11) Forming and Solving Equations.pptx
•Download as PPTX, PDF•
0 likes•49 views
The document discusses forming and solving equations from word problems. It provides examples of solving equations, forming equations from word problems about numbers, rectangles, triangles and shapes with equal areas. Students are asked to solve sample problems by writing the appropriate equations and solving for the unknown values.
Report
Share
Report
Share
Recommended
Factorising Quadratics
The document provides instructions on factorizing quadratic equations. It begins by explaining what quadratic equations are and provides examples. It then discusses factorizing quadratics where the coefficient of x^2 is 1 by finding two numbers whose product is the last term and sum is the middle term. The document continues explaining how to factorize when the coefficient of x^2 is not 1 and predicts the signs of the factors based on the signs of the terms in the quadratic equation. It provides examples of factorizing different quadratic equations.
1 1 solving simple equations
This document provides examples and explanations for solving one-step equations involving addition, subtraction, multiplication, and division. It also gives examples of writing and solving equations to solve word problems. Key steps include defining a variable, writing an equation, solving the equation, and answering the question. Common language in word problems like "is", "of", and "per" indicate the operation to use when writing the equation.
7.5 proportions in triangles
The document discusses proportional relationships in triangles using theorems about parallel lines and angle bisectors. It provides examples of applying the side-splitter theorem and triangle-angle-bisector theorem to find unknown values in various geometric figures by setting up proportional relationships between corresponding sides or segments. Readers are given practice problems applying these proportional relationship theorems to find specific variable values in diagrams.
Solving 2 step equations
This document provides instructions for solving two-step equations. It explains that two-step equations require breaking the problem into two steps - the first step involves adding or subtracting, while the second step involves multiplying or dividing. Several examples are worked through step-by-step to demonstrate the process of isolating the variable by first undoing addition/subtraction and then undoing multiplication/division. Students are provided practice problems and instructed to show their work.
Solving quadratic inequalities
To solve quadratic inequalities:
1. Express the inequality in standard form ax^2 + bx + c > 0.
2. Determine the boundary points by setting the equation equal to 0 and solving for x.
3. Set intervals to the left and right of the boundary points.
4. Pick a test point in each interval and check if it makes the inequality true.
5. Write the solution intervals.
Basic proportionality theorem
The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle, intersecting the other two sides at distinct points, the lengths of the segments of the two sides will be divided in the same ratio. The proof involves drawing additional lines perpendicular to the parallel line and original sides of the triangle, allowing the areas of different triangles to be set equal and proving that the ratios of the corresponding segments are equal.
A1 ch03 06 blue
This document provides instruction on solving compound inequalities with one variable. It begins with examples of writing compound inequalities to represent real-world contexts involving ranges, and solving simple inequalities connected by "AND" or "OR". The key aspects are: (1) for "AND", the intersection of the two inequalities' solutions is graphed; (2) for "OR", the union of the two solution sets is graphed. Later examples cover writing inequalities from given graphs. The lesson quiz provides practice solving, graphing, and writing compound inequalities.
Area of a triangle
To be able to calculate the area of a triangle using trigonometry up to Grade A*. By the end of the lesson, all students will be able to identify when to find the area of a triangle using trigonometry. Most students will be able to calculate the area of a triangle using the formula. Some students will be able to calculate GCSE area of triangle problems using trigonometry up to Grade A*. The document then provides examples and practice problems for students to calculate the area, missing sides and missing angles of triangles using trigonometry.
Recommended
Factorising Quadratics
The document provides instructions on factorizing quadratic equations. It begins by explaining what quadratic equations are and provides examples. It then discusses factorizing quadratics where the coefficient of x^2 is 1 by finding two numbers whose product is the last term and sum is the middle term. The document continues explaining how to factorize when the coefficient of x^2 is not 1 and predicts the signs of the factors based on the signs of the terms in the quadratic equation. It provides examples of factorizing different quadratic equations.
1 1 solving simple equations
This document provides examples and explanations for solving one-step equations involving addition, subtraction, multiplication, and division. It also gives examples of writing and solving equations to solve word problems. Key steps include defining a variable, writing an equation, solving the equation, and answering the question. Common language in word problems like "is", "of", and "per" indicate the operation to use when writing the equation.
7.5 proportions in triangles
The document discusses proportional relationships in triangles using theorems about parallel lines and angle bisectors. It provides examples of applying the side-splitter theorem and triangle-angle-bisector theorem to find unknown values in various geometric figures by setting up proportional relationships between corresponding sides or segments. Readers are given practice problems applying these proportional relationship theorems to find specific variable values in diagrams.
Solving 2 step equations
This document provides instructions for solving two-step equations. It explains that two-step equations require breaking the problem into two steps - the first step involves adding or subtracting, while the second step involves multiplying or dividing. Several examples are worked through step-by-step to demonstrate the process of isolating the variable by first undoing addition/subtraction and then undoing multiplication/division. Students are provided practice problems and instructed to show their work.
