This document provides the weekly syllabus for mathematics for class 10 for the 2011-2012 school year. It is divided into two terms, with the first term covering chapters on numbers, algebra, geometry, trigonometry, and statistics. The second term covers additional chapters on algebra, geometry, mensuration, trigonometry, coordinate geometry, and probability. Each week outlines the chapter, examples, and activities to be covered. Suggested activities for formative assessments are also included.
Analysis and algebra on differentiable manifoldsSpringer
ย
This chapter discusses tensor fields and differential forms on manifolds. It provides definitions of tensor fields, differential forms, vector bundles, and the exterior derivative. It also introduces the Lie derivative and interior product. The chapter contains examples of vector bundles like the Mรถbius strip. It aims to make the reader proficient with computations involving vector fields, differential forms, and other concepts. Problems are included to help develop skills in computing integral distributions and differential ideals.
This document contains lecture notes on exponential growth and decay from a Calculus I class at New York University. It begins with announcements about an upcoming review session, office hours, and midterm exam. It then outlines the topics to be covered, including the differential equation y=ky, modeling population growth, radioactive decay including carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving various differential equations representing exponential growth or decay. The document explains that many real-world situations exhibit exponential behavior due to proportional growth rates.
Lesson 13: Exponential and Logarithmic Functions (Section 021 slides)Matthew Leingang
ย
This document contains lecture notes on exponential and logarithmic functions from a Calculus I class at New York University. It begins with announcements about a graded midterm exam and an upcoming homework assignment. It then provides objectives and an outline for sections 3.1 and 3.2 on exponential functions. The bulk of the document derives definitions and properties of exponential functions for various exponents through examples and conventions to preserve desired properties.
The document is a lecture on inverse trigonometric functions from a Calculus I class at New York University. It defines inverse trig functions like arcsin, arccos, and arctan and discusses their domains, ranges, and relationships to the original trig functions. It also provides examples of evaluating inverse trig functions at specific values.
Toeplitz Hermitian Positive Definite (THPD) matrices play an important role in signal processing and computer graphics and circular models, related to angular / periodic data, have vide applications in various walks of life. Visualizing a circular model through THPD matrix the required computations on THPD matrices using single bordering and double bordering are discussed. It can be seen that every tridiagonal THPD leads to Cardioid model.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
ย
The document presents a new method called the Laplace Substitution Method (LSM) for solving partial differential equations involving mixed partial derivatives. LSM uses Laplace transforms to obtain an exact solution with less computation compared to other methods. The method is demonstrated on three examples, finding the exact solutions. However, LSM is not applicable when the general linear term Ru(x,y) is non-zero. LSM shows promise for solving equations that arise in various fields when Ru(x,y)=0.
A Study on Differential Equations on the Sphere Using Leapfrog Methodiosrjce
ย
In this article, a new method of analysis of the differential equations on the sphere using Leapfrog
method is presented. To illustrate the effectiveness of the Leapfrog method, an example of the differential
equations on the sphere has been considered and the solutions were obtained using methods taken taken from
the literature [17] and Leapfrog method. The obtained discrete solutions are compared with the exact solutions
of the differential equations on the sphere. Solution graphs for the differential equations on the sphere have
been presented in the graphical form to show the efficiency of this Leapfrog method. This Leapfrog method can
be easily implemented in a digital computer and the solution can be obtained for any length of time
Lesson 14: Derivatives of Logarithmic and Exponential FunctionsMatthew Leingang
ย
The document is a lecture on derivatives of exponential and logarithmic functions. It begins with announcements about homework and an upcoming midterm. It then provides objectives and an outline for sections on exponential and logarithmic functions. The body of the document defines exponential functions, establishes conventions for exponents of all types, discusses properties of exponential functions, and graphs various exponential functions. It focuses on setting up the necessary foundations before discussing derivatives of these functions.
Analysis and algebra on differentiable manifoldsSpringer
ย
This chapter discusses tensor fields and differential forms on manifolds. It provides definitions of tensor fields, differential forms, vector bundles, and the exterior derivative. It also introduces the Lie derivative and interior product. The chapter contains examples of vector bundles like the Mรถbius strip. It aims to make the reader proficient with computations involving vector fields, differential forms, and other concepts. Problems are included to help develop skills in computing integral distributions and differential ideals.
This document contains lecture notes on exponential growth and decay from a Calculus I class at New York University. It begins with announcements about an upcoming review session, office hours, and midterm exam. It then outlines the topics to be covered, including the differential equation y=ky, modeling population growth, radioactive decay including carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving various differential equations representing exponential growth or decay. The document explains that many real-world situations exhibit exponential behavior due to proportional growth rates.
Lesson 13: Exponential and Logarithmic Functions (Section 021 slides)Matthew Leingang
ย
This document contains lecture notes on exponential and logarithmic functions from a Calculus I class at New York University. It begins with announcements about a graded midterm exam and an upcoming homework assignment. It then provides objectives and an outline for sections 3.1 and 3.2 on exponential functions. The bulk of the document derives definitions and properties of exponential functions for various exponents through examples and conventions to preserve desired properties.
The document is a lecture on inverse trigonometric functions from a Calculus I class at New York University. It defines inverse trig functions like arcsin, arccos, and arctan and discusses their domains, ranges, and relationships to the original trig functions. It also provides examples of evaluating inverse trig functions at specific values.
Toeplitz Hermitian Positive Definite (THPD) matrices play an important role in signal processing and computer graphