where the statements are true. An example question is provided where evaluating each roman numeral choice as true or false leads to determining the answer is choice D, as roman numerals II and III are true statements.
The document introduces key concepts in algebra including variables, constants, types of numbers (counting, integers, rational, irrational, real), graphs, averages, and positive and negative numbers. It provides examples and guidelines for understanding these concepts. Variables represent quantities that can vary, while constants represent fixed values. Different number sets are explained and visualized on a number line. Averages are calculated by adding values and dividing by the total count. Positive numbers are greater than zero, while negative numbers are less than zero.
1. The document discusses subsets of real numbers including natural numbers, whole numbers, integers, and rational numbers.
2. Natural numbers are used for counting and start at 1. Whole numbers are formed by adding 0 to the natural numbers. Integers are formed by adding the negatives of natural numbers to whole numbers.
3. Rational numbers can be expressed as fractions a/b where a and b are integers and b is not equal to 0. Their decimal representations either terminate or repeat.
This document defines and explains key concepts related to real numbers and algebraic expressions. It introduces sets and subsets of real numbers like integers, rational numbers, and irrational numbers. It describes properties of real numbers including addition, multiplication, order, and absolute value. It also covers representing real numbers on a number line, algebraic expressions, and properties of negatives.
The document discusses how to identify the slope and y-intercept of a line given in standard form. It shows working through examples of changing lines from standard form (Ax + By = C) to slope-intercept form (y = mx + b). Through solving the equations for y, the slope (m) and y-intercept (b) can be determined. Graphing lines on a coordinate plane is also demonstrated.
The document discusses different types of numbers and operations involving positive and negative numbers. It explains rules for addition, subtraction, multiplication, and division of positive and negative numbers. It also covers order of operations using PEMDAS and provides examples of solving expressions using proper order. Finally, it discusses properties and rules for exponents, including adding, subtracting, multiplying, and dividing terms with the same base and combining exponents.
The document discusses inverse functions. It defines a one-to-one function as a function where the horizontal line test shows that every horizontal line intersects the graph at most one point. This ensures that each input is mapped to a single output. An inverse function undoes the original function - if f(x) is the original function, its inverse f^-1(x) satisfies f^-1(f(x)) = x.
The document discusses operations with integers such as addition, subtraction, multiplication, and division. It explains that the minus sign can indicate a negative number, the opposite of an expression, or subtraction. It provides examples of using counters or blocks to model integer addition and subtraction by putting on and taking off quantities. Patterns are noticed, such as opposites adding to zero. Multiplication of integers results in positive or negative numbers depending on the signs of the factors. Division is related to the inverse operation of multiplication.
1) Rational numbers are numbers that can be written as a quotient of two integers, such as a/b where b does not equal 0. They include integers as well as fractions and repeating decimals.
2) The document provides examples of determining if numbers are rational and plotting them on a number line. It also gives examples of quotients that result in rational numbers and representing them on a number line.
3) Exercises are provided to have the reader locate and plot various rational numbers on a single number line.
This document contains a 50 question multiple choice math test covering topics like coordinate geometry, linear equations, functions, and logic. The questions require students to identify properties of linear equations and functions, determine if statements are true or false, identify parts of logical arguments, and choose answers involving math concepts like slope, solutions to inequalities, and properties of shapes. Scripture is included between questions.
The document discusses multiplication of integers. It explains that there are three ways to write multiplication and defines the rules for multiplying positive and negative numbers. A positive number multiplied by a positive number is positive, a negative number multiplied by a negative number is positive, and a positive number multiplied by a negative number or a negative number multiplied by a positive number is negative. It provides examples of multiplying integers and evaluating expressions with integers using order of operations.
The document discusses properties of real numbers. It defines real numbers and distinguishes between rational and irrational numbers. Rational numbers can be expressed as ratios of integers, while irrational numbers have non-terminating, non-repeating decimals. It also outlines relationships between subsets of real numbers and properties that real number operations satisfy, such as commutativity, associativity, identities, inverses, and distribution.
This document discusses different types of real numbers including natural numbers, integers, rational numbers, irrational numbers, and real numbers. It defines each type of number and provides examples. It also defines the absolute value or modulus of a real number, listing properties such as the modulus being non-negative and greater than or equal to both the number and its opposite. Formulas are given for the absolute value of products and sums of real numbers.
The document contains notes about Khan Academy assignments being due, exam grades being posted, and notebooks being collected on different days of the week. It also includes examples of writing inequalities, graphing linear inequalities, and solving word problems involving inequalities describing the number of coins a person could have with less than $5.
This document is a worksheet about parallel and perpendicular lines. It contains questions about determining the slope of lines from their equations, identifying whether pairs of lines are parallel, perpendicular, or neither, and properties of parallel and perpendicular lines. The questions cover finding the slope and identifying relationships between lines from their equations in slope-intercept form, standard form, and word problems.
1) Students will complete a two-part writing assignment on polynomial functions.
