Quadratic equations presentation
•Download as PPT, PDF•
0 likes•312 views
This document discusses quadratic equations, their standard form of ax^2 + bx + c, and how to solve them using the discriminant and completing the square method. It also explains how the sign of the discriminant determines the number of solutions and shows graphs of parabolas with positive and negative coefficients to demonstrate their orientation.
Report
Share
Report
Share
Recommended
Methods of Solving Quadratic Equations
The quadratic equation is about the polynomial equation in the single variable where the highest exponent of a variable is only 2. If you want to know solving quadratic equations, you will have three main ways to solve the quadratic equation.
Cal 3
This lecture discusses distance, midpoint, slope, lines, symmetries of graphs, equations of circles, and quadratic equations. It defines distance as the square root of the sum of the squared differences of x- and y-coordinates between two points. The midpoint formula finds the midpoint of a line segment between two points. Slope is defined as the rise over the run between two points on a line. Lines can be written in point-slope form, slope-intercept form, and intercept forms. Parallel and perpendicular lines are identified based on equal or negative reciprocal slopes. Symmetries of graphs include reflections across the x-axis, y-axis, or origin. The equation of a circle is given by (x-h)2
2 lesson 1 the factoring method
This document provides an overview of topics covered in Chapter 2 on quadratic equations and inequalities, including the factoring method, completing the square method, the quadratic formula, equations that lead to quadratics, applications, and quadratic and rational inequalities. It specifically discusses using the zero-factor property and a four-step process for solving quadratic equations by factoring the left side of the equation into two binomial factors and setting each factor equal to zero.
Chapter#8
This document discusses tables, graphs, and linear regression analysis in engineering. It covers:
1) Using tables to present technical data with independent variables on the left and dependent variables on the right.
2) Using graphs to represent tabulated data, with the dependent variable on the y-axis and independent on the x-axis.
3) Performing linear regression analysis to determine the linear equation that best fits a set of data points by minimizing the residuals.
Calculus
This lecture discusses inequalities, absolute values, and graphs of solutions to inequalities on a coordinate plane. Key points covered include:
- Inequalities relate values that are different using symbols like < and >. Operations on inequalities follow rules like adding/subtracting a positive number or multiplying/dividing by a negative number requires changing the inequality symbol.
- Absolute value expressions use | | to represent the distance from zero. Operations inside | | follow different rules than normal order of operations.
- Graphing solutions to inequalities involves open/closed circles and drawing lines left/right to represent <, >, ≤, or ≥. Examples are worked through to demonstrate graphing linear and quadratic inequalities.
matrices and function ( matrix)
This document is an introduction to matrices presented by Reza At-Tanzil of the Department of Pharmacy at Comilla University. It defines what a matrix is, describes different types of matrices including column/row matrices, rectangular matrices, square matrices, diagonal matrices, identity matrices, null matrices, and scalar matrices. It also covers matrix operations such as matrix multiplication, transpose of a matrix, symmetric matrices, inverse of a matrix, and adjoint matrices.
ABC Math Project
This document contains definitions and explanations of various math terms starting from A to Z. Some of the key terms defined include:
- Angle of rotation which is the shortest angle an object can be turned around its center.
- Bedmas which outlines the order of operations for solving equations.
- Coefficients which are numbers used to multiply variables in an equation.
- Exponents which indicate how many times to multiply a base number by itself.
- Fractions which are numbers below 1 and can be converted to decimals.
- Hypotenuse which is the longest side of a right triangle opposite the right angle.
- Pythagorean theorem which uses the formula a2 + b2 = c2 to
Notes of Matrices and Determinants
This document covers matrices, determinants, and their properties. Some key points:
- A matrix is a rectangular arrangement of numbers. The order of a m×n matrix is defined by its m rows and n columns.
- A square matrix is symmetric if it is equal to its transpose, and skew-symmetric if it is equal to the negative of its transpose.
- The determinant of a square matrix provides a number associated with the matrix, denoted |A| or detA.
- Properties of determinants include that the value does not change under row/column interchange operations, and that multiplying a row/column by a constant k multiplies the determinant by k.
Recommended
Methods of Solving Quadratic Equations
The quadratic equation is about the polynomial equation in the single variable where the highest exponent of a variable is only 2. If you want to know solving quadratic equations, you will have three main ways to solve the quadratic equation.
