October 3, 2014
•Download as PPTX, PDF•
1 like•565 views
This document contains notes from a math class. It includes the topics covered for the day: literal and other equations, warm-up problems on number sense, and sample math equations to solve. Warm-up problems involve rounding population numbers and calculating how many objects would fit in a space. Example math equations include solving for variables, using formulas to find missing dimensions, and multi-step problems involving fractions and exponents.
Report
Share
Report
Share
Recommended
Pythagorean Theorem
today we reviewed the Pythagorean Theorem and there was one sheet handed out to the B and D class and two handed out to the C class.
B and D make sure both sides are done, C make sure the front of each is done.
Pythagoras theorem
Pythagoras was an ancient Greek philosopher and mathematician born on the island of Samos in around 570 BC. He is best known for the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. While Pythagoras likely did not discover this theorem himself, he is credited as being the first to prove why it is true. The Pythagorean theorem is one of the earliest and most important theorems in mathematics.
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It was named after the Greek mathematician Pythagoras, who lived in the 6th century BC. The theorem can be used to calculate unknown side lengths in right triangles. Some examples are also given to demonstrate applying the theorem.
Pythagoras Theorem Explained
Pythagoras discovered that the ancient Egyptians used a 3:4:5 right triangle to build the pyramids. He investigated this further and deduced the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras proved this by drawing squares on each side of right triangles and showing that the areas added up. The Pythagorean theorem has been used since ancient times in architecture, engineering, and more recently in technology like screens.
Pythagoras theorem
- Pythagoras, a Greek philosopher, discovered an important property of right triangles, which was also discovered independently by the Indian mathematician Baudhayan.
- In a right triangle, the hypotenuse is the side opposite the right angle, and the other two sides are called the legs.
- According to the Pythagorean theorem, for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. This theorem can be used to find the length of the third side of a right triangle if the other two sides are known.
Pythagorean Theorem Lesson
The document discusses the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It defines the key terms hypotenuse, legs, and explains the a^2 + b^2 = c^2 formula. Examples are given to demonstrate applying the theorem to find the unknown side of a right triangle given the other two sides. Practice problems are provided to reinforce the concept.
Pythagorean theorem
This document discusses the Pythagorean theorem. It begins with an introduction of the theorem, followed by examples of using it to solve for the length of a triangle's hypotenuse given the lengths of the other two sides. The document then provides task cards with real world problems for students to solve using the Pythagorean theorem. It concludes with a post-test asking students to use the theorem to find hypotenuse lengths.
Pythagorean Theorem
Pythagoras was an ancient Greek thinker, but he was not the founder of the Pythagorean theorem. That honor goes to his followers, known as the Pythagorean Brotherhood, who established the theorem over 100 years after Pythagoras' death. The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This relationship has many practical applications in fields like engineering, construction, physics, and astronomy that involve calculating distances.
Recommended
Pythagorean Theorem
today we reviewed the Pythagorean Theorem and there was one sheet handed out to the B and D class and two handed out to the C class.
B and D make sure both sides are done, C make sure the front of each is done.
Pythagoras theorem
Pythagoras was an ancient Greek philosopher and mathematician born on the island of Samos in around 570 BC. He is best known for the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. While Pythagoras likely did not discover this theorem himself, he is credited as being the first to prove why it is true. The Pythagorean theorem is one of the earliest and most important theorems in mathematics.
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It was named after the Greek mathematician Pythagoras, who lived in the 6th century BC. The theorem can be used to calculate unknown side lengths in right triangles. Some examples are also given to demonstrate applying the theorem.
Pythagoras Theorem Explained
Pythagoras discovered that the ancient Egyptians used a 3:4:5 right triangle to build the pyramids. He investigated this further and deduced the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras proved this by drawing squares on each side of right triangles and showing that the areas added up. The Pythagorean theorem has been used since ancient times in architecture, engineering, and more recently in technology like screens.
Pythagoras theorem
- Pythagoras, a Greek philosopher, discovered an important property of right triangles, which was also discovered independently by the Indian mathematician Baudhayan.
- In a right triangle, the hypotenuse is the side opposite the right angle, and the other two sides are called the legs.
- According to the Pythagorean theorem, for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. This theorem can be used to find the length of the third side of a right triangle if the other two sides are known.
Pythagorean Theorem Lesson
The document discusses the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It defines the key terms hypotenuse, legs, and explains the a^2 + b^2 = c^2 formula. Examples are given to demonstrate applying the theorem to find the unknown side of a right triangle given the other two sides. Practice problems are provided to reinforce the concept.
Pythagorean theorem
This document discusses the Pythagorean theorem. It begins with an introduction of the theorem, followed by examples of using it to solve for the length of a triangle's hypotenuse given the lengths of the other two sides. The document then provides task cards with real world problems for students to solve using the Pythagorean theorem. It concludes with a post-test asking students to use the theorem to find hypotenuse lengths.
Pythagorean Theorem
Pythagoras was an ancient Greek thinker, but he was not the founder of the Pythagorean theorem. That honor goes to his followers, known as the Pythagorean Brotherhood, who established the theorem over 100 years after Pythagoras' death. The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This relationship has many practical applications in fields like engineering, construction, physics, and astronomy that involve calculating distances.
Pythagorean theorem powerpoint
1) The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It can be used to find the length of any side of a right triangle if the other two sides are known.