2) In part one, students must factor a polynomial, find all its roots, sketch its graph, and explain its end behavior and behavior at roots using formal algebra.
3) In part two, students must construct a polynomial in standard form given its roots, explaining the theorems used to find remaining roots and showing calculation steps.
The document discusses the distributive property in algebra. It provides definitions of key terms like term, coefficient, and like terms. It gives examples of using the distributive property to simplify expressions and solve problems involving perimeter. The distributive property allows multiplying a number by the sum of two other numbers, distributing the number factor across the addition.
The document discusses various methods for solving inequalities, including:
- Properties for adding, subtracting, multiplying, and dividing terms within an inequality
- Using set-builder and interval notation to describe the solution set of an inequality
- Graphical representations using open and closed circles to indicate whether a number is or isn't part of the solution set
The document provides examples of applying these different techniques to solve specific inequalities.
The document describes how to solve simultaneous equations using non-graphical methods. It involves numbering the equations, eliminating one of the unknowns by combining the equations, solving for the eliminated unknown, and then substituting back into one of the original equations to solve for the other unknown. Several examples are provided showing the steps of eliminating an unknown through addition or changing coefficients to match, then solving for the unknowns.
This document provides information about geometric sequences including their key properties and formulas. It defines a geometric sequence as one where the ratio between consecutive terms is constant, known as the common ratio. Formulas given include the recursive formula an = an-1r and explicit formula an = a1rn-1. Examples are provided for identifying geometric sequences and using the formulas to find missing terms. Additional notes state that arithmetic sequences have linear graphs while geometric sequences have exponential graphs.
This document contains NCERT solutions for Class 8 Maths Chapter 1 on Rational Numbers. It includes solutions to 11 questions from Exercise 1.1 that involve finding additive and multiplicative inverses of rational numbers, identifying properties used in multiplication, determining if a number is its own reciprocal, and filling in blanks about rational numbers and their reciprocals. The questions cover key concepts about rational numbers such as their properties and operations involving addition, subtraction, multiplication and division.
Roman numerals are used in SAT math and reading questions to represent answer choices. Each roman numeral should be considered a separate true/false statement. The correct answer will be the roman numeral choices where the statements are true. An example question is provided where evaluating each roman numeral choice as true or false leads to determining the answer is choice D, as roman numerals II and III are true statements.
The document introduces key concepts in algebra including variables, constants, types of numbers (counting, integers, rational, irrational, real), graphs, averages, and positive and negative numbers. It provides examples and guidelines for understanding these concepts. Variables represent quantities that can vary, while constants represent fixed values. Different number sets are explained and visualized on a number line. Averages are calculated by adding values and dividing by the total count. Positive numbers are greater than zero, while negative numbers are less than zero.
1. The document discusses subsets of real numbers including natural numbers, whole numbers, integers, and rational numbers.
2. Natural numbers are used for counting and start at 1. Whole numbers are formed by adding 0 to the natural numbers. Integers are formed by adding the negatives of natural numbers to whole numbers.
3. Rational numbers can be expressed as fractions a/b where a and b are integers and b is not equal to 0. Their decimal representations either terminate or repeat.
This document defines and explains key concepts related to real numbers and algebraic expressions. It introduces sets and subsets of real numbers like integers, rational numbers, and irrational numbers. It describes properties of real numbers including addition, multiplication, order, and absolute value. It also covers representing real numbers on a number line, algebraic expressions, and properties of negatives.
The document discusses how to identify the slope and y-intercept of a line given in standard form. It shows working through examples of changing lines from standard form (Ax + By = C) to slope-intercept form (y = mx + b). Through solving the equations for y, the slope (m) and y-intercept (b) can be determined. Graphing lines on a coordinate plane is also demonstrated.
The document discusses different types of numbers and operations involving positive and negative numbers. It explains rules for addition, subtraction, multiplication, and division of positive and negative numbers. It also covers order of operations using PEMDAS and provides examples of solving expressions using proper order. Finally, it discusses properties and rules for exponents, including adding, subtracting, multiplying, and dividing terms with the same base and combining exponents.
The document discusses inverse functions. It defines a one-to-one function as a function where the horizontal line test shows that every horizontal line intersects the graph at most one point. This ensures that each input is mapped to a single output. An inverse function undoes the original function - if f(x) is the original function, its inverse f^-1(x) satisfies f^-1(f(x)) = x.
The Federal Reserve System is a system set up by the federal government to supervise and regulate member banks and help them serve the public efficiently. All national banks must join the FRS, and state banks may join. Banking systems are used to finance many aspects of life like homes, businesses, crops, education, goods, and infrastructure. Commercial banks offer a wide range of financial services like checking and savings accounts, loans, and other services. Electronic funds transfer refers to using computers and technology for banking activities like ATMs, direct deposit, and automatic bill payment.