Cal 3
This lecture discusses distance, midpoint, slope, lines, symmetries of graphs, equations of circles, and quadratic equations. It defines distance as the square root of the sum of the squared differences of x- and y-coordinates between two points. The midpoint formula finds the midpoint of a line segment between two points. Slope is defined as the rise over the run between two points on a line. Lines can be written in point-slope form, slope-intercept form, and intercept forms. Parallel and perpendicular lines are identified based on equal or negative reciprocal slopes. Symmetries of graphs include reflections across the x-axis, y-axis, or origin. The equation of a circle is given by (x-h)2
2 lesson 1 the factoring method
This document provides an overview of topics covered in Chapter 2 on quadratic equations and inequalities, including the factoring method, completing the square method, the quadratic formula, equations that lead to quadratics, applications, and quadratic and rational inequalities. It specifically discusses using the zero-factor property and a four-step process for solving quadratic equations by factoring the left side of the equation into two binomial factors and setting each factor equal to zero.
Chapter#8
This document discusses tables, graphs, and linear regression analysis in engineering. It covers:
1) Using tables to present technical data with independent variables on the left and dependent variables on the right.
2) Using graphs to represent tabulated data, with the dependent variable on the y-axis and independent on the x-axis.
3) Performing linear regression analysis to determine the linear equation that best fits a set of data points by minimizing the residuals.
Calculus
This lecture discusses inequalities, absolute values, and graphs of solutions to inequalities on a coordinate plane. Key points covered include:
- Inequalities relate values that are different using symbols like < and >. Operations on inequalities follow rules like adding/subtracting a positive number or multiplying/dividing by a negative number requires changing the inequality symbol.
- Absolute value expressions use | | to represent the distance from zero. Operations inside | | follow different rules than normal order of operations.
- Graphing solutions to inequalities involves open/closed circles and drawing lines left/right to represent <, >, ≤, or ≥. Examples are worked through to demonstrate graphing linear and quadratic inequalities.
matrices and function ( matrix)
This document is an introduction to matrices presented by Reza At-Tanzil of the Department of Pharmacy at Comilla University. It defines what a matrix is, describes different types of matrices including column/row matrices, rectangular matrices, square matrices, diagonal matrices, identity matrices, null matrices, and scalar matrices. It also covers matrix operations such as matrix multiplication, transpose of a matrix, symmetric matrices, inverse of a matrix, and adjoint matrices.
ABC Math Project
This document contains definitions and explanations of various math terms starting from A to Z. Some of the key terms defined include:
- Angle of rotation which is the shortest angle an object can be turned around its center.
- Bedmas which outlines the order of operations for solving equations.
- Coefficients which are numbers used to multiply variables in an equation.
- Exponents which indicate how many times to multiply a base number by itself.
- Fractions which are numbers below 1 and can be converted to decimals.
- Hypotenuse which is the longest side of a right triangle opposite the right angle.
- Pythagorean theorem which uses the formula a2 + b2 = c2 to
Notes of Matrices and Determinants
This document covers matrices, determinants, and their properties. Some key points:
- A matrix is a rectangular arrangement of numbers. The order of a m×n matrix is defined by its m rows and n columns.
- A square matrix is symmetric if it is equal to its transpose, and skew-symmetric if it is equal to the negative of its transpose.
- The determinant of a square matrix provides a number associated with the matrix, denoted |A| or detA.
- Properties of determinants include that the value does not change under row/column interchange operations, and that multiplying a row/column by a constant k multiplies the determinant by k.
MATRICES AND ITS TYPE
The document presents information on matrices and their types. It defines a matrix as an arrangement of numbers, symbols or expressions in rows and columns. It discusses different types of matrices including row matrices, column matrices, square matrices, rectangular matrices, diagonal matrices, scalar matrices, unit/identity matrices, symmetric matrices, complex matrices, hermitian matrices, skew-hermitian matrices, orthogonal matrices, unitary matrices, and nilpotent matrices. It provides examples and definitions for hermitian matrices, orthogonal matrices, idempotent matrices, and nilpotent matrices. The presentation was given by Himanshu Negi on matrices and their types.
Matrices y determinants
This document discusses matrices and their properties. It defines a matrix as a rectangular array of numbers arranged in rows and columns. It describes several types of matrices including line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also explains common operations that can be performed on matrices such as addition, subtraction, scalar multiplication, and multiplication. Key properties of these matrix operations are provided.