2) The distance formula calculates the distance between two points in a plane by using the differences between their x- and y-coordinates, based on the Pythagorean theorem. You find the distance by taking the square root of the sum of the squared differences of the x- and y-coordinates.
3) The example calculates the distance between points (4, -3) and (7, 2) using the distance formula
Pythagorean Theorem
The document provides an overview of the Pythagorean theorem presented by Tanya Van Dam Kalles. It discusses Pythagoras and the development of the theorem. Examples are given to demonstrate how to use the theorem to solve problems related to right triangles, including finding the distance from home plate to second base in baseball and calculating the height of a window using the length of a leaning ladder.
Pythagorean Theorem and its various Proofs
The document discusses several proofs of the Pythagorean theorem provided by different mathematicians. It begins by stating the theorem, then provides 6 different proofs: the first given by President James Garfield in 1876 using a trapezoid approach; the second using similarity of triangles; the third constructing a square from 4 copies of a right triangle; the fourth also using similarity; the fifth by rearrangement of the formula; and the sixth using a geometric representation of the areas. It also discusses some applications of the theorem in fields like architecture, navigation, and coordinate geometry.
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras, a Greek mathematician, is credited with discovering this theorem. The theorem can be used to calculate an unknown side of a right triangle if the other two sides are known. Worked examples are provided to demonstrate finding an unknown hypotenuse or leg using the Pythagorean theorem.
Pythagorean Theorem Tutorial
This document provides a tutorial on using the Pythagorean theorem to solve for missing sides of right triangles. It explains the theorem and its formula, how to identify the sides of a right triangle, and how to solve for both missing hypotenuses and legs. Examples are worked through step-by-step and opportunities for practice are provided throughout the tutorial. The goal is for students to demonstrate mastery in solving for missing sides of right triangles.
The Pythagorean Theorem Lesson
1. Pythagoras was a Greek mathematician from the island of Samos in the 6th century BCE who is often credited with discovering the Pythagorean theorem.
2. The Pythagorean theorem, which states that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides, was likely known long before Pythagoras but he may have been the first to prove it.
3. The theorem can be used to calculate the length of the third side of a right triangle if the other two sides are known, as demonstrated through examples of solving for c, b, and a given values for the other sides.
Pythagoras theorem
This document presents information about Pythagoras and his famous theorem. It discusses that Pythagoras was a Greek philosopher from Samos in the 6th century BC who made important contributions to mathematics and philosophy. It provides two proofs of Pythagoras' theorem - that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document also includes animations demonstrating proofs of the theorem through manipulating squares built on the sides of right triangles.
What I Spi
The document discusses the history and properties of the mathematical constant pi (π). It covers:
- Pi is the ratio of a circle's circumference to its diameter.
- Pi is an irrational number that repeats endlessly. Early cultures estimated pi to around 3 or 3.14. Archimedes first approximated it as between 223/71 and 22/7.
- Pi is useful for calculating the circumference and area of circles. Many fields of science rely on pi in their equations.
The Pythagorean Theorem
The document explains the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It provides examples of using the theorem to determine if a triangle is a right triangle, and to find the length of missing sides when the other two sides are known.
Grade 9 pythagorean theorem
The document discusses the Pythagorean theorem. It defines the terms leg and hypotenuse in a right triangle. The Pythagorean theorem states that the sum of the squares of the legs equals the square of the hypotenuse. The document provides examples of using the Pythagorean theorem to solve for missing lengths in right triangles.
The Pythagoras Theorem
Check out this PowerPoint I made about the famous Pythagoras Theorem! I hope you learn something new in it!
Pythagoras' Theorem
Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document explains how to use Pythagoras' theorem to find the length of any side of a right-angled triangle if the other two sides are known. It provides examples of calculating missing side lengths and notes that the theorem can be rearranged to find a non-hypotenuse side if the hypotenuse is known instead. Correct notation for showing working is emphasized.
Pythagoras’ Theorem
This document discusses Pythagoras' theorem and how to use it to solve problems involving right triangles. It explains that Pythagoras' theorem relates the lengths of the sides of a right triangle, where the hypotenuse is the side opposite the right angle. The learning objectives are to understand this relationship and how to use Pythagoras' theorem to find the length of an unknown side of a right triangle. Examples are provided for students to practice applying the theorem to solve problems.
Pythagorean Proof
The document provides a proof of the Pythagorean theorem. It constructs a right triangle ABC with sides of lengths a, b, and c. It extends the sides to form a larger square with side length a+b. This creates 4 right triangles within the larger square. Equating the total area of the larger square to the sum of the areas of the 4 triangles and the square on hypotenuse c yields a2 + b2 = c2, proving the Pythagorean theorem.
Pythagoras Theorem
Pythagoras theorem states that for any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It was invented by the Greek philosopher and mathematician Pythagoras around 582-497 BC and has various applications, including determining if a triangle is right-angled or finding the height of an object using ladder lengths and distances.
History of pi
This PPT is on the history of PI. It includes everything that one may require. This ppt is interesting as well as informative.
10 pythagorean theorem, square roots and irrational numbers
The document discusses rational and irrational numbers. It begins by defining fractions, decimals, and percentages as rational numbers that can be expressed as ratios of whole numbers. It then explains that some quantities, like the length of the diagonal of a 1x1 square, cannot be precisely represented by rational numbers. This length, known as the square root of 2, or √2, is shown to be irrational using the Pythagorean theorem. Most numbers are in fact irrational, requiring infinite decimal expansions. The document concludes by defining square roots and providing examples of evaluating square roots of positive numbers.