The document discusses proposed changes to US labor laws under the Employee Free Choice Act (EFCA) and RESPECT Act that would make it easier for employees to unionize. Specifically, it summarizes that EFCA would eliminate secret ballot elections and instead allow unions to be certified solely based on authorization cards signed by a majority of employees, as well as impose binding arbitration if a union contract is not negotiated within 90 days. It also discusses strategies for employers to prevent unionization in the changing political climate.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help alleviate symptoms of mental illness and boost overall mental well-being.
The document discusses the transit of Venus, which involves Venus passing directly between the Earth and the Sun. Measuring the timing of transits from different locations on Earth allows scientists to calculate the distance between the Earth and the Sun. The transit of Venus in 1769 was observed by Captain Cook in Tahiti and helped provide an early accurate measurement of the astronomical unit. The document proposes a project to video record the upcoming transit of Venus in 2012 to allow precise timing measurements and involve amateur astronomers.
This document discusses using gamification to improve the effectiveness of international marketing. It describes how gamification can be used to engage employees and improve learning at work. Examples discussed include having employees live stream their jobs, implementing job shadowing, and using games to help people master skills and reduce the fear of failure. The presentation encourages thinking about how gamification principles like themes, victory states, and constraints can help spread important skills within an organization.
This document provides a summary and table of contents for "The Amazing Web 2.0 Projects Book" edited by Terry Freedman. The book contains over 100 case studies of educational projects from around the world that utilize various Web 2.0 technologies like blogs, wikis, social networking, and more. It is organized into 5 sections covering different age groups from primary/elementary school through adult education. The case studies provide details about how specific classes and schools have integrated technologies to enhance teaching and learning.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Tugas akhir ini membahas penyederhanaan fungsi Boolean menggunakan peta Karnaugh dalam bentuk SOP (sum of product) untuk memperoleh bentuk minimal dari fungsi tersebut. Langkah-langkahnya meliputi pengisian peta Karnaugh berdasarkan variabel fungsi, penemuan blok yang dapat dihubungkan, dan penyederhanaan fungsi menjadi bentuk gerbang logika.
Greenfield foreign direct investment (FDI) showed signs of recovery in 2013, increasing 10.94% to $618.62 billion globally. Asia-Pacific remained the top destination with $184.67 billion in FDI, though China and India saw declines while Vietnam, Myanmar, and Japan saw strong growth. Western Europe was the largest source of outbound FDI at $176.4 billion, a 13% increase, while FDI from Asia-Pacific fell slightly. The recovery in FDI was driven by market-seeking investments in sectors like oil and gas, communications, and construction.
The document discusses various concepts related to pricing, including factors that influence price sensitivity, methods for estimating demand and costs, strategies for setting prices, and approaches for initiating or responding to price changes. It provides examples to illustrate concepts like price discrimination, product mix pricing, and how companies may respond to competitors' price adjustments.
Patents provide inventors with the exclusive right to make, sell, and use a new product or process, preventing other companies from copying the invention without permission. Copyright protects the creative works of authors, composers, and artists for their lifetime plus 50 years after death. Trademarks are words, symbols, or designs linked to a specific company or product that are registered with the government. A monopoly exists when a business controls the entire market for a particular good or service.
Dokumen tersebut membahas tentang penyederhanaan fungsi logika boolean menggunakan peta Karnaugh dan penggambaran hasilnya kedalam bentuk gerbang logika. Fungsi logika Z ditulis sebagai kombinasi dari beberapa minterm. Peta Karnaugh digunakan untuk menemukan blok-blok yang dapat disederhanakan dan menghasilkan bentuk akhir fungsi Z. Hasil penyederhanaan kemudian digambarkan menggunakan gerbang-gerbang
The document discusses cooperation between the Department of Defense (DOD) and the Federal Bureau of Investigation (FBI) using biometrics. By comparing biometric datasets, they discovered that many individuals captured in war zones in Iraq and Afghanistan had prior criminal histories in the United States. This led to greater collaboration between the agencies. It also outlines several government organizations involved in coordinating biometrics science and technology and identity management.
The document outlines the critical path to success in a course, which includes always arriving on time, prepared with materials like notebooks and pencils, attempting all homework, reviewing notes daily, and asking questions when help is needed. It also provides strategies and examples for factoring expressions, including checking for common factors, using factoring forms, and the quadratic formula. Students are given homework assignments to practice factoring different expressions.
This document is an instructional material for mathematics grade 3 published by the Department of Education of the Republic of the Philippines. It was collaboratively developed by educators and contains lessons on multiplication and division of whole numbers up to 3 digits long, including properties of multiplication and division. The material is freely available for public use but prior approval is needed for commercial exploitation.
This document discusses rules for multiplying and dividing integers. It provides two rules for multiplying integers: the product of integers with the same sign is positive, and the product of integers with different signs is negative. It also provides two rules for dividing integers: the quotient of integers with the same sign is positive, and the quotient of integers with different signs is negative. The document then works through several sample problems applying these rules to multiply, divide, and combine operations on integers. It emphasizes solving expressions using proper order of operations.