Solving quadratic inequalities
To solve quadratic inequalities:
1. Express the inequality in standard form ax^2 + bx + c > 0.
2. Determine the boundary points by setting the equation equal to 0 and solving for x.
3. Set intervals to the left and right of the boundary points.
4. Pick a test point in each interval and check if it makes the inequality true.
5. Write the solution intervals.
Basic proportionality theorem
The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle, intersecting the other two sides at distinct points, the lengths of the segments of the two sides will be divided in the same ratio. The proof involves drawing additional lines perpendicular to the parallel line and original sides of the triangle, allowing the areas of different triangles to be set equal and proving that the ratios of the corresponding segments are equal.
A1 ch03 06 blue
This document provides instruction on solving compound inequalities with one variable. It begins with examples of writing compound inequalities to represent real-world contexts involving ranges, and solving simple inequalities connected by "AND" or "OR". The key aspects are: (1) for "AND", the intersection of the two inequalities' solutions is graphed; (2) for "OR", the union of the two solution sets is graphed. Later examples cover writing inequalities from given graphs. The lesson quiz provides practice solving, graphing, and writing compound inequalities.
Area of a triangle
To be able to calculate the area of a triangle using trigonometry up to Grade A*. By the end of the lesson, all students will be able to identify when to find the area of a triangle using trigonometry. Most students will be able to calculate the area of a triangle using the formula. Some students will be able to calculate GCSE area of triangle problems using trigonometry up to Grade A*. The document then provides examples and practice problems for students to calculate the area, missing sides and missing angles of triangles using trigonometry.
Addition and subtraction of rational expression
To add or subtract fractions with unlike denominators:
1. Find the least common denominator (LCD), which contains all prime factors of each denominator raised to the highest power.
2. Convert the fractions to equivalent fractions with the LCD as the denominator.
3. Perform the addition or subtraction on the numerators and write the sum or difference over the common denominator.
Presentation on quadratic equation
IT'S A PRESENTATION ON QUADRATIC EQUATION PART 1, CLASS 10, CHAPTER 4, IT STARTS WITH THE SHAPE PARABOLA AND IT'S DAY TO DAY LIFE EXAMPLES, AS WE PROCEED FURTHER WE SOLVE SOME EXPRESSIONS, WE COVERT IT INTO QUADRATIC EQUATIONS. AFTERWARDS, WE LEARN HOW TO FORM STANDARD QUADRATIC EQUATIONS WITH EXAMPLES (WORD PROBLEMS).
Power of Power Exponent Rule
The document discusses exponential population growth and the "power of power" rule. It provides an example of how a population starting at 1 person that doubles each generation through having 4 children per person would grow exponentially from 1 to 4 to 16 to 64 etc. It then explains the rules for expanding exponential expressions using exponents, such as multiplying exponents when the base is the same under multiplication or addition, and subtracting exponents when dividing terms with the same base. Examples are provided to demonstrate simplifying expressions using these exponent rules.
(8) Lesson 2.1 - Solve Equations with Rational Coefficients
This document provides instruction on solving linear equations with one variable. It begins by defining key terms like multiplicative inverse and coefficient. It then provides examples of solving various equations by multiplying or dividing both sides of the equation by the same term to isolate the variable. These examples include equations with fractions, decimals, and percentages. The document emphasizes using the inverse operation property to solve equations and checking solutions. It aims to help students solve equations that may require expanding and combining like terms.
Expanding two brackets
The document discusses expanding and simplifying expressions within brackets. It provides examples of multiplying out terms within brackets for expressions like (2a + 3)(4a + 2) and (3b + 2)(4b - 6). The key steps are to multiply out each corresponding term, then collect like terms. Distributing negatives requires being careful about the signs of multiplied terms. The document encourages practicing expanding several example expressions within time limits to check understanding.
Distributive property in algebra power point
The document discusses the distributive property in algebra. The distributive property allows terms inside parentheses to be distributed so that expressions can be simplified out of order from the standard order of operations. It involves multiplying the number outside of the parentheses by each term inside the parentheses. Examples are provided to demonstrate how to use the distributive property to simplify expressions.
Order of operations
This document provides instruction on the order of operations for solving mathematical expressions. It explains that there are specific rules to follow when solving expressions, known as the order of operations. These rules are: 1) complete all operations within parentheses first, 2) perform all exponents next, 3) multiply and divide from left to right, and 4) add and subtract from left to right. The document provides examples of solving expressions using the proper order of operations and encourages remembering the order using the acronym PEMDAS.
Inequalities
This document discusses inequalities and their graphs. It defines an inequality as a statement that two expressions are not equal. It explains the symbols used in inequalities like <, >, ≤, and ≥ and how to graph them correctly, with open or closed circles depending on if it's a < or ≤. Examples are provided of writing and graphing simple one-variable inequalities and having the reader practice graphing some on their own. Key points covered include understanding the direction the solution goes based on what side the variable is on and coloring in or leaving open the circle depending on the symbol used.
Linear Equation In one variable class 7
This document defines and provides examples of linear equations in one variable. It explains that a linear equation is an equation that can be written in the form ax + b = c or ax = b, where a, b, c are constants and a ≠ 0. Examples of linear equations given include 3x + 9 = 0 and 7x + 5 = 2x - 9. The document also discusses how to determine if a value is a solution to a linear equation by substitution and simplification. Steps for solving linear equations are provided, which include isolating the variable using inverse operations like addition/subtraction and multiplication/division.