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras, a Greek mathematician, is credited with discovering this theorem. The theorem can be used to calculate an unknown side of a right triangle if the other two sides are known. Worked examples are provided to demonstrate finding an unknown hypotenuse or leg using the Pythagorean theorem.
History of pie
The document provides information about pi (π) in 3 paragraphs. It states that pi is the ratio of a circle's circumference to its diameter, is an irrational number, and has been calculated to over 206 billion digits. The history of pi is discussed, noting it was proven irrational in 1761 and transcendental in 1882. Methods of calculating pi are also summarized, including a supercomputer calculating over 206 billion digits in 1999.
Perimeter
The document discusses perimeter and how to calculate it for different shapes. It defines perimeter as the distance around a shape and provides formulas to calculate perimeter for rectangles and polygons. For rectangles, the perimeter formula is P=2l+2w, where l is the length and w is the width. For polygons, you add up the lengths of all the sides. The document also shows how to use algebra to solve for missing side lengths when given the perimeter.
June 9, 2014
- The document reviews material for a final exam including mixture type problems, rational expressions vs. equations, and word problems involving mixtures, coins, work, and distance.
- It provides examples of solving mixture type word problems where different items are mixed together at various unit costs to determine the cost and amounts of each item.
- A review of solving radical equations through distributing, factoring, and solving for x is also presented along with examples worked through step-by-step.
June 5, 2014
The document provides instruction on simplifying rational expressions and equations, including complex fractions. It reviews concepts like multiplication and division of rational expressions, addition and subtraction of rational expressions, finding the lowest common denominator, and working with complex fractions. Examples are provided to demonstrate these concepts and techniques for simplifying rational expressions and solving rational equations.
More Related Content
What's hot
Pythagorean theorem powerpoint
1) The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It can be used to find the length of any side of a right triangle if the other two sides are known.
2) The distance formula calculates the distance between two points in a plane by using the differences between their x- and y-coordinates, based on the Pythagorean theorem. You find the distance by taking the square root of the sum of the squared differences of the x- and y-coordinates.
3) The example calculates the distance between points (4, -3) and (7, 2) using the distance formula
Pythagorean Theorem
The document provides an overview of the Pythagorean theorem presented by Tanya Van Dam Kalles. It discusses Pythagoras and the development of the theorem. Examples are given to demonstrate how to use the theorem to solve problems related to right triangles, including finding the distance from home plate to second base in baseball and calculating the height of a window using the length of a leaning ladder.
Pythagorean Theorem and its various Proofs
The document discusses several proofs of the Pythagorean theorem provided by different mathematicians. It begins by stating the theorem, then provides 6 different proofs: the first given by President James Garfield in 1876 using a trapezoid approach; the second using similarity of triangles; the third constructing a square from 4 copies of a right triangle; the fourth also using similarity; the fifth by rearrangement of the formula; and the sixth using a geometric representation of the areas. It also discusses some applications of the theorem in fields like architecture, navigation, and coordinate geometry.
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras, a Greek mathematician, is credited with discovering this theorem. The theorem can be used to calculate an unknown side of a right triangle if the other two sides are known. Worked examples are provided to demonstrate finding an unknown hypotenuse or leg using the Pythagorean theorem.
Pythagorean Theorem Tutorial
This document provides a tutorial on using the Pythagorean theorem to solve for missing sides of right triangles. It explains the theorem and its formula, how to identify the sides of a right triangle, and how to solve for both missing hypotenuses and legs. Examples are worked through step-by-step and opportunities for practice are provided throughout the tutorial. The goal is for students to demonstrate mastery in solving for missing sides of right triangles.
The Pythagorean Theorem Lesson
1. Pythagoras was a Greek mathematician from the island of Samos in the 6th century BCE who is often credited with discovering the Pythagorean theorem.
2. The Pythagorean theorem, which states that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides, was likely known long before Pythagoras but he may have been the first to prove it.
3. The theorem can be used to calculate the length of the third side of a right triangle if the other two sides are known, as demonstrated through examples of solving for c, b, and a given values for the other sides.
Pythagoras theorem
This document presents information about Pythagoras and his famous theorem. It discusses that Pythagoras was a Greek philosopher from Samos in the 6th century BC who made important contributions to mathematics and philosophy. It provides two proofs of Pythagoras' theorem - that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document also includes animations demonstrating proofs of the theorem through manipulating squares built on the sides of right triangles.
What I Spi
The document discusses the history and properties of the mathematical constant pi (π). It covers:
- Pi is the ratio of a circle's circumference to its diameter.
- Pi is an irrational number that repeats endlessly. Early cultures estimated pi to around 3 or 3.14. Archimedes first approximated it as between 223/71 and 22/7.
- Pi is useful for calculating the circumference and area of circles. Many fields of science rely on pi in their equations.
The Pythagorean Theorem
The document explains the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It provides examples of using the theorem to determine if a triangle is a right triangle, and to find the length of missing sides when the other two sides are known.
Grade 9 pythagorean theorem
The document discusses the Pythagorean theorem. It defines the terms leg and hypotenuse in a right triangle. The Pythagorean theorem states that the sum of the squares of the legs equals the square of the hypotenuse. The document provides examples of using the Pythagorean theorem to solve for missing lengths in right triangles.
The Pythagoras Theorem
Check out this PowerPoint I made about the famous Pythagoras Theorem! I hope you learn something new in it!