This document provides a daily lesson log for a Grade 9 mathematics class. It outlines the objectives, content, learning resources and procedures for lessons on the nature of roots of quadratic equations, including the sum and product of roots, and equations that can be transformed into quadratic equations. Key concepts covered are using the discriminant to characterize roots, the relationship between coefficients and roots, and solving various types of equations. Examples and follow-up questions are provided to discuss and practice the new skills.
This document contains a review for Mrs. Labuski's math class covering lessons 1-8 on identities, operations, expressions, properties, and geometry. Students are asked to fill in blanks, write expressions, evaluate expressions, and answer questions about division, multiplication, exponents, area, perimeter, and volume. The review covers key concepts like the relationship between multiplication/division and addition/subtraction, order of operations, properties of operations, and using formulas to find geometric measures.
The document provides information about identifying multiples and factors of numbers up to 100. It defines multiples as the products obtained by multiplying a number by counting numbers, and provides examples of writing the first few multiples of numbers like 3, 5, and 10. Factors are defined as pairs of numbers that multiply to give the original number. Examples are provided of finding all the factors of sample numbers like 24, 39, and 70. Various exercises are included for students to practice finding multiples and factors.
The document provides an overview of problem solving techniques including:
- Using inductive and deductive reasoning to evaluate arguments and solve problems.
- Identifying patterns in sequences to derive nth term formulas.
- Applying Polya's four-step problem solving strategy of understanding the problem, devising a plan, carrying out the plan, and reviewing the solution.
- Using work principles and a five-step process to systematically solve problems.
Examples are provided to illustrate each technique.
The document is a table of contents for a mathematics textbook for third grade students in the Philippines. It lists 46 lessons on topics like multiplication, division, properties of operations, and solving word problems involving these operations. The document also provides information about copyright and permissions for using materials in the book. It was developed by the Department of Education of the Republic of the Philippines.
The document is a lesson plan on factoring polynomials from St. Mary's Academy. It begins with definitions of factoring and examples of factoring polynomials with a common monomial factor. It then discusses factoring by grouping, factoring the difference of two squares using the formula (x + y)(x - y), and factoring the sum or difference of two cubes using the formulas (a + b)(a^2 - ab + b^2) and (a - b)(a^2 + ab + b^2). It concludes with an example word problem involving factoring polynomials.
This document contains an answer sheet for a math module with learning tasks on sequences, polynomials, and equations. The tasks include filling tables, identifying patterns as arithmetic or geometric sequences, performing sequence operations like finding the nth term, dividing polynomials using long division, applying the remainder and factor theorems, factoring polynomials, and solving polynomial equations. The summary provides an overview of the key concepts and skills covered rather than the details of each individual task.
1. The document discusses exponents and exponential notation. It provides examples of how to write expressions like 3 x 3 x 3 x 3 in exponential form as 34, where 3 is the base and 4 is the exponent.
2. Students are asked questions to test their understanding of identifying the base and exponent in exponential expressions, writing expressions in exponential form, and evaluating numerical expressions written in exponential notation.
3. The document provides practice problems and answers for students to demonstrate their mastery of working with exponents and expressions in exponential notation.
This document contains a 24 question benchmark assessment for 5th grade mathematics standards in Ohio. The assessment covers 12 standards that are scheduled to be taught in the first two quarters of the school year. Many questions have multiple parts and include higher-order thinking by having students show their work. The assessment allows students to demonstrate understanding beyond just finding the right answer.
Strategic intervention material discriminant and nature of the rootsmaricel mas
This document provides guidance on identifying the nature of roots for quadratic equations. It begins by explaining that the discriminant, which is calculated as b^2 - 4ac, can be used to determine if the roots are real, rational, equal, etc. Several examples are worked through to demonstrate rewriting equations in standard form, finding a, b, and c values, and calculating the discriminant. Activities are included for students to practice these skills. The document concludes by summarizing that a positive discriminant indicates real, unequal roots, a negative discriminant indicates non-real roots, and a zero discriminant indicates real, equal roots.
This document provides a daily lesson log for a 7th grade mathematics class covering operations on integers. The lesson covers addition, subtraction, multiplication, and division of integers over four sessions. Each session includes objectives, content, learning resources, procedures, and an evaluation. The procedures describe activities to motivate students, present examples, discuss concepts, and apply the skills to word problems. The goal is for students to understand and be able to perform the four fundamental operations on integers.
This document provides a summary of a lecture on solving systems of equations. It discusses two methods for solving systems of equations: 1) setting both equations equal to each other and combining like terms, and 2) substituting the x or y value of one equation into the other equation. It includes examples and practice problems applying both methods. Students are asked to identify their preferred method and set up a sample problem using both methods.
The document provides a daily lesson log for a Grade 9 mathematics class covering quadratic equations. It includes the objectives, content standards, and performance standards for the lesson. The log details the activities and examples covered each day, which focus on illustrating quadratic equations, solving them by extracting square roots, factoring, and using the quadratic formula. Examples of solving quadratic equations in simplest form and by factoring are provided. Students practice identifying quadratic equations and solving them using different methods.