Percentages and discounts tutorial
This document provides information and examples for working with percentages and discounts. It covers converting between fractions, decimals, and percentages; finding percentages of quantities; calculating profit and loss; reversing percentages to find original values; and writing quantities as percentages of others. Examples are provided for each topic without and with a calculator. The next session will cover working with ratios.
Factoring perfect-square-trinomials
To factor perfect square trinomials:
1. Get the square root of the first and last terms.
2. List down the square root as the sum or difference of two terms.
3. Factor the expression into the form (term 1 ± term 2)2.
2 expressions and linear expressions
The document discusses expressions in mathematics. It defines expressions as calculation procedures written with numbers, variables, and operation symbols that calculate outcomes. Expressions can be combined by collecting like terms. Linear expressions take the form of ax + b, where terms can be combined by adding or subtracting the coefficients of the same variable. The example shows combining the terms of the expression 2x - 4 + 9 - 5x.
Substitution Method of Systems of Linear Equations
This document provides examples of solving systems of linear equations by substitution. The method involves choosing one equation to isolate a variable, substituting that expression into the other equation, then solving the resulting equation for the remaining variable and back-substituting to find the solution set. The examples demonstrate these steps clearly, showing the process of identifying which equation to transform, performing the substitutions, solving for variables, and checking the solutions.
Chapter 3. linear equation and linear equalities in one variables
Here are the steps to solve this inequality problem:
1) Write an expression for the perimeter in terms of x
2) Set the perimeter expression ≤ 40
3) Isolate x by undoing the operations
4) Write the solution set
The solution is 0 ≤ x ≤ 7
Systems of Equations by Elimination
This document provides instructions for solving systems of equations using elimination. It demonstrates eliminating variables by adding or subtracting equations. Sample systems are worked through, showing the steps of identifying which variable to eliminate, combining the equations accordingly, solving for one variable, then substituting back into the original equations to solve for the other. The solutions are checked in both equations to verify they satisfy the system.
Multiplication Properties of Exponents
Here are the steps to solve this problem:
1) Write the area of Samoa in scientific notation: 2.9 × 103 km2
2) The area of Texas is 2.3 × 102 times as great as Samoa
3) Multiply the area of Samoa by 2.3 × 102:
(2.9 × 103 km2) × (2.3 × 102) = 6.67 × 105 km2
The approximate area of Texas is 6.67 × 105 km2.
Basics about exponents
Exponents are used to represent repeated multiplication of a number, called the base. The exponent indicates how many times the base is multiplied. Some key laws for exponents include: when multiplying the same bases, add the exponents; when dividing the same bases, subtract the exponents; when raising a power to another power, multiply the exponents. Exponents provide a shorthand way to write very large or small numbers.
Properties of addition & multiplication
The document discusses the seven properties of addition and multiplication. It defines the commutative, associative, additive identity, multiplicative identity, multiplication property of zero, opposites for addition, and opposites for multiplication properties. Examples are provided to illustrate each property, and an interactive game is included to help students identify which property applies in different mathematical expressions.
Solving 2 step equations
This document provides instruction on how to solve two-step equations. It explains that two-step equations involve two separate steps of adding/subtracting and then multiplying/dividing. Two examples are worked through, showing the process of isolating the variable by first undoing addition/subtraction and then undoing multiplication/division. Students are then provided practice problems and instructed to show their work in breaking each problem into two steps to solve for the variable.
November 3, 2014
- The document discusses an upcoming math final exam and provides examples to review rational equations, expressions with fractions, and formulas.
- Topics to review for the final exam include translations, order of operations, integers, and simplifying expressions. Example problems are provided to work through.
- Additional examples cover solving equations with variables on both sides, working with fractional equations, and operations with fractions and decimals such as adding, subtracting, multiplying, and dividing.
September 22, 2014
This document provides an agenda for a math class that includes reviewing equations, completing class work and assignments, and learning new topics in Khan Academy. It outlines the week's lessons on two-step equations, equations with variables on both sides, and writing and interpreting decimals. Upcoming topics are absolute value equations and opposites/inverses. Students are given practice problems to work through involving different types of equations and shown steps for solving equations, including those with fractions and decimals.
More Related Content
What's hot
Addition and subtraction of rational expression
To add or subtract fractions with unlike denominators:
1. Find the least common denominator (LCD), which contains all prime factors of each denominator raised to the highest power.
2. Convert the fractions to equivalent fractions with the LCD as the denominator.
3. Perform the addition or subtraction on the numerators and write the sum or difference over the common denominator.
Presentation on quadratic equation
IT'S A PRESENTATION ON QUADRATIC EQUATION PART 1, CLASS 10, CHAPTER 4, IT STARTS WITH THE SHAPE PARABOLA AND IT'S DAY TO DAY LIFE EXAMPLES, AS WE PROCEED FURTHER WE SOLVE SOME EXPRESSIONS, WE COVERT IT INTO QUADRATIC EQUATIONS. AFTERWARDS, WE LEARN HOW TO FORM STANDARD QUADRATIC EQUATIONS WITH EXAMPLES (WORD PROBLEMS).