ABC Math Book
This document provides definitions and explanations of math terms from A to Z. It summarizes key concepts for each letter, including definitions of algebra, BEDMAS order of operations, coefficients, the distributive property, exponents, fractions, greater than symbols, independent variables, like terms, the Pythagorean theorem, variables, the x-axis, and the y-axis. The document is intended to be an alphabetical math glossary covering a wide range of foundational math concepts from the ABC Math Book.
Math 7 vocabulary powerpoint
The document defines key mathematical terms including:
- Coefficient - A number multiplied with a term in an expression.
- Exponent - How many times a number is used in a multiplication.
- Domain - The set of input values for which a function is defined.
- Factors - Numbers that can be multiplied together to get another number.
Matrices
This document defines and provides examples of different types of matrices including upper triangular, lower triangular, transpose, symmetric, and inverse matrices. It also describes common operations that can be performed on matrices such as addition, subtraction, scalar multiplication, and matrix multiplication. These operations have specific properties like associativity, neutral elements, and distributivity.
Math vocabulary A-Z
This document defines various mathematical terms:
- Addition is taking two amounts and adding them together, with examples like 2+8=10.
- A base is the bottom of any shape besides a circle.
- A catenary is the curve formed by a chain suspended between two points.
- Division determines how many times one quantity contains another, with examples of division problems.
- A graph is a set of points called vertices connected by lines called edges.
Matrices
Matrices are a key tool in linear algebra and can be used to represent linear transformations and track coefficients in systems of linear equations. For square matrices, the determinant and inverse matrix (when it exists) govern the behavior of solutions. Symmetric matrices are equal to their transpose, triangular matrices have null elements above or below the main diagonal, and augmented matrices are used to solve systems of linear equations by combining the matrix with an identity matrix. Matrix multiplication is defined when the number of columns in the left matrix equals the number of rows in the right matrix, and the determinant of a square matrix represents a scale factor under linear transformations.
TIU CET Review Math Session 6 - part 1 of 2
College Entrance Test Review
Math Session 6 - part 1 of 2
Equations
Rational Equations
Radical Equations
Absolute Value Equations
Matrices
matrices
The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.
It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive.
Tetrachoric Correlation Coefficient
The tetrachoric correlation coefficient is used to measure the correlation between two dichotomous variables. It is calculated based on a 2x2 contingency table and can range from -1 to 1. Values close to 0 indicate a weak correlation while values close to -1 or 1 indicate a strong correlation. The coefficient can be used to determine if two dichotomous variables, like passing/failing an exam, are positively or negatively correlated. It provides information about relationships that can help answer questions involving traits and outcomes.
Graphing sytems inequalities
This document provides instructions for graphing systems of linear inequalities. It explains how to write inequalities in slope-intercept form, plot points to draw the line, and shade the appropriate region based on whether it is <, ≤, >, or ≥. An example problem is worked through step-by-step to demonstrate how to graph two inequalities and find the overlapping region that satisfies both inequalities. Practice problems are then provided for the reader to work through on their own.
Linear inequalities in two variables
The document discusses linear inequalities in two variables and their graphical representations. It introduces the Cartesian coordinate system developed by Rene Descartes and its importance. It explains how to graph linear inequalities by first drawing the line as an equation, then determining whether to shade above or below the line based on whether a test point satisfies the inequality. Students are assigned to bring graphing paper, coloring materials, and a ruler to class on Monday to graph linear inequalities.
Tmp2023
This document discusses teaching students about integers and their relationship to vectors. It explains that students should understand how to use integers to represent positive and negative descriptions. Integers are also related to vectors in mathematics, as subtracting vectors is the same as adding the negative of one vector. Understanding the positive and negative directions of integers will help students also grasp the positive and negative directions of vectors.
Matrices
This document defines and describes various types of matrices. It defines a matrix as a rectangular array of numbers or functions with m rows and n columns referred to as an m x n matrix. It then lists and defines the following types of matrices: row matrix, column matrix, null matrix, rectangular matrix, square matrix, diagonal matrix, scalar matrix, unit matrix, symmetric matrix, and skew-symmetric matrix. It provides examples of each type of matrix and their general syntax.
Matrix.
The document defines and provides examples of different types of matrices, including:
- Square matrices, where the number of rows equals the number of columns.
- Rectangular matrices, where the number of rows does not equal the number of columns.
- Row matrices, with only one row.
- Column matrices, with only one column.