Pythagoras' Theorem
Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document explains how to use Pythagoras' theorem to find the length of any side of a right-angled triangle if the other two sides are known. It provides examples of calculating missing side lengths and notes that the theorem can be rearranged to find a non-hypotenuse side if the hypotenuse is known instead. Correct notation for showing working is emphasized.
Pythagoras’ Theorem
This document discusses Pythagoras' theorem and how to use it to solve problems involving right triangles. It explains that Pythagoras' theorem relates the lengths of the sides of a right triangle, where the hypotenuse is the side opposite the right angle. The learning objectives are to understand this relationship and how to use Pythagoras' theorem to find the length of an unknown side of a right triangle. Examples are provided for students to practice applying the theorem to solve problems.
Pythagorean Proof
The document provides a proof of the Pythagorean theorem. It constructs a right triangle ABC with sides of lengths a, b, and c. It extends the sides to form a larger square with side length a+b. This creates 4 right triangles within the larger square. Equating the total area of the larger square to the sum of the areas of the 4 triangles and the square on hypotenuse c yields a2 + b2 = c2, proving the Pythagorean theorem.
Pythagoras Theorem
Pythagoras theorem states that for any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It was invented by the Greek philosopher and mathematician Pythagoras around 582-497 BC and has various applications, including determining if a triangle is right-angled or finding the height of an object using ladder lengths and distances.
History of pi
This PPT is on the history of PI. It includes everything that one may require. This ppt is interesting as well as informative.
10 pythagorean theorem, square roots and irrational numbers
The document discusses rational and irrational numbers. It begins by defining fractions, decimals, and percentages as rational numbers that can be expressed as ratios of whole numbers. It then explains that some quantities, like the length of the diagonal of a 1x1 square, cannot be precisely represented by rational numbers. This length, known as the square root of 2, or √2, is shown to be irrational using the Pythagorean theorem. Most numbers are in fact irrational, requiring infinite decimal expansions. The document concludes by defining square roots and providing examples of evaluating square roots of positive numbers.
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras, a Greek mathematician, is credited with discovering this theorem. The theorem can be used to calculate an unknown side of a right triangle if the other two sides are known. Worked examples are provided to demonstrate finding an unknown hypotenuse or leg using the Pythagorean theorem.
History of pie
The document provides information about pi (π) in 3 paragraphs. It states that pi is the ratio of a circle's circumference to its diameter, is an irrational number, and has been calculated to over 206 billion digits. The history of pi is discussed, noting it was proven irrational in 1761 and transcendental in 1882. Methods of calculating pi are also summarized, including a supercomputer calculating over 206 billion digits in 1999.
Perimeter
The document discusses perimeter and how to calculate it for different shapes. It defines perimeter as the distance around a shape and provides formulas to calculate perimeter for rectangles and polygons. For rectangles, the perimeter formula is P=2l+2w, where l is the length and w is the width. For polygons, you add up the lengths of all the sides. The document also shows how to use algebra to solve for missing side lengths when given the perimeter.
What's hot (20)
10 pythagorean theorem, square roots and irrational numbers
10 pythagorean theorem, square roots and irrational numbers
Viewers also liked
June 9, 2014
- The document reviews material for a final exam including mixture type problems, rational expressions vs. equations, and word problems involving mixtures, coins, work, and distance.
- It provides examples of solving mixture type word problems where different items are mixed together at various unit costs to determine the cost and amounts of each item.
- A review of solving radical equations through distributing, factoring, and solving for x is also presented along with examples worked through step-by-step.
June 5, 2014
The document provides instruction on simplifying rational expressions and equations, including complex fractions. It reviews concepts like multiplication and division of rational expressions, addition and subtraction of rational expressions, finding the lowest common denominator, and working with complex fractions. Examples are provided to demonstrate these concepts and techniques for simplifying rational expressions and solving rational equations.
September 23, 2014
This document contains notes and examples from a math lesson that covered several topics:
1) Simplifying expressions using order of operations and solving equations. Examples included 10 – 2 -3 + 36 ÷ 4 • 9 and -1 - 2 - 3 • 4 - 5 = -20.
2) Translating phrases to algebraic expressions such as "8 less than the square of a number" becoming x^2 – 8.
3) Solving fractional equations using the same process regardless of appearance, with examples like 1/3 x + 5/7 = 1/2.
4) Writing and solving word problems that can be translated to equations, such as one about Jay, Kay, and
November 12th, 2014
Fifteen is the largest number that can be obtained by subtracting three from another number. The document states that fifteen is at most a number decreased by three, implying that fifteen equals the maximum value of a number minus three. In other words, fifteen is the greatest number that results from subtracting three from the original number.
October 17, 2014
The document provides an agenda and notes for a math class that includes:
- Warm-up exercises on fractions, absolute value, and algebra
- Upcoming assignments and tests on Khan Academy, absolute value, and a star math test
- Information on submitting past due work for partial credit
- Lessons on adding/subtracting fractions and an introduction to absolute value including the definition, using absolute value bars, and evaluating expressions with absolute value.
December 10.1, 2014
The document provides an overview of a math class that focuses on fractions, decimals, and percents. It includes:
1) A warm-up with fraction problems asking students to describe their solving process without calculating.
2) Definitions and conversions between fractions, decimals, and percents. It explains that decimals represent tenths and percents represent percentages out of 100.
3) Methods for changing between decimals, fractions, and percents by moving decimals or dividing/multiplying by 100.