Power of Power Exponent Rule
The document discusses exponential population growth and the "power of power" rule. It provides an example of how a population starting at 1 person that doubles each generation through having 4 children per person would grow exponentially from 1 to 4 to 16 to 64 etc. It then explains the rules for expanding exponential expressions using exponents, such as multiplying exponents when the base is the same under multiplication or addition, and subtracting exponents when dividing terms with the same base. Examples are provided to demonstrate simplifying expressions using these exponent rules.
(8) Lesson 2.1 - Solve Equations with Rational Coefficients
This document provides instruction on solving linear equations with one variable. It begins by defining key terms like multiplicative inverse and coefficient. It then provides examples of solving various equations by multiplying or dividing both sides of the equation by the same term to isolate the variable. These examples include equations with fractions, decimals, and percentages. The document emphasizes using the inverse operation property to solve equations and checking solutions. It aims to help students solve equations that may require expanding and combining like terms.
Expanding two brackets
The document discusses expanding and simplifying expressions within brackets. It provides examples of multiplying out terms within brackets for expressions like (2a + 3)(4a + 2) and (3b + 2)(4b - 6). The key steps are to multiply out each corresponding term, then collect like terms. Distributing negatives requires being careful about the signs of multiplied terms. The document encourages practicing expanding several example expressions within time limits to check understanding.
Distributive property in algebra power point
The document discusses the distributive property in algebra. The distributive property allows terms inside parentheses to be distributed so that expressions can be simplified out of order from the standard order of operations. It involves multiplying the number outside of the parentheses by each term inside the parentheses. Examples are provided to demonstrate how to use the distributive property to simplify expressions.
Order of operations
This document provides instruction on the order of operations for solving mathematical expressions. It explains that there are specific rules to follow when solving expressions, known as the order of operations. These rules are: 1) complete all operations within parentheses first, 2) perform all exponents next, 3) multiply and divide from left to right, and 4) add and subtract from left to right. The document provides examples of solving expressions using the proper order of operations and encourages remembering the order using the acronym PEMDAS.
Inequalities
This document discusses inequalities and their graphs. It defines an inequality as a statement that two expressions are not equal. It explains the symbols used in inequalities like <, >, ≤, and ≥ and how to graph them correctly, with open or closed circles depending on if it's a < or ≤. Examples are provided of writing and graphing simple one-variable inequalities and having the reader practice graphing some on their own. Key points covered include understanding the direction the solution goes based on what side the variable is on and coloring in or leaving open the circle depending on the symbol used.
Linear Equation In one variable class 7
This document defines and provides examples of linear equations in one variable. It explains that a linear equation is an equation that can be written in the form ax + b = c or ax = b, where a, b, c are constants and a ≠ 0. Examples of linear equations given include 3x + 9 = 0 and 7x + 5 = 2x - 9. The document also discusses how to determine if a value is a solution to a linear equation by substitution and simplification. Steps for solving linear equations are provided, which include isolating the variable using inverse operations like addition/subtraction and multiplication/division.
Percentages and discounts tutorial
This document provides information and examples for working with percentages and discounts. It covers converting between fractions, decimals, and percentages; finding percentages of quantities; calculating profit and loss; reversing percentages to find original values; and writing quantities as percentages of others. Examples are provided for each topic without and with a calculator. The next session will cover working with ratios.
Factoring perfect-square-trinomials
To factor perfect square trinomials:
1. Get the square root of the first and last terms.
2. List down the square root as the sum or difference of two terms.
3. Factor the expression into the form (term 1 ± term 2)2.
2 expressions and linear expressions
The document discusses expressions in mathematics. It defines expressions as calculation procedures written with numbers, variables, and operation symbols that calculate outcomes. Expressions can be combined by collecting like terms. Linear expressions take the form of ax + b, where terms can be combined by adding or subtracting the coefficients of the same variable. The example shows combining the terms of the expression 2x - 4 + 9 - 5x.
Substitution Method of Systems of Linear Equations
This document provides examples of solving systems of linear equations by substitution. The method involves choosing one equation to isolate a variable, substituting that expression into the other equation, then solving the resulting equation for the remaining variable and back-substituting to find the solution set. The examples demonstrate these steps clearly, showing the process of identifying which equation to transform, performing the substitutions, solving for variables, and checking the solutions.
Chapter 3. linear equation and linear equalities in one variables
Here are the steps to solve this inequality problem:
1) Write an expression for the perimeter in terms of x
2) Set the perimeter expression ≤ 40
3) Isolate x by undoing the operations
4) Write the solution set
The solution is 0 ≤ x ≤ 7
Systems of Equations by Elimination
This document provides instructions for solving systems of equations using elimination. It demonstrates eliminating variables by adding or subtracting equations. Sample systems are worked through, showing the steps of identifying which variable to eliminate, combining the equations accordingly, solving for one variable, then substituting back into the original equations to solve for the other. The solutions are checked in both equations to verify they satisfy the system.