- Null or zero matrices, with all elements equal to zero.
- Diagonal matrices, with all elements equal to zero except those on the main diagonal.
The document also discusses transpose, adjoint, and addition of matrices.
Algebra booklet
This document provides an introduction to algebra and quadratic expressions and equations, including definitions of key terms like variables, coefficients, and algebraic expressions. It covers topics like expanding, simplifying, and factorizing quadratic expressions using various methods. Real-world applications of quadratic equations are discussed, such as their use in physics, finance, and everyday contexts involving areas, profits, speeds, lenses, and mirrors.
Matrices
The document provides an introduction to matrix operations including addition, subtraction, multiplication, and determinants. It defines what a matrix is and how they are represented and sized. It then explains how to perform addition and subtraction of matrices by adding or subtracting the corresponding entries. Matrix multiplication is defined as being possible only when the number of columns of the first matrix equals the rows of the second. Determinants are explained as being unique to square matrices, and formulas are given for finding the determinants of 2x2 and 3x3 matrices. Homework problems are assigned involving computing various matrix operations.
Integers
This document discusses how integers are related to vectors and how understanding integers can help students learn vectors. It explains that integers, like vectors, have positive and negative values that represent direction. Subtracting vectors is the same as adding the negative of the second vector, changing its direction. The document emphasizes that if students learn about integers and how they can be positive or negative, it will be easier for them to understand vectors and how they too have direction represented by their signs.
NUMERICAL APPROXIMATION
Numerical approximation methods provide alternative procedures to analytical methods for solving mathematical problems that are complex or do not have exact solutions. These methods use iteration to systematically approximate the true value of a variable. Accuracy refers to how close an approximation is to the actual value, while precision refers to the number of significant figures. For a numerical method to work well, it must converge, meaning the approximations get closer to the true value with more iterations, and be stable. The appropriate method depends on factors like the type of problem, complexity of the model, and characteristics of the numerical method itself such as speed of convergence and stability.
Lar calc10 ch03_sec5
This document discusses limits at infinity and horizontal asymptotes of functions. It defines limits at infinity as the value a function approaches as the input variable increases or decreases without bound. Rational functions always have the same horizontal asymptote as x approaches positive or negative infinity, determined by dividing the highest-order terms of the numerator and denominator. Other functions may have different horizontal asymptotes on the left and right. Examples show how to evaluate finite and infinite limits at infinity and determine any horizontal asymptotes graphically.
MATH-QUADRATIC EQUATIONS.pptx
This document discusses quadratic equations and functions. It covers topics such as solving quadratic equations by factoring, completing the square, and using the quadratic formula. It also discusses quadratic inequalities, the discriminant, graphing quadratic functions, and problem solving with quadratics. Key steps for solving quadratic equations are to rearrange the equation so one side is zero, fully factorize the other side, and solve the resulting linear equations. Completing the square can be used when a quadratic cannot be easily factorized. The quadratic formula provides the solution for any quadratic equation in standard form.
Grade 8-math-quarter-1-pacing-guide (1)22
This document provides a curriculum map for 8th grade mathematics for the first quarter. Students will develop an understanding of irrational numbers by approximating them with rational numbers. They will use square roots and cube roots to solve equations. Students will also apply the Pythagorean theorem and its converse to solve problems involving right triangles. Additionally, they will learn to solve linear equations with rational number coefficients.
More Related Content
What's hot
MATRICES AND ITS TYPE
The document presents information on matrices and their types. It defines a matrix as an arrangement of numbers, symbols or expressions in rows and columns. It discusses different types of matrices including row matrices, column matrices, square matrices, rectangular matrices, diagonal matrices, scalar matrices, unit/identity matrices, symmetric matrices, complex matrices, hermitian matrices, skew-hermitian matrices, orthogonal matrices, unitary matrices, and nilpotent matrices. It provides examples and definitions for hermitian matrices, orthogonal matrices, idempotent matrices, and nilpotent matrices. The presentation was given by Himanshu Negi on matrices and their types.
Matrices y determinants
This document discusses matrices and their properties. It defines a matrix as a rectangular array of numbers arranged in rows and columns. It describes several types of matrices including line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also explains common operations that can be performed on matrices such as addition, subtraction, scalar multiplication, and multiplication. Key properties of these matrix operations are provided.