Tameeka Final Exam (Answer Key)1.Solve the following line.docxdeanmtaylor1545
Tameeka Final Exam (Answer Key)
1. Solve the following linear equation using equivalent equations to isolate the variable. Write your solution as a whole number.
Answer: ____________________
2. Solve the following linear equation using equivalent equations to isolate the variable. Write your solution as a whole number.
Answer: ____________________
3. Solve the following linear equation using equivalent equations to isolate the variable. Write your solution as a whole number.
Answer: ____________________
4. Evaluate the expression.
Answer: ____________________
5. Evaluate the following expression.
Answer: ____________________
6. Evaluate the following expression.
Answer: ____________________
7. Find the following sum:
Answer: ____________________
8. Compute the value of the following sum.
Answer: ____________________
9. Determine whether or not the given number is a solution to the given equation by substituting and then evaluating.
A)
B)
10.
Find the following sum.
.
Answer: _______________
11. Find the following difference.
Answer: ____________________
12. Evaluate the following expression:
Answer: _______________
13. Evaluate the following expression:
Answer: _______________
14. Find the quotient.
A) __________ B) undefined
15. Find the quotient.
A) __________ B) undefined
16. Find the value of the following expression using the rules for order of operations.
Answer: ____________________
17. Evaluate the given expression at .
Answer: ____________________
18. Simplify the algebraic expression by performing the indicated operations and combining the similar (or like) terms.
Answer: ____________________
19. Solve the linear equation using equivalent equations to isolate the variable. Express your answer as an integer.
Answer: ____________________
20. Solve the linear equation using equivalent equations to isolate the variable. Express your answer as an integer.
Answer: ____________________
21. Solve the linear equation using equivalent equations to isolate the variable. Express your answer as an integer.
Answer: ____________________
22.
Solve the following equation. Combine like terms whenever necessary.
Answer: _______________
23. Change the following mixed number to an improper fraction. Reduce if possible.
Answer: ____________________
24. Change the following improper fraction to a mixed number with the fraction part reduced to lowest terms.
Answer: ____________________
25. Find the product in lowest terms.
Answer: ____________________
26. Find the product in lowest terms.
Answer: ____________________
27. Divide the following and reduce the answer to its simplest terms.
Answer: ____________________
28. Find the following quotient. Reduce to lowest terms.
Answer: ____________________
29. Compute the sum indicated and simplify your answer.
Answer: ____.
Tameeka Final Exam (Answer Key)1.Solve the following line.docxbradburgess22840
Tameeka Final Exam (Answer Key)
1. Solve the following linear equation using equivalent equations to isolate the variable. Write your solution as a whole number.
Answer: ____________________
2. Solve the following linear equation using equivalent equations to isolate the variable. Write your solution as a whole number.
Answer: ____________________
3. Solve the following linear equation using equivalent equations to isolate the variable. Write your solution as a whole number.
Answer: ____________________
4. Evaluate the expression.
Answer: ____________________
5. Evaluate the following expression.
Answer: ____________________
6. Evaluate the following expression.
Answer: ____________________
7. Find the following sum:
Answer: ____________________
8. Compute the value of the following sum.
Answer: ____________________
9. Determine whether or not the given number is a solution to the given equation by substituting and then evaluating.
A)
B)
10.
Find the following sum.
.
Answer: _______________
11. Find the following difference.
Answer: ____________________
12. Evaluate the following expression:
Answer: _______________
13. Evaluate the following expression:
Answer: _______________
14. Find the quotient.
A) __________ B) undefined
15. Find the quotient.
A) __________ B) undefined
16. Find the value of the following expression using the rules for order of operations.
Answer: ____________________
17. Evaluate the given expression at .
Answer: ____________________
18. Simplify the algebraic expression by performing the indicated operations and combining the similar (or like) terms.
Answer: ____________________
19. Solve the linear equation using equivalent equations to isolate the variable. Express your answer as an integer.
Answer: ____________________
20. Solve the linear equation using equivalent equations to isolate the variable. Express your answer as an integer.
Answer: ____________________
21. Solve the linear equation using equivalent equations to isolate the variable. Express your answer as an integer.
Answer: ____________________
22.
Solve the following equation. Combine like terms whenever necessary.
Answer: _______________
23. Change the following mixed number to an improper fraction. Reduce if possible.
Answer: ____________________
24. Change the following improper fraction to a mixed number with the fraction part reduced to lowest terms.
Answer: ____________________
25. Find the product in lowest terms.
Answer: ____________________
26. Find the product in lowest terms.
Answer: ____________________
27. Divide the following and reduce the answer to its simplest terms.
Answer: ____________________
28. Find the following quotient. Reduce to lowest terms.
Answer: ____________________
29. Compute the sum indicated and simplify your answer.
Answer: ____.
This document contains a lesson plan for teaching factoring non-perfect trinomials in Math 8. The lesson plan outlines intended learning outcomes, learning content including subject matter and reference materials, learning experiences through various activities, an evaluation, and assignment. Students will learn to define trinomials, factor non-perfect square trinomials, and apply factoring trinomials to geometric figures through guided practice with algebra tiles and examples.