Multiplication Properties of Exponents
Here are the steps to solve this problem:
1) Write the area of Samoa in scientific notation: 2.9 × 103 km2
2) The area of Texas is 2.3 × 102 times as great as Samoa
3) Multiply the area of Samoa by 2.3 × 102:
(2.9 × 103 km2) × (2.3 × 102) = 6.67 × 105 km2
The approximate area of Texas is 6.67 × 105 km2.
Basics about exponents
Exponents are used to represent repeated multiplication of a number, called the base. The exponent indicates how many times the base is multiplied. Some key laws for exponents include: when multiplying the same bases, add the exponents; when dividing the same bases, subtract the exponents; when raising a power to another power, multiply the exponents. Exponents provide a shorthand way to write very large or small numbers.
Properties of addition & multiplication
The document discusses the seven properties of addition and multiplication. It defines the commutative, associative, additive identity, multiplicative identity, multiplication property of zero, opposites for addition, and opposites for multiplication properties. Examples are provided to illustrate each property, and an interactive game is included to help students identify which property applies in different mathematical expressions.
Solving 2 step equations
This document provides instruction on how to solve two-step equations. It explains that two-step equations involve two separate steps of adding/subtracting and then multiplying/dividing. Two examples are worked through, showing the process of isolating the variable by first undoing addition/subtraction and then undoing multiplication/division. Students are then provided practice problems and instructed to show their work in breaking each problem into two steps to solve for the variable.
What's hot (20)
(8) Lesson 2.1 - Solve Equations with Rational Coefficients
(8) Lesson 2.1 - Solve Equations with Rational Coefficients
Substitution Method of Systems of Linear Equations
Substitution Method of Systems of Linear Equations
Chapter 3. linear equation and linear equalities in one variables
Chapter 3. linear equation and linear equalities in one variables
Similar to 11) Forming and Solving Equations.pptx
November 3, 2014
- The document discusses an upcoming math final exam and provides examples to review rational equations, expressions with fractions, and formulas.
- Topics to review for the final exam include translations, order of operations, integers, and simplifying expressions. Example problems are provided to work through.
- Additional examples cover solving equations with variables on both sides, working with fractional equations, and operations with fractions and decimals such as adding, subtracting, multiplying, and dividing.
September 22, 2014
This document provides an agenda for a math class that includes reviewing equations, completing class work and assignments, and learning new topics in Khan Academy. It outlines the week's lessons on two-step equations, equations with variables on both sides, and writing and interpreting decimals. Upcoming topics are absolute value equations and opposites/inverses. Students are given practice problems to work through involving different types of equations and shown steps for solving equations, including those with fractions and decimals.
Linear Equations in one variable ppt maths
This document discusses linear equations in one variable. It defines expressions and equations, identifies one-variable linear equations, and explains how to simplify and solve one-variable linear equations. Specifically, it provides examples of algebraic expressions and equations, defines linear equations as having the highest power of the variable being 1, and demonstrates how to isolate the variable on one side of the equation and solve for its value using addition, subtraction, multiplication, or division.
5. absolute value , sq , sq roots
This document provides information about absolute value, square roots, and quadratic equations. It defines absolute value as the distance from zero on a number line. It explains that the absolute value of a number x is equal to x if x is positive and equal to -x if x is negative. It gives examples of finding the absolute value of different numbers. It also defines the square root as the positive value of a radical. The document provides examples of solving absolute value and quadratic equations and explains the absolute value-square root theorem, which states that the square root of a squared expression is the same as the absolute value of the expression.
Module 3 topic 2 notes
This document discusses solving multi-step linear equations in 3 sentences or less:
The document provides examples and steps for solving multi-step linear equations, which may require using the distributive property, combining like terms, or having variables on both sides of the equation. It also discusses setting up and solving equations related to consecutive integers and word problems involving linear equations with more than one step.
Module 3, topic 2 notes
This document discusses solving multi-step linear equations in 3 sentences or less:
The document provides examples and steps for solving multi-step linear equations, which may require using the distributive property, combining like terms, or having variables on both sides of the equation. It also discusses setting up and solving equations related to consecutive integers and word problems involving linear equations with more than one step.
MATH-9-Q1-M1-L4-PPT.pptx
This document outlines lessons from a module on solving problems involving quadratic and rational algebraic equations. The module contains two lessons: [1] solving quadratic equations using extracting square roots, factoring, and completing the square; and [2] solving rational algebraic equations by translating word problems into equations and using techniques like cross multiplying, factoring, and finding roots. Example problems presented include finding dimensions of a rectangular table given its area and perimeter, and determining how long it would take individuals working alone to complete a job they can finish together in a given time.
30 Simple Algebra Tricks for Students
This document provides 30 algebra tricks to help students master the subject more easily. Some key tricks discussed include:
- Understanding basic rules like how signs change when terms are transferred across the equal sign in addition, subtraction, multiplication and division.
- Simplifying expressions by turning all negative signs positive or using cross-multiplication to solve fractional equations more quickly.
- Using techniques for squaring numbers like recognizing numbers are a certain amount above or below a multiple of 10.