ABC Math Book
This document provides definitions and explanations of math terms from A to Z. It summarizes key concepts for each letter, including definitions of algebra, BEDMAS order of operations, coefficients, the distributive property, exponents, fractions, greater than symbols, independent variables, like terms, the Pythagorean theorem, variables, the x-axis, and the y-axis. The document is intended to be an alphabetical math glossary covering a wide range of foundational math concepts from the ABC Math Book.
Math 7 vocabulary powerpoint
The document defines key mathematical terms including:
- Coefficient - A number multiplied with a term in an expression.
- Exponent - How many times a number is used in a multiplication.
- Domain - The set of input values for which a function is defined.
- Factors - Numbers that can be multiplied together to get another number.
Matrices
This document defines and provides examples of different types of matrices including upper triangular, lower triangular, transpose, symmetric, and inverse matrices. It also describes common operations that can be performed on matrices such as addition, subtraction, scalar multiplication, and matrix multiplication. These operations have specific properties like associativity, neutral elements, and distributivity.
Math vocabulary A-Z
This document defines various mathematical terms:
- Addition is taking two amounts and adding them together, with examples like 2+8=10.
- A base is the bottom of any shape besides a circle.
- A catenary is the curve formed by a chain suspended between two points.
- Division determines how many times one quantity contains another, with examples of division problems.
- A graph is a set of points called vertices connected by lines called edges.
Matrices
Matrices are a key tool in linear algebra and can be used to represent linear transformations and track coefficients in systems of linear equations. For square matrices, the determinant and inverse matrix (when it exists) govern the behavior of solutions. Symmetric matrices are equal to their transpose, triangular matrices have null elements above or below the main diagonal, and augmented matrices are used to solve systems of linear equations by combining the matrix with an identity matrix. Matrix multiplication is defined when the number of columns in the left matrix equals the number of rows in the right matrix, and the determinant of a square matrix represents a scale factor under linear transformations.
TIU CET Review Math Session 6 - part 1 of 2
College Entrance Test Review
Math Session 6 - part 1 of 2
Equations
Rational Equations
Radical Equations
Absolute Value Equations
Matrices
matrices
The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.
It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive.
Tetrachoric Correlation Coefficient
The tetrachoric correlation coefficient is used to measure the correlation between two dichotomous variables. It is calculated based on a 2x2 contingency table and can range from -1 to 1. Values close to 0 indicate a weak correlation while values close to -1 or 1 indicate a strong correlation. The coefficient can be used to determine if two dichotomous variables, like passing/failing an exam, are positively or negatively correlated. It provides information about relationships that can help answer questions involving traits and outcomes.
Graphing sytems inequalities
This document provides instructions for graphing systems of linear inequalities. It explains how to write inequalities in slope-intercept form, plot points to draw the line, and shade the appropriate region based on whether it is <, ≤, >, or ≥. An example problem is worked through step-by-step to demonstrate how to graph two inequalities and find the overlapping region that satisfies both inequalities. Practice problems are then provided for the reader to work through on their own.
Linear inequalities in two variables
The document discusses linear inequalities in two variables and their graphical representations. It introduces the Cartesian coordinate system developed by Rene Descartes and its importance. It explains how to graph linear inequalities by first drawing the line as an equation, then determining whether to shade above or below the line based on whether a test point satisfies the inequality. Students are assigned to bring graphing paper, coloring materials, and a ruler to class on Monday to graph linear inequalities.
Tmp2023
This document discusses teaching students about integers and their relationship to vectors. It explains that students should understand how to use integers to represent positive and negative descriptions. Integers are also related to vectors in mathematics, as subtracting vectors is the same as adding the negative of one vector. Understanding the positive and negative directions of integers will help students also grasp the positive and negative directions of vectors.
Matrices
This document defines and describes various types of matrices. It defines a matrix as a rectangular array of numbers or functions with m rows and n columns referred to as an m x n matrix. It then lists and defines the following types of matrices: row matrix, column matrix, null matrix, rectangular matrix, square matrix, diagonal matrix, scalar matrix, unit matrix, symmetric matrix, and skew-symmetric matrix. It provides examples of each type of matrix and their general syntax.
Matrix.
The document defines and provides examples of different types of matrices, including:
- Square matrices, where the number of rows equals the number of columns.
- Rectangular matrices, where the number of rows does not equal the number of columns.
- Row matrices, with only one row.
- Column matrices, with only one column.
- Null or zero matrices, with all elements equal to zero.