4) Examples of mental math calculations with percents, such as finding 10% or 20% of a number.
October 17
This document discusses multi-step and compound inequalities. It begins with warm-up questions solving various inequalities. It then works through examples of solving multi-step inequalities by combining like terms and solving for x. It introduces compound inequalities using "and", where both inequalities must be true for the solution set. The solution set of a compound inequality is the intersection of the individual inequalities. Class work problems are assigned from sections 5-3 and 5-4.
October 10, 2014
Today's math class agenda includes a warm-up, a literal equation test, and a deadline to submit last week's classwork. Students must also complete Khan Academy assignments by Sunday evening. The test prep covers solving a literal equation for y and equations with zero, one, or infinite solutions. Students are reminded to bring scratch paper, pencils, erasers, and the correct login code for the test, and calculators are optional, but phones are prohibited. The test prep also provides an example equation to solve for x.
January 9
The passage discusses the importance of summarization for processing large amounts of text data. It notes that automatic summarization systems aim to produce concise summaries while retaining the most important concepts from the original text in 1-3 sentences. The challenges of building such systems that can accurately determine salience across different domains and genres of text are also briefly touched upon.
December 4
Lucy spent $42 on food, which was 14% of her weekly paycheck. To calculate her total paycheck, divide the amount spent on food by the percentage it was of her total paycheck. So $42/0.14=$300 was her total paycheck, meaning she deposited $300-$42=$258 into her savings account.
To calculate the total cost of the gift if the down payment was 20% and cost $32, divide the down payment amount by the percentage down (0.20) to get the full price. So $32/0.20=$160 is the total cost of the gift.
Sally put $200 in the bank earning 5% interest each year
Sept. 18, 2014
The document provides an overview of classroom activities for today:
1) Warm-up exercises and a review of questions missed on the last test.
2) Preparing for a test on Tuesday by working through examples of equation types commonly missed on the previous test.
3) Warm-up problems include writing and solving different types of equations, as well as word problems involving equations. Showing work is required to receive credit. Students should ask for help if unsure.
Sept. 15, 2014
This document provides information and instructions for an upcoming algebra test. It discusses Khan Academy assignments that are due by Sunday at 7:00 pm. It also details the format and content of the test, which will be tomorrow and will include topics like order of operations, integers, simplifying expressions, translating expressions and equations, and identifying parts of algebraic expressions and equations. The document provides sample problems for a warm-up review covering these test topics.
January 29 30
The document provides practice problems on simplifying monomial expressions and dividing monomials. It begins with examples of dividing monomials using the property that when dividing powers with the same base, you subtract the exponents. It then provides practice problems for students to divide monomial expressions and simplify expressions using exponent properties. Sample problems are worked through step-by-step as examples.
December 9, 2014
This document is a summary of a math class that includes warm-up problems, lessons on fractions, decimals, factoring, and vocabulary. It contains practice problems on these topics. The warm-up includes problems on averages, converting fractions to decimals, adding and subtracting mixed fractions. The lessons define fractions and their relationship to decimals, and how to simplify fractions using the greatest common factor. Practice problems apply these skills to factoring and solving inequalities.
Sept. 29, 2014
This document contains class notes and materials on solving various types of algebraic equations. It discusses tips for solving literal equations, such as distributing terms when a variable is inside parentheses. It also explains the three possible outcomes when solving equations with variables on both sides: a single number solution, no solution, or an identity. The document provides examples of solving proportions and fractional equations. It concludes with examples of problems students most missed on a post-test related to rocket burning times, equations with fractions, and finding the largest of three consecutive even numbers.
November 6th, 2014
This document provides a summary of a math class that covered inequalities. It introduces inequalities and their symbols, including discussing how the inequality sign must be flipped when multiplying or dividing by a negative number. Examples are provided of solving basic inequalities algebraically and graphing them on a number line. The class work assigned involves solving and graphing various inequality problems.
September 9, 2014
This document contains notes from an algebra class that covers order of operations, expressions vs equations, working with large and small numbers, and properties of algebraic rules and equations. The class work assigns problems on finding sums of consecutive odd numbers that are due the next day. Key topics covered include the difference between expressions and equations, working through problems both with and without algebra, and rules for solving various types of equations.
May 30, 2014
1. The document provides notes about test dates and study materials for a math class. It lists the dates for rational expressions and final exams.
2. Students should complete Khan Academy assignments by June 3rd and find graph paper in their notebooks.
3. The document also contains examples of simplifying rational expressions through adding and subtracting fractions with unlike denominators. It reviews finding the lowest common denominator and combining like terms.
May 29, 2014
1. The document provides notes and information about an upcoming math test and final exam. It includes test dates for rational expressions and the final exam. It also lists assignments due and notes on graphing inequalities and simplifying rational expressions.
2. The document reviews graphing inequalities and systems of inequalities. It also contains examples of simplifying rational expressions, including identifying excluded values. Steps for simplifying rational expressions are outlined.
3. Examples are provided to simplify rational expressions and identify excluded values with explanations of the steps involved. Assignments are given to complete class work and examples.
Viewers also liked (19)
Similar to October 3, 2014
Oct.2, 2014
The document contains class notes on solving literal and other equations, including tips and examples. It also provides a schedule for Khan Academy work and math classwork for the day. Students are asked to submit outstanding forms, work on literal and other equations, and review topics on Khan Academy. The document gives the dimensions of two-dimensional and three-dimensional objects, the formula for volume of a rectangular prism, and examples of solving various equation types. Warm-up activities are provided for the math periods involving solving literal equations, rewriting equations using correct formulas, and proportion word problems.