The document provides examples and explanations for multiplying and dividing fractions. It discusses multiplying the numerators and denominators when multiplying fractions, and using reciprocals to rewrite division as multiplication when dividing fractions. It provides 8 practice problems for students to complete on their notes.
This 4 page document does not contain any text and is composed entirely of blank pages. As there is no information provided, a meaningful summary cannot be generated from the given input.
This 6-page document appears to be a multi-page PDF with no title or visible text. As the document contains no readable words or identifiable content, it is not possible to provide a meaningful summary in 3 sentences or less.
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This document discusses when to use the greatest common factor (GCF) or least common multiple (LCM) to solve word problems. It provides examples of GCF and LCM problems and then presents 6 sample word problems, asking the reader to identify whether each uses GCF or LCM. The document also provides the answers, identifying problems 1, 2, and 6 as GCF problems and problems 3, 4, and 5 as LCM problems. It includes additional examples of GCF and LCM word problems.
Third partial exam Integral Calculus EM13 - solutionsCarlos Vázquez
This document contains solutions to problems from a third partial exam. It lists 4 problems, each with a function f(x) and g(x) defined, likely algebra problems solving for where the two functions are equal.
The document describes how to find the dimensions of a rectangle with the largest area that can be made from a 1 meter string. It involves:
1) Drawing a picture of the rectangle with base x;
2) Using the perimeter formula to write the height in terms of x;
3) Writing the area formula in terms of x; and
4) Setting the area formula equal to zero and solving for x to find the maximum base length.
This document discusses trigonometric limits and provides examples. It outlines important limits such as the limits of sine, cosine, and tangent as the angle approaches 0. Examples are given to demonstrate how to evaluate various trigonometric limits. The document concludes with homework problems and additional examples for practice.
The document discusses limits and examples of evaluating limits. It covers rewriting functions when the limit is an indeterminate form of 0/0. Examples are provided of evaluating limits by sketching graphs or using left and right evaluations for values close to x. Methods like algebra, graphing, or left/right evaluations are presented for determining limits.
The document provides examples of composition of functions. It gives the functions f(x) = 4 - x^2 and g(x) = sqrt(x) and calculates their composition, as well as finding the domain of each case. It then gives another example with the functions f(x) = sqrt(x) and g(x) = x^2 - 4, and again calculates their composition and domains. It provides exercises to calculate additional compositions of functions and their domains.
The document discusses limits in mathematics. It defines a limit as the intended height of a function as values get closer and closer to a given number. Examples are provided of evaluating limits, including finding limits of expressions as x approaches 1 and determining whether limits exist or are infinite. Common types of limits like one-sided limits and limits at infinity are also mentioned.
The document provides examples of functions and calculations involving functions. It gives the functions f(x) and g(x) and calculates f(x) + g(x), f(x) - g(x), and f(x)/g(x). It also finds the domain and range for each example, without graphing in one case. The document covers algebra of functions and composition of functions.
The document discusses piecewise defined functions. It defines a piecewise function as one where the function definition changes depending on the interval of x-values. It provides examples of sketching piecewise functions and finding their domains and ranges. Specifically, it gives the examples of the functions y=-2, f(x)=2x for -2<=x<=3, and g(x)=-(3/2)x+1. It also defines a piecewise function as having different expressions on various intervals.
The document reviews trigonometry concepts including the unit circle and finding trigonometric functions of special angles. It provides examples of the unit circle with coordinates marked around it and homework problems involving finding the trigonometric functions of various angles in radians and degrees. The review is intended to help remember things learned in trigonometry class.
The document provides examples and explanations of operations with fractions, including adding, subtracting, multiplying, and dividing fractions. It also explains how to rationalize the denominator of a fraction by moving a root from the bottom of a fraction to the top. Some examples of rationalizing denominators are shown. Finally, it lists some exercises involving solving equations, rationalizing denominators, and performing operations with fractions.
1. The document discusses different math topics covered on Day 3 including: solving a word problem to find two numbers given their sum and difference, using the quadratic formula, operations with fractions, and rationalizing denominators.
2. Rationalizing denominators involves moving a root such as a square root from the bottom of a fraction to the top of the fraction.
3. Examples are provided for rationalizing denominators including rationalizing (2+3)/(8-3) and (a+1)/(1+a+1).
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
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Slideshare: http://www.slideshare.net/PECBCERTIFICATION
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
2. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always be on time for class.
3. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials
needed.
4. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials
needed.
5. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials
needed.
Notebooks
6. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials
needed.
Notebooks
7. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials
needed.
Pencil
Notebooks
8. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials
needed.
Pencil
Notebooks
9. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials
needed.
Pencil
Notebooks
Pen(s)
10. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always attempt ALL their homework assignments.
11. Critical Path to Success!!
A student who wants to succeed in this course will:
• Review their class notes every night before going to bed.