- Diagonal matrices, with all elements equal to zero except those on the main diagonal.
The document also discusses transpose, adjoint, and addition of matrices.
Algebra booklet
This document provides an introduction to algebra and quadratic expressions and equations, including definitions of key terms like variables, coefficients, and algebraic expressions. It covers topics like expanding, simplifying, and factorizing quadratic expressions using various methods. Real-world applications of quadratic equations are discussed, such as their use in physics, finance, and everyday contexts involving areas, profits, speeds, lenses, and mirrors.
Matrices
The document provides an introduction to matrix operations including addition, subtraction, multiplication, and determinants. It defines what a matrix is and how they are represented and sized. It then explains how to perform addition and subtraction of matrices by adding or subtracting the corresponding entries. Matrix multiplication is defined as being possible only when the number of columns of the first matrix equals the rows of the second. Determinants are explained as being unique to square matrices, and formulas are given for finding the determinants of 2x2 and 3x3 matrices. Homework problems are assigned involving computing various matrix operations.
Integers
This document discusses how integers are related to vectors and how understanding integers can help students learn vectors. It explains that integers, like vectors, have positive and negative values that represent direction. Subtracting vectors is the same as adding the negative of the second vector, changing its direction. The document emphasizes that if students learn about integers and how they can be positive or negative, it will be easier for them to understand vectors and how they too have direction represented by their signs.
NUMERICAL APPROXIMATION
Numerical approximation methods provide alternative procedures to analytical methods for solving mathematical problems that are complex or do not have exact solutions. These methods use iteration to systematically approximate the true value of a variable. Accuracy refers to how close an approximation is to the actual value, while precision refers to the number of significant figures. For a numerical method to work well, it must converge, meaning the approximations get closer to the true value with more iterations, and be stable. The appropriate method depends on factors like the type of problem, complexity of the model, and characteristics of the numerical method itself such as speed of convergence and stability.
Lar calc10 ch03_sec5
This document discusses limits at infinity and horizontal asymptotes of functions. It defines limits at infinity as the value a function approaches as the input variable increases or decreases without bound. Rational functions always have the same horizontal asymptote as x approaches positive or negative infinity, determined by dividing the highest-order terms of the numerator and denominator. Other functions may have different horizontal asymptotes on the left and right. Examples show how to evaluate finite and infinite limits at infinity and determine any horizontal asymptotes graphically.
What's hot (20)
Similar to Quadratic equations presentation
MATH-QUADRATIC EQUATIONS.pptx
This document discusses quadratic equations and functions. It covers topics such as solving quadratic equations by factoring, completing the square, and using the quadratic formula. It also discusses quadratic inequalities, the discriminant, graphing quadratic functions, and problem solving with quadratics. Key steps for solving quadratic equations are to rearrange the equation so one side is zero, fully factorize the other side, and solve the resulting linear equations. Completing the square can be used when a quadratic cannot be easily factorized. The quadratic formula provides the solution for any quadratic equation in standard form.
Grade 8-math-quarter-1-pacing-guide (1)22
This document provides a curriculum map for 8th grade mathematics for the first quarter. Students will develop an understanding of irrational numbers by approximating them with rational numbers. They will use square roots and cube roots to solve equations. Students will also apply the Pythagorean theorem and its converse to solve problems involving right triangles. Additionally, they will learn to solve linear equations with rational number coefficients.
Solving a linear equation single and multi step
This document discusses strategies for solving linear equations. It explains that the goal is to isolate the variable by using properties of equality to transform equations into equivalent forms with fewer terms. The key properties discussed are adding or subtracting the same quantity to both sides, multiplying or dividing both sides by the same non-zero quantity, and the distributive property. An example equation is then worked through to demonstrate this process. Students are reminded that inverse operations and these properties can be applied to simplify equations until the variable is alone on one side in the form of x = a constant.
0011 chapter iv
This document provides instruction on solving various types of equations, including quadratic equations, equations containing radicals, and equations that can be reduced to quadratic form. It includes examples of solving equations that are quadratic in form by rewriting them in standard form and substituting a variable, then solving the resulting quadratic equation. It also provides examples of solving equations containing radicals by isolating radicals and raising both sides of the equation to appropriate powers. Students are expected to learn to identify different equation types, select appropriate solution methods, and solve various quadratic and radical equations.
Linear Inequality slayerix
1) Solving linear inequalities involves using the same concepts as solving linear equations to isolate the variable, but inequalities have infinite solutions rather than a single solution.