April 10
The document provides steps for completing the square to solve quadratic equations:
1. Divide the equation by the leading coefficient to set the a-value to 1.
2. Rewrite the equation in the form ax + by = c.
3. Find half of the b value, square it, and add it to both sides of the equation.
4. Rewrite the left side as a perfect square binomial and take the square root of both sides.
5. Solve for x by isolating the variable.
November 18, 2015
Today's tasks include:
1) Practicing the last Khan Academy topic for the week on literal equations
2) Focusing on solving literal equations for a specified variable
3) Making significant progress on Classwork 2.3, which is due November 18th and involves solving various equations for unknown variables.
November 18, 2015
Today's tasks include:
1) Practicing the last Khan Academy topic for the week on literal equations
2) Focusing on solving literal equations for a specified variable
3) Making significant progress on Classwork 2.3, which is due November 18th and involves solving various equations for unknown variables.
November 16, 2015
The document is a class notes document that contains:
1) Information about upcoming tests, Khan Academy topics, and the day's lessons which include introducing literal equations and working on class work problems.
2) Examples of solving literal equations by isolating the variable being solved for and working through examples without and with variables.
3) Tips for solving literal and other equations by distributing, clearing fractions, and isolating variables.
4) A few practice problems for solving literal equations and calculating rates.
November 16, 2015
The document is a class notes document that contains the following information:
1. It discusses solving literal equations by isolating the variable being solved for on one side of the equation, just as with normal equations.
2. It provides tips for solving literal equations, such as distributing first if the variable is inside parentheses.
3. It gives examples of solving literal equations, such as solving 3m - n = k for m.
4. It provides the formula for calculating the speed of light from the sun and uses it with information provided to calculate the distance light travels in a given time period.
GREKing: The most repeated type of quants problem.
GREKing the most repeated types of quants problems which can be scoring for the initial section.
GREKing is one of the best websites for GRE preparation and GRE exam. (www.greking.com)
Honors precalc warm ups
This document contains a collection of math problems and warm-ups covering topics like geometry, trigonometry, algebra, and calculus. There are over 30 problems presented without solutions for students to work through. The problems involve finding areas and perimeters of shapes, solving equations, working with functions, and more.
Trig right triangle trig
This document provides examples and explanations of right triangle trigonometry concepts, including:
1) Finding trigonometric ratios (sine, cosine, tangent) for given angles in right triangles.
2) Using trigonometric functions to find missing side lengths, including for special 30-60-90 and 45-45-90 right triangles.
3) Applying trigonometry to real-world problems involving angles of elevation/depression and finding distances.
Reciprocal trig functions (cosecant, secant, cotangent) and the Pythagorean theorem are also discussed. Practice problems are provided to test understanding.
Sept. 26, 2014
This document provides an agenda and content for a math class. It includes:
1) An agenda for the class outlining make-up tests, a warm-up, reviewing test 2, equations, and assigning Khan Academy work due by Sunday.
2) Sample warm-up and writing/solving equation problems including writing an equation to calculate an electrician's costs for 9 hours of work.
3) A review of the 5 most missed problems on test 2, including solving multi-step equations and finding the largest number in a set of consecutive even numbers.
4) An explanation of solving literal equations by isolating variables and examples of solving for variables in different equations.
5) Using
Core sub math_att_4pythagoreantheorem
The document provides information about the Pythagorean theorem:
1) It states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
2) It gives examples of right triangles that satisfy the theorem, such as ones with sides of 3, 4, 5 or 5, 12, 13.
3) It includes an animated proof of the theorem showing how the area of the square on the hypotenuse equals the combined areas of the squares on the other two sides.
Algebra 2
This document provides information about algebra 2 concepts including sequences, progressions, and word problems. It discusses arithmetic progressions, geometric progressions, and harmonic progressions. It defines key terms used in progressions like common difference, common ratio, and nth term formulas. The document also provides examples and step-by-step instructions for solving different types of word problems involving work, age, motion, mixtures, money, and time. It ends with 20 practice questions testing these algebra 2 concepts.
Chapter2009
This document contains a countdown round from the 2009 MATH COUNTS chapter competition, consisting of 62 multiple choice math questions with answers. The questions cover a wide range of math topics including arithmetic, algebra, geometry, probability, and word problems. The summary provides an overview of the type and scope of questions included in the document without reproducing any specific questions or answers.
Sept.. 30 2014
The document provides information about dimensions, volume, and tips for solving literal equations. It defines dimensions as the measure of an object in a given direction, with length and width being the dimensions of 2D objects and length, width, and height being the dimensions of 3D objects. It gives the formula for volume of a rectangular object as length x width x height. It then lists several tips for solving literal equations, such as distributing terms when a variable is inside parentheses.
GCSE-TrigonometryOfRightAngledTriangles.pptx
This document provides an overview of trigonometry of right-angled triangles. It contains three main points:
1. It outlines objectives of finding unknown sides and angles in right-angled triangles using trigonometric ratios and inverse trigonometric functions.
2. It advertises an online resource for teaching videos, topic tests, and interactive practice questions on trigonometry organized by topic and difficulty.
3. It shares a personal anecdote of how the author first learned trigonometry and was able to apply it to write a computer program to draw an analogue clock.