12. The Curve of Forgetting...
Describes how we retain or get rid of information that
we take in.
It´s based on a one-hour lecture.
13. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always ask LOTS of questions about anything they don’t
understand.
14. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always gets extra help from the
teacher when they feel they
are falling behind.
15. 3. Opener
2
a) What polynomial do you subtract from 3x − 8 to
get 5x −10 ?
b) Distribute: −2x 2 (4 x 5 − 5)
c) Simplify:
€ €
4 2 5 −2 ⎛10x ⎞−3
€ (5x ) (5x ) ⎜ 3 ⎟
⎝ 5x ⎠
d) What does Manero’s Steakhouse in Greenwich, CN, offer to
€ any baby born in the restaurant?
€
16. Day 2
1. Opener.
1. What is the first step in any factoring problem?
2. What is the first step to factor -x2 + 8x - 15?
3. On a test, Luis Gonzalez wrote the following, but the
teacher considered it to be incomplete. Explain why
15x2 - 21x - 18 = (5x + 3)(3x - 6)
4. What appetizer is most requested with a last meal?
23. 3. Factoring Strategy.
greatest common factor
Step 1. Always check for the _____________________ first.
24. Step 2.Is the expression a -termed expression?
If yes, then try one of these three forms:
1. _______________________________:
2. _______________________________:
3. _______________________________:
25. Step 2.Is the expression a two -termed expression?
If yes, then try one of these three forms:
1. _______________________________:
2. _______________________________:
3. _______________________________:
26. Step 2.Is the expression a two -termed expression?
If yes, then try one of these three forms:
a2 - b2 = (a + b)(a - b)
1. _______________________________:
2. _______________________________:
3. _______________________________:
27. Step 2.Is the expression a two -termed expression?
If yes, then try one of these three forms:
a2 - b2 = (a + b)(a - b)
1. _______________________________:
a3 + b3 = (a + b)(a2 - ab + b2)
2. _______________________________:
3. _______________________________:
28. Step 2.Is the expression a two -termed expression?
If yes, then try one of these three forms:
a2 - b2 = (a + b)(a - b)
1. _______________________________:
a3 + b3 = (a + b)(a2 - ab + b2)
2. _______________________________:
a3 - b3 = (a - b)(a2 + ab + b2)
3. _______________________________:
29. Step 3.If it is a -termed expression (or trinomial), it may fall into one
of these groups:
1.The coefficient of is 1. Example: ________________. Find two
numbers whose sum is ______ and whose product is ______.
They are ______ and ______:
30. Step 3.If it is a three -termed expression (or trinomial), it may fall into one
of these groups:
1.The coefficient of is 1. Example: ________________. Find two
numbers whose sum is ______ and whose product is ______.
They are ______ and ______:
31. Step 3.If it is a three -termed expression (or trinomial), it may fall into one
of these groups:
1.The coefficient of x is 1. Example: ________________. Find two
numbers whose sum is ______ and whose product is ______.
They are ______ and ______:
32. Step 3.If it is a three -termed expression (or trinomial), it may fall into one
of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________. Find two
numbers whose sum is ______ and whose product is ______.
They are ______ and ______:
33. Step 3.If it is a three -termed expression (or trinomial), it may fall into one
of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________. Find two
-17
numbers whose sum is ______ and whose product is ______.
They are ______ and ______:
34. Step 3.If it is a three -termed expression (or trinomial), it may fall into one
of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________. Find two
-17
numbers whose sum is ______ and whose product is ______. -60
They are ______ and ______:
35. Step 3.If it is a three -termed expression (or trinomial), it may fall into one
of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________. Find two
-17
numbers whose sum is ______ and whose product is ______. -60
-20
They are ______ and ______:
36. Step 3.If it is a three -termed expression (or trinomial), it may fall into one
of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________. Find two
-17
numbers whose sum is ______ and whose product is ______. -60
-20 3
They are ______ and ______:
37. 2. The coefficient of is not 1. Example: ________________.
a. Find the product of first and last coefficients: ___________
= _____.
b. Look for two numbers whose product is ______ and whose
sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
38. 2. The coefficient of x is not 1. Example: ________________.
a. Find the product of first and last coefficients: ___________
= _____.
b. Look for two numbers whose product is ______ and whose
sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
39. 6x2 - 7x - 3
2. The coefficient of x is not 1. Example: ________________.
a. Find the product of first and last coefficients: ___________
= _____.
b. Look for two numbers whose product is ______ and whose
sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
40. 6x2 - 7x - 3
2. The coefficient of x is not 1. Example: ________________.
(6)(-3)
a. Find the product of first and last coefficients: ___________
= _____.
b. Look for two numbers whose product is ______ and whose
sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
41. 6x2 - 7x - 3
2. The coefficient of x is not 1. Example: ________________.
(6)(-3)
a. Find the product of first and last coefficients: ___________
-18
= _____.
b. Look for two numbers whose product is ______ and whose
sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
42. 6x2 - 7x - 3
2. The coefficient of x is not 1. Example: ________________.
(6)(-3)
a. Find the product of first and last coefficients: ___________
-18
= _____.