2) Inequality signs (<, >, ≤, ≥) indicate whether values are less than, greater than, less than or equal to, or greater than or equal to another value.
3) Graphing linear inequalities on a number line or coordinate plane involves graphing the corresponding equality and then shading the appropriate side based on the inequality sign and whether it includes the endpoint or not.
Ratios, proportions, similar figures
1) Ratios and proportions are used in many areas including map reading, scale drawings, and solving problems.
2) A ratio compares two quantities by division, and ratios that make the same comparison are equivalent ratios. Proportions are equations that state two ratios are equal.
3) Similar figures have the same shape but not necessarily the same size, with corresponding angles being congruent and corresponding sides forming equivalent ratios. Ratios and proportions can be used to solve for unknown sides or quantities in similar figures.
RATIOS_PROPORTIONS_AND_SIMILAR_FIGURES.ppt
This document discusses ratios, proportions, and similar figures. It provides examples of using ratios to compare quantities and solve problems involving scale drawings. A ratio compares two quantities using division, and ratios that make the same comparison are equivalent ratios. Proportions state that two ratios are equal, and can be used to solve for unknown values. Figures are similar if corresponding angles are congruent and corresponding sides are proportional, forming equivalent ratios. Examples are given of setting up and solving proportions to find unknown side lengths of similar figures.
Week_1_Y10-Done.pptx
Here are some suggestions for extending the lesson:
- Have learners solve more complex problems involving multiple applications of trigonometric ratios, Pythagoras' theorem and angle properties. Real-world scenarios work well.
- Introduce the unit circle and have learners locate trig function values for angles between 0-360 degrees.
- Review trig identities like sin^2(x) + cos^2(x) = 1 and extend to derive others like 1 + tan^2(x) = sec^2(x).
- Introduce the inverse trig functions (arcsin, arccos, arctan) and have learners practice evaluating and using them.
- For advanced
Study of Correlation Theory with Different Views and Methodsamong Variables i...
Correlation among two numbers is an important concept and this relationship among two variables may be direct or indirect/inverse. Generally, correlation of two numbers is studyin statistics .The different types of correlation among numbers may be positively correlated, negatively correlated and perfectly correlated in statistics. Generally theserelationship is direct or indirect/inverse.So,in this paper it is tried to explore correlation among numbers/variables inunitary methods, ratio and proportion, variation methods.
Ecuaciones y Desigualdades.pdf
This document provides an overview of solving linear equations, formulas, and problem solving techniques. It begins by introducing the basic properties of equality used to solve linear equations, such as distributing terms and adding/subtracting terms to isolate the variable. Examples are provided to demonstrate solving equations with fractions and solving literal equations for a specified variable. The document also discusses identities, contradictions, and using a general formula to solve families of linear equations. It concludes by outlining a problem solving guide to organize the steps of reading, visualizing, and developing an equation model to solve word problems.
Tmp2023
This document discusses how integers are related to vectors and how understanding integers can help students learn vectors. It explains that integers, like vectors, have positive and negative values that represent direction. Subtracting vectors is the same as adding the negative of the second vector, and changing a vector's direction requires applying a negative sign. Mastering the concept of positive and negative integers will therefore help students grasp the similar concept of direction for vectors.
Section 7.5 version 2 AM new ppt for every
- Matrices are equal if they have the same dimensions and corresponding entries are equal. Two matrices can be added by adding corresponding entries, provided they have the same dimensions. A matrix can be multiplied by a scalar by multiplying each entry of the matrix by the scalar.
- Matrix multiplication is defined by multiplying the rows of the first matrix with the columns of the second. The product of matrices is only defined if the number of columns of the first equals the number of rows of the second. The identity matrix satisfies the property that when multiplied by a matrix, the original matrix is obtained.
Additional Mathematics Revision
This document provides a summary of topics related to algebra, functions, and calculus including: linear and quadratic expressions, simultaneous equations, completing the square, trigonometric ratios, differentiation, tangents, normals, and finding stationary points through higher derivatives. It outlines key steps and methods for solving various types of problems within these topics.
Quadratic equation
The document provides an overview of quadratic equations, including:
1) Quadratic equations take the form of ax^2 + bx + c = 0 and involve an unknown (x) and known coefficients (a, b, c).
2) Quadratic equations can be solved through factoring, completing the square, using the quadratic formula, or graphing.