Internship exam round1
The document contains 24 math and logic problems with numerical answers. It tests skills such as number patterns, probability, combinatorics, algorithms and data structures. The maximum time complexity of an algorithm described is O(n*k) where k is the number of bits to represent n. The minimum number of scalar multiplications needed for the matrix multiplication problem is 38.
Calculator Paper Quiz
The document contains a series of maths questions across different topics and difficulty levels ranging from 1 to 5 points. For each question, the correct answer is provided after it is passed to the other team. The questions would be useful for students to practice different maths skills and concepts in preparation for exams.
Ordinary Differential Equation
This document provides an overview of methods for solving higher order ordinary differential equations (ODEs), including variation of parameters and Laplace transforms. It presents the general steps for each method and works through examples of applying each method to solve higher order nonhomogeneous ODEs. The document also discusses applications of higher order ODEs to model physical systems like a bungee jumper attached to a cord. It works through several problems modeling the bungee jumper's motion to determine properties like the maximum jump height.
Results of Round 1
There are 20 multiple choice questions related to mathematics, algorithms, and data structures. For each question, the document provides the question, possible answers, and the correct answer. The questions cover a variety of topics including graphs, hashing, time complexity analysis, and probability.
Ac1.4cMorePracticeProblems
The document contains instructions and questions for identifying angles and properties of triangles. It asks the reader to name angles, classify them as acute, right, obtuse or straight, and find missing angle measures using properties of angle sums in triangles. It emphasizes drawing diagrams for each problem and setting up equations to solve for unknown angle measures.
Similar to October 3, 2014 (20)
GREKing: The most repeated type of quants problem.
GREKing: The most repeated type of quants problem.
More from khyps13
August 23, 2016
The document provides classwork and practice problems related to algebraic expressions and one-step equations. New vocabulary terms introduced are coefficient and like terms. Examples are given of adding and subtracting like terms. There are also practice problems for translating expressions, solving one-step equations, and word problems involving algebraic relationships between variables.
August 22, 2016
This document provides instructions and examples for students on organizing their math notebooks. It includes examples of how to categorize different math concepts like properties, formulas, and vocabulary in the resource section. It also provides warm-up problems covering large and small numbers. Students are instructed to complete homework assignment 1.1 by the due date of August 23, 2016. They are also given examples of translating expressions and equations.
August 19, 2016
This document contains a math lesson on large and small numbers, number relationships, and problem solving. It includes warm-up questions about numbers greater than or less than a trillion, billions, and millions. It also has questions about the width of a human hair, distance from Earth to the Sun, and how fast a hummingbird flaps its wings. The document provides answers to the warm-up questions and has an end of week review on number operations and translating word problems into algebraic equations. It concludes with an example of solving a multi-step word problem algebraically to find the individual weights of Mike, Bob, and Don.
August 18, 2016
This document contains reminders for school supplies needed by Monday, an overview of the 5 essential understandings of algebra, and 5 fraction practice questions. The 5 essential understandings are: 1) Algebra is a method for solving math problems, not the problems themselves. 2) Mathematics uses symbols as shortcuts. 3) Algebra rules come from natural number rules. 4) Algebra examines patterns and relationships between numbers. 5) Look for equality and use it to your advantage when solving problems. Mastering multiplication tables is also emphasized.
Aug 17, 2016
The document outlines the daily routine and learning process for a math class. It includes:
1. A warm-up with 4-5 review or new problems to introduce topics for the day. Class work is to be completed during class time and any unfinished work should be done outside of class.
2. New concepts are introduced through demonstration by the teacher, then practiced together through examples before students work independently.
3. Additional learning resources like online math sites are provided to support studying outside of class, since class time is limited to 60 minutes per day.
4. A short practice test is included covering translating expressions, order of operations, and fractions to gauge readiness.
Ultimate guide to systems of equations
i) The document discusses various methods for solving systems of linear equations, including graphing, substitution, elimination, and cross-multiplication.
ii) It also addresses solving systems that can be reduced to linear equations, such as transforming non-linear equations using substitution.
iii) Examples are provided to illustrate each method for deriving the solution of a system of equations.
March 29, 2016
The document provides examples for solving systems of equations through various methods like elimination, substitution, and word problems. It demonstrates setting up systems as equations based on information provided, choosing an elimination method by adding or multiplying equations, isolating variables, substituting values, and checking solutions. Word problems are converted to systems of equations and then solved to find unknown variable values.
March 28, 2016
The document provides information about assignments and tests for today and upcoming dates. It includes notes about 4th quarter grade trackers, make-up tests during lunch, systems of equations lessons for some periods today and tomorrow, and distributing worksheets. The document also contains math content on solving systems of equations by graphing, substitution, and elimination.
March 31, 2016
The document discusses reviewing Khan Academy topics on systems of equations and solving 3x3 systems. It includes examples of solving systems of equations by elimination, addition, and substitution. Students will review methods, complete assignments, and take a five question quiz on solving systems of equations.
March 30, 2016
The document provides instructions for practicing Khan Academy topics on systems of equations word problems. It also reminds the student to make progress on homework 4.1-4.2 which is due on Friday for full credit. Examples are given for solving systems of equations by substitution and word problems involving jeans/shirts and movie tickets.