-18
b. Look for two numbers whose product is ______ and whose
sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
43. 6x2 - 7x - 3
2. The coefficient of x is not 1. Example: ________________.
(6)(-3)
a. Find the product of first and last coefficients: ___________
-18
= _____.
-18
b. Look for two numbers whose product is ______ and whose
-7
sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
44. 6x2 - 7x - 3
2. The coefficient of x is not 1. Example: ________________.
(6)(-3)
a. Find the product of first and last coefficients: ___________
-18
= _____.
-18
b. Look for two numbers whose product is ______ and whose
-7 -9
sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
45. 6x2 - 7x - 3
2. The coefficient of x is not 1. Example: ________________.
(6)(-3)
a. Find the product of first and last coefficients: ___________
-18
= _____.
-18
b. Look for two numbers whose product is ______ and whose
-7 -9
sum is _____: _____ and ______. 2
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
46. 6x2 - 7x - 3
2. The coefficient of x is not 1. Example: ________________.
(6)(-3)
a. Find the product of first and last coefficients: ___________
-18
= _____.
-18
b. Look for two numbers whose product is ______ and whose
-7 -9
sum is _____: _____ and ______. 2
c. Write the expression as four terms:
6x2 - 9x +2x - 3
d. Proceed to use Step 4 as follows:
47. Step 4.If it is a -termed expression, try factoring by grouping.
Example:
48. Step 4.If it is a four-termed expression, try factoring by grouping.
Example:
49. Step 4.If it is a four-termed expression, try factoring by grouping.
Example: 2x2 - 3xy - 4x + 6y
50. 4. Exercises
Factor each expression completely.
4 2 3
1. x − 9x 2. x − 27
3 2
3. x + 8 4. 4t + 16t + 16
2 2
5. y − 9y + 20 6. 6m + 5m − 4
52. Day 3
1. Opener
A person is standing at the top of a building, and throws a
ball upwards from a height of 60 ft, with an initial velocity
of 30 ft per second. How long will it take for the ball to
reach a height of 25 ft from the floor?
1 2
Use the formula h = − gt + v0t + h0
2
55. Day 4
1. Opener
1. True or False:
a) A function is a set of ordered pairs.
b) A relation is a set of ordered pairs where the first
element of each ordered pair is never repeated.
2. What is the most recognizable ad icon of the 20th
century?
65. Are the following relations functions, or just relations?
Vertical Line Test.
Sweep a vertical line across the graph of the function. If
the line crosses the graph more than once it is not a
function, only a relation.
66. Day 7
1. Domain and Range.
What is the domain and range of the following function?
67. Day 7
1. Domain and Range.
What is the domain and range of the following function?
Domain.
Is the set of "input" or argument values for which the
function is defined.
68. Day 7
1. Domain and Range.
What is the domain and range of the following function?
Domain.
Is the set of "input" or argument values for which the
function is defined.
Range.
Refers to the output of a function.
69. What is the domain and range of the following function?
70. 2. Examples.
What is the domain and range of the following functions?
1. f (x) = 4 − x
1
2. g(x) =
2x + 3
3. y = 1− 2x
72. 1. Quiz 1.
Factor the following, completely:
2
1. x − 3x − 40
2. 2x 2 + 3x − 35
2
3. x − 49
2
4. z + 12z + 36
3
5. x + 8
Use the cuadratic formula to solve:
2
5x − 2x + 7 = 0
Editor's Notes
\n
Want to be successful in this class (or any class)? Be on time.\n
What do you need? This is what you NEED to bring to class everyday. Having penS is an advantage for you.\n
What do you need? This is what you NEED to bring to class everyday. Having penS is an advantage for you.\n
What do you need? This is what you NEED to bring to class everyday. Having penS is an advantage for you.\n
What do you need? This is what you NEED to bring to class everyday. Having penS is an advantage for you.\n
What do you need? This is what you NEED to bring to class everyday. Having penS is an advantage for you.\n
What do you need? This is what you NEED to bring to class everyday. Having penS is an advantage for you.\n
Attempt ALL you homework every night. If you make a mistake with your homework, you will know where you have to practice more. Also, you will be able to share your mistakes with your teacher. Doing this will help you to LEARN.\n
This will help you to sleep.\n
Here&#x2019;s a problem: you will start forgetting what you learned in class. Day 2, Day 7. How do you stop the curve of forgetting? You review your notes. Each time you do it, it&#x2019;s gonna take less time to review IF YOU&#x2019;RE DOING IT EVERYDAY.\n
Do not walk out of this room thinking: Man, I don&#x2019;t know what he was talking about. School&#x2019;s about learning, and learning IS A CONVERSATION. For some reason, students are afraid of asking questions. You will be a hero to your classmates, &#x2018;cause they will be like &#x201C;I&#x2019;m so glad that he asked that question&#x201D;.\n