- Memorizing tricks for multiplying or dividing specific numbers like 11 or numbers closer to bases like 10 or 100.
- Learning indicators for divisibility like a number being divisible by 3 if the sum of its digits is divisible by 3.
September 11, 2014
This document contains notes and reminders from an algebra class. It discusses preparing for an upcoming test on topics like simplifying expressions, solving equations, and translating sentences to math. The warm-up questions involve solving simple equations. Class work will cover order of operations, integers, writing and solving equations. The test topics are also listed.
Similarity day 1 with activity
1. The document provides instructions and objectives for geometry drill 3.17, which includes solving ratios and proportions to find unknown values.
2. It also contains examples of using ratios and proportions to find missing angle measures in a triangle given the ratio of the existing angles, and examples of setting up and solving proportions to find unknown side lengths when given a scale drawing.
3. Key concepts covered include ratios, proportions, similar polygons, scale factors, and using properties of proportions to solve problems involving similar figures.
mathplus-module-FINALREVISED-2023.pdf
This document provides an introduction to algebra and ratio and proportion concepts. It begins with defining algebra as the study of mathematical symbols and the rules for manipulating them. The document then covers order of operations, including the PEMDAS method, and provides examples of simplifying expressions and solving equations. It also defines ratios as a comparison of quantities and proportions as equal ratios. Examples are given for setting up and solving ratio and proportion word problems.
0010 chapter iii
Here are the steps to solve this quadratic equation using the quadratic formula:
1. Identify the coefficients: a = 3, b = -1, c = -5/2
2. Plug the coefficients into the quadratic formula:
x = (-b ± √(b2 - 4ac)) / 2a
x = (-(-1) ± √((-1)2 - 4(3)(-5/2))) / 2(3)
3. Simplify:
x = (1 ± √(1 + 30)) / 6
4. Evaluate the square root:
x = (1 ± 5√3) / 6
Therefore, the solutions are:
Directions Please show all of your work for each problem.If.docx
Directions
: Please show all of your work for each problem.
If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word.
There is a tutorial on using this equation editor in Module 1 Lecture Notes.
You also have the option of hand writing your work and scanning it.
1.
Find the greatest common factor.
4, 6, 12.
2.
Factor.
24
x
3
+ 30
x
2
3.
Factor out the GCF with a negative coefficient.
–24
m
2
n
6
– 8
mn
5
– 32
n
4
4.
Factor completely by factoring out any common factors and then factoring by grouping.
6
x
2
– 5
xy
+ 6
x
– 5
y
5.
The GCF of 15
y
+ 20 is 5.
The GCF of 15
y
+ 21 is 3.
Find the GCF of the product (15
y
+ 20)(15
y
+ 21).
6.
The area of a rectangle of length
x
is given by 15
x
–
x
2
.
Find the width of the rectangle in terms of
x
.
7.
Factor the trinomial completely.
x
2
+ 8
x
– 9
8.
Factor the trinomial completely.
2
x
2
+ 16
x
+ 32
9.
Complete the following statement.
6
a
2
– 5
a
+ 1 = (3
a
– 1)(__
?
__)
10.
State whether the following is true or false.
x
2
– 7
x
– 30 = (
x
+ 3)(
x
– 10)
11.
Factor completely.
x
2
+ 11
x
+ 28
12.
Factor completely.
15
x
2
+ 23
x
+ 4
13.
Factor completely.
6
z
3
– 27
z
2
+ 12
z
14.
The number of hot dogs sold at the concession stand during each hour
ii
h
after opening at a soccer tournament is given by the polynomial 2
h
2
– 19
h
+ 24.
Write this polynomial in factored form.
15.
Find a positive value for
k
for which the polynomial can be factored.
x
2
–
kx
+ 29
16.
Factor completely.
9
x
2
+ 4
17.
Determine whether the following trinomial is a perfect square.
If it is, factor the binomial.
x
2
– 12
x
+ 36
18.
Factor completely.
25
x
2
+ 40
xy
+ 16
y
2
19.
Factor.
s
2
(
t
–
u
) – 9
t
2
(
t
–
u
)
20.
State which method should be applied as the first step for factoring the polynomial.
6
x
3
+ 9
x
21.
State which method should be applied as the first step for factoring the polynomial.
2
a
2
+ 9
a
+ 10
22.
Solve the quadratic equation.
5
x
2
+ 17
x =
–6
23.
Solve the quadratic equation.
3
x
(2
x
– 15) = –84
24.
The sum of an integer and its square is 30.
Find the integer.
25.
If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm
2
.
What were the dimensions of the original square?
26.
Write in simplest form.
27.
Write in simplest form.
28.
Write the expression in simplest form.
29.
The area of the rectangle is represented by 5
x
2
+ 19
x
+ 12.
What is the length?
5
x
+ 4
30.
Multiply.
31.
Multiply.
32.
Divide.
33.
Divide.
34.
Perform the indicated operations.
35.
Find the area of the rectangle shown.
36.
Subtract.
Express your answer in simplest form.
37.
Subtract.
Express your answer in simplest form.
38.
Add.
Express your answer in simplest form.
39.