3) The quadratic formula provides the general solution for quadratic equations as x = (-b ± √(b^2 - 4ac))/2a.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...
The main purpose of this research is to find out the best method through iterative methods for solving the nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st degree based iterative methods. After that, the graphical development is established here with the help of the four iterative methods and these results are tested with various functions. An example of the algebraic equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two examples of the algebraic and transcendental equation are applied to verify the best method, as well as the level of errors, are shown graphically.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...
The main purpose of this research is to find out the best method through iterative methods for solving the nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st degree based iterative methods. After that, the graphical development is established here with the help of the four iterative methods and these results are tested with various functions. An example of the algebraic equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two examples of the algebraic and transcendental equation are applied to verify the best method, as well as the level of errors, are shown graphically.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...
The main purpose of this research is to find out the best method through iterative methods for solving the
nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the
nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st
degree based iterative methods. After that, the graphical development is established here with the help of
the four iterative methods and these results are tested with various functions. An example of the algebraic
equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two
examples of the algebraic and transcendental equation are applied to verify the best method, as well as the
level of errors, are shown graphically.
Maths notes for 4038 and 4016 paper
This document provides tips for acing the Additional Mathematics (AM) and Elementary Mathematics (EM) exams. It summarizes key statistics on topics that are highly tested, such as differentiation and integration making up 27.8% of the AM exam. It recommends focusing on the 11 chapters that make up 74.6% of the exam. Sample questions are provided for topics like trigonometry, logarithms, linear laws, and matrices. Strategies are outlined for solving different types of questions on these topics.
Applied Mathematics and Sciences: An International Journal (MathSJ)
The main goal of this research is to give the complete conception about numerical integration including
Newton-Cotes formulas and aimed at comparing the rate of performance or the rate of accuracy of
Trapezoidal, Simpson’s 1/3, and Simpson’s 3/8. To verify the accuracy, we compare each rules
demonstrating the smallest error values among them. The software package MATLAB R2013a is applied to
determine the best method, as well as the results, are compared. It includes graphical comparisons
mentioning these methods graphically. After all, it is then emphasized that the among methods considered,
Simpson’s 1/3 is more effective and accurate when the condition of the subdivision is only even for solving
a definite integral.
Similar to Quadratic equations presentation (20)
Study of Correlation Theory with Different Views and Methodsamong Variables i...
Study of Correlation Theory with Different Views and Methodsamong Variables i...
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...
Applied Mathematics and Sciences: An International Journal (MathSJ)
Applied Mathematics and Sciences: An International Journal (MathSJ)
Recently uploaded
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
مصحف أحرف الخلاف للقراء العشرةأعد أحرف الخلاف بالتلوين وصلا سمير بسيوني غفر الله له
Temple of Asclepius in Thrace. Excavation results
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
The History of Stoke Newington Street Names
Presented at the Stoke Newington Literary Festival on 9th June 2024
www.StokeNewingtonHistory.com
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...Nguyen Thanh Tu Collection
https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneHow to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
A Visual Guide to 1 Samuel | A Tale of Two Hearts
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
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.
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh
BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
Benner "Expanding Pathways to Publishing Careers"
This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...Nguyen Thanh Tu Collection
https://app.box.com/s/qhtvq32h4ybf9t49ku85x0n3xl4jhr15RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Physical pharmaceutics notes for B.pharm students
How to deliver Powerpoint Presentations.pptx
"How to make and deliver dynamic presentations by making it more interactive to captivate your audience attention"
Recently uploaded (20)
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
B. Ed Syllabus for babasaheb ambedkar education university.pdf
B. Ed Syllabus for babasaheb ambedkar education university.pdf
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Quadratic equations presentation
- 2. This is an example of a quadratic equation: where a and b are co efficiets and c is a constant variable.
- 3. this formula is more helpful and may be usedto solve quadratic equations.
- 4. as i aready discuss about the positive and negative discriminant, this example shows how to use discriminant and how the graph may look like the discriminant is +/-/=0.
- 5. completing the squre methods is used when the factors of the constant value which is 32 satisfy the equation.To know that the factors satisfy the equation,a learner may add/subtract the factors to get the middle term,if not so you may use other methods.
- 6. this graph represent the positive co efficient of a quadratic equation,that is why it faced upward this graph represent a negative coefficient of a quadratic equation,that is why is faced downwards.