March 21, 2016
This document provides information about upcoming tests, review material, and math concepts to be covered in class. It includes:
- Details on making up remaining tests and reviewing for the final exam
- The 5 most missed questions from the last test
- Vocabulary and terms related to systems of equations to be covered
- Sample word problems and equations involving ratios, rates, percents, and lines to work on for the next class
April 5, 2016
The document provides examples and steps for solving systems of inequalities and linear equations. It discusses graphing a single inequality, the steps for graphing systems of inequalities, and provides an example of solving a two-variable linear system of inequalities. Sample problems include determining the number of hours until costs are the same for two plumbing companies and graphing the inequality y < 5x + 1.
April 4, 2016
This document contains a daily agenda and warm-up problems for math class including:
1) Solving systems of equations by graphing, substitution, and elimination. Example problems include solving for costs of flowers and costs of different internet providers over time.
2) Review of fractions, inequalities, and solving multi-step equations.
3) An example of solving a 3x3 system of equations by eliminating a variable and substituting values.
4) Warm-up questions ask students to write and solve systems of equations modeling real-world scenarios like costs of soccer equipment and costs of fitness clubs over time.
April 6, 2016
The document provides a review of topics related to solving systems of equations and inequalities including:
1) There are two methods for solving systems - elimination or substitution. An example problem is worked through using elimination.
2) When graphing systems of inequalities, each line must be drawn and labeled as above, below, or dashed before moving to the next line.
3) Word problems can be modeled with systems and solved, such as determining the number of chickens and pigs given the total number of legs.
April 1, 2016
This document contains examples of solving systems of equations word problems. It begins with a warm-up problem about a math test worth a total of 63 points made up of 2-point and 3-point problems. Then it provides steps for solving systems of equations, including labeling variables, writing equations, solving, and checking. Finally, it applies these steps to two word problems, one about movie tickets and one about flowers for Valentine's Day.
February 17 2015
The document provides instruction on calculating and interpreting slope. It defines slope as the ratio of rise over run between two points on a line. It gives the formula for calculating slope as the change in y over the change in x between two points. Several examples are worked out step-by-step to demonstrate calculating slope from graphs and point pairs. Key concepts covered include identifying horizontal and vertical lines that have slopes of 0 and undefined respectively.
February 18 2016
The document discusses various formulas used to represent lines in the coordinate plane, including:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y – y1 = m(x – x1), where (x1, y1) is a known point on the line and m is the slope.
- Standard form: Ax + By = C, where A, B, and C are constants and A and B cannot both be 0.
It provides examples of writing equations of lines in different forms given information like the slope, a point, or the graph of the line. Converting between
February 16 2016
The document provides information about an upcoming test on coordinate planes and linear functions. It includes:
- A review of topics to be covered on the test like functions, ordered pairs, slope of a line, and standard form of a line.
- Examples of problems about domain and range, graphing lines, finding intercepts, and interpreting graphs.
- Instructions to have materials like graph paper and a calculator ready for working through sample problems.
- A reminder that attempting all problems is better than leaving them blank on the test.
February 9 2016
The document outlines an agenda for a math class that includes a warm-up on missed test questions, learning about functions and their domains and ranges, using the vertical line test to determine if a relation is a function, and interpreting graphs. It provides examples of mapping relations to check if they are functions and using the vertical line test. Students are given practice problems to determine if relations are functions and to graph relations and use the vertical line test.
February 10 2016
This document provides instruction on determining the domain and range of functions, identifying functions using mapping and the vertical line test, and interpreting graphs. It includes examples of determining domain and range for various functions defined by equations. Warm-up questions are provided to have students plot points and draw lines from equations. Students are reminded that their class work CW 3.4 is due for full credit.
More from khyps13 (20)
October 3, 2014
- 1. October 3, 2014 Today: News & Notes Warm –Up Class Work: Literal & other Equations Khan due Sunday Can we take a piece of paper out, please.
- 2. Warm-Up: Number Sense 1a. What is the current population of Saipan? Round to the nearest 1,000 1b. What is the current population of Guam? Round to the nearest 10,000 1a. Answer: 48,000 1b. Answer: 180,000
- 3. Rounded to the nearest 1,000 how many basketballs would it take to fill up the gym at MHS?
- 4. Warm-Up: Number Sense 2. How many people does this Stadium hold? Round to the nearest 1,000 Answer: 108,000
- 5. Warm-Up: Number Sense 3. How many people does this Stadium hold? Round to the nearest 1,000
- 6. Warm-Up: Number Sense 4. How many passengers can this plane carry? Round to nearest 10
- 9. How many of these.. Can fit it this.. ≈ 20,000
- 10. 4 – y = 1 2y 2 8 – 2y = 2y 8 = 4y; y = 2
- 13. Warm-Up: Literal Equations Solve for a: Q = 3a + 5ac What can be factored out of both terms? Solve for h: A = ퟏ ퟐ ah - ퟏ ퟐ bh L = 19 Find the missing dimension: P = 60 Same Rules; don’t do anything different! Lastly, this beauty... −ퟑ ퟓ ퟓ − ퟏퟎ퐱 ퟑ ퟒ ퟐퟒ퐱 + ퟒ
- 14. 3rd & 4th Periods Warm Up Write the equation, then solve Rewrite using the correct formula, then solve −ퟑ ퟓ Lastly, this beauty... ퟓ − ퟏퟎ퐱 ퟑ ퟒ ퟐퟒ퐱 + ퟒ 푵 ퟑ - 2 A number is doubled, and then 5 is added. When then divided by 3, the result is 7. A triangle has an area of 28 ft.2 and a base of 4 sq. feet. What is the height of the triangle?