Add.
Express yo.
Multiply and Divide, Big and Small
This document outlines instructional strategies for teaching multiplication and division of whole numbers, decimals, and fractions using the concrete-representational-abstract (CRA) approach. It provides examples of using physical objects, drawings, and standard algorithms to develop conceptual understanding at each stage. The CRA approach is demonstrated for topics like multiplying large whole numbers, dividing with decimals, and solving word problems involving fractions.
September 23, 2013
This document provides steps for solving equations with fractions. It gives examples of solving single-term fractional equations by clearing fractions through multiplying terms by the least common denominator. It also works through an example of solving a multi-term fractional equation by first combining like terms, then finding the least common denominator and clearing fractions. Additional examples are provided for clearing decimals from equations and solving equations with fractions in parentheses. The document concludes with examples of other equation types and an announcement that the current week's class work will focus on equations.
Developing Expert Voices
The document discusses problems related to trigonometric identities, probability, and transformations. It includes a proof of the identity sinx + cosx + 1 = 2cscx cosx + 1 sinx. It also includes problems on determining the probability of an event in a basketball game, graphing tidal data with a sinusoidal function, and counting outcomes in a card game.
Skill27 solvingequations
This document provides examples of solving increasingly complex equations, starting with one-step equations and progressing to multi-step equations involving fractions, distributive property, combining like terms, and literal equations. Key steps covered include undoing operations, distributing terms, combining like terms, isolating variables, and replacing fractions with decimals. Practice problems are provided ranging from easy one-step equations to more challenging multi-step equations and literal equations without numbers.
Tricks to remember the quadratic equation.ACTION RESEARCH ON MATHS
This document provides information about different methods for solving quadratic equations. It discusses factoring the equation, using the quadratic formula, and completing the square. Step-by-step explanations are provided for each method. Factoring involves finding two binomials that multiply to give the quadratic term and add to the linear term. The quadratic formula is given as x = (-b ±√(b2 - 4ac))/2a. Completing the square requires grouping like terms and completing the square of the quadratic term.
6) Equations involving x².pptx
The document discusses solving equations that involve x^2 terms. It explains that to solve these equations:
1) The x^2 term must be isolated by adding or subtracting terms from both sides of the equation.
2) Then the whole equation can be square rooted to remove the x^2, resulting in two separate equations to solve for x since the square of a negative number is positive.
3) This means there may be two possible solutions for x, as both the positive and negative square roots must be considered. Working through several examples illustrates this process.
Directions Please show all of your work for each problem. If app.docx
Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. The option of hand writing your work and scanning it is acceptable.
1. List all the factors of 88.
2. List all the prime numbers between 25 and 60.
3. Find the GCF for 16 and 17.
4. Find the LCM for 13 and 39.
5. Write the fraction in simplest form.
6. Multiply. Be sure to simplify the product.
7. Divide. Write the result in simplest form.
8. Add.
9. Perform the indicated operation. Write the result in simplest form. –
10. Perform the indicated operation. Write the result in simplest form. ÷
11. Find the decimal equivalent of rounded to the hundredths place.
12. Write 0.12 as a fraction and simplify.
13. Perform the indicated operation. 8.50 – 1.72
14. Divide.
15. Write 255% as a decimal.
16. Write 0.037 as a percent.
17. Evaluate. 56 ÷ 7 – 28 ÷ 7
18. Evaluate. 9 42
19. Multiply: (-1/4)(8/13)
20. Translate to an algebraic expression: Twice x, plus 5, is the same as -14.
21. Identify the property that is illustrated by the following statement. 5 + 15 = 15 + 5
22. Identify the property that is illustrated by the following statement.
(6 · 13) 10 = 6 · (13 · 10)
23. Identify the property that is illustrated by the following statement.
10 (3 + 11) = 10 3 + 10 11
24. Use the distributive property to remove the parentheses in the following expression. Then simplify your result where possible. 3.1(3 + 7)
25. Add. 14 + (–6)
26. Subtract. –17 – 6
27. Evaluate. 3 – (–3) – 13 – (–5)
28. Multiply.
29. Divide.
30. Evaluate. (–6)2 – 52
31. Evaluate. (–9)(0) + 13
32. A man lost 36 pounds (lb) while dieting. If he lost 3 pounds each week, how long has he been dieting?
33. Write the following phrase using symbols: 2 times the sum of v and p
34. Write the following phrase using symbols. Use the variable x to represent the number: The quotient of a number and 4
35. Dora puts 50 cents in her piggy bank every night before she goes to bed. If M represents the money (in dollars) in her piggy bank this morning, how much money (in dollars) is in her piggy bank when she goes to bed tonight?
36. Write the following geometric expression using the given symbols.
times the Area of the base (A) times the height(h)
37. Evaluate if x = 12, y = , and z = .
38. A formula that relates Fahrenheit and Celsius temperature is . If the current temperature is 59°F, what is the Celsius temperature?
39. If the circumference of a circle whose radius is r is given by C = 2πr, in which π ≈ 3.14, find the circumference when r = 15 meters (m).
40. Combine like terms: 9v + 6w + 4v
41. A rectangle has sides of 3x – 4 and 7x + 10. Provide a simplified expression for its perimeter.
42. Subtract 4ab3 from the sum of 10ab3 and 2ab3.
43. Use the distributive property to remove the p.
Similar to 11) Forming and Solving Equations.pptx (20)
Directions Please show all of your work for each problem.If.docx
Directions Please show all of your work for each problem.If.docx
Tricks to remember the quadratic equation.ACTION RESEARCH ON MATHS
Tricks to remember the quadratic equation.ACTION RESEARCH ON MATHS
Directions Please show all of your work for each problem. If app.docx
Directions Please show all of your work for each problem. If app.docx
More from Balvinder4
8) Equations with X on both sides (Higher).ppt
The document discusses solving equations that have the variable x on both sides. It recaps the balancing method for solving equations and shows how this method can be extended to equations where x is on both sides. The additional step is to first rearrange the equation so that like terms involving x are together, and then apply the balancing method, being sure to move the smallest x value to one side of the equation. Examples are provided and discussed.
5) Equations - X on one side.ppt
This document provides a lesson on solving equations with the variable x on one side. It includes examples of solving equations with addition, subtraction, multiplication and division. The key steps are to inverse the operations on one side and apply the same operations to the other side, then isolate the variable x. The objective is to separate the algebraic terms from the numerical terms to solve for the value of x. It concludes with a practice problem combining several steps to solve a more complex equation.
4) Meaning of an Equation.ppt
This document discusses equations and how to solve them. It explains that an equation links two algebraic expressions and shows examples of equations involving variables and operations. It then demonstrates how to solve equations by reversing the operations, such as subtracting one side and dividing both sides. The goal is to learn how to understand equations and find the value of a variable by manipulating the operations.
1) Changing the Subject - Easier.ppt
This document discusses changing the subject of a formula. It explains that changing the subject involves rearranging a formula with more than one unknown value to isolate a different unknown as the subject. The document provides examples of changing the subject for formulas with one, two, and three unknowns. It demonstrates the steps of subtracting, dividing, multiplying, and expanding brackets to rearrange formulas and isolate the variable to become the new subject.
3) Solving an Equation - 1 step.ppt
The document discusses solving equations in one step. It provides examples of equations where the operator is addition, subtraction, multiplication or division, and shows that to solve for x, the inverse operation must be performed. For instance, if x is added by a number, that number must be subtracted. The document emphasizes understanding and writing down the step taken to solve each equation.
12) Equations Including Fractions.ppt
This document discusses solving equations that include fractions. It provides examples of making fractions equivalent before combining like terms, such as when there are multiple fractions on one side of the equation. The examples show setting fractions equal to each other, isolating the variable, and solving for the variable value. Key steps involve making denominators the same and then adding or subtracting fractions with the same denominator.
10) Equations with Brackets.ppt
This document discusses solving equations with brackets. It provides examples of expanding single and multiple brackets in equations, then solving the resulting equations. Learning objectives are presented for expanding single and multiple brackets and solving the resulting equations. Example problems are worked through step-by-step to demonstrate the process. Finally, some plenary equations are presented as practice problems applying the skills learned.
2) Changing the Subject - Harder.pptx
This document discusses rearranging formulae to make a variable the subject. It provides examples of rearranging equations to make x, r, π, y, b, and d the subject. The techniques demonstrated include subtracting, dividing, multiplying, factorizing, and using square and cube roots. The document emphasizes collecting all terms with the intended subject on the same side before dividing or factorizing to isolate that variable.
More from Balvinder4 (8)
Recently uploaded
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.
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
DRUGS AND ITS classification slide share
Any substance (other than food) that is used to prevent, diagnose, treat, or relieve symptoms of a
disease or abnormal condition
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
The Diamonds of 2023-2024 in the IGRA collection
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
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.BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdBBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Recently uploaded (20)
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
11) Forming and Solving Equations.pptx
- 2. Starter Solve each of the equations below using the methods you have been taught: 6x + 5 = 47 15 = 29 - x 8x + 4 = 5x + 22 7x - 5 = 10 – 3x
- 3. Forming and Solving Equations • Today we will be using our knowledge of equation solving to answer worded problems • Some worded problems can be simplified by creating an equation for them • It continues to be important to show your workings clearly!
- 4. Forming and Solving Equations I think of a number. I add 3 then divide it by 2. My answer is 12. Form an equation and solve it to find my number.
- 5. Forming and Solving Equations The perimeter of the rectangle below is 42cm. Calculate the lengths of the sides by forming an equation and solving it. x + 5 x - 2
- 6. Forming and Solving Equations A triangle has 3 sides. One side can be labelled x. One of the other sides is 8cm more than that and the final side is double the first side. The perimeter of the triangle is 26cm. Sketch the triangle and calculate the lengths of the sides.
- 7. Forming and Solving Equations The Areas of the shapes below are equal. Calculate the lengths of the sides. 2x - 3 5 4x + 2 2
- 8. Plenary
- 9. Summary • We have recapped how to solve many types of equation • We have seen how to form equations from worded questions • We have also looked at an extended question in the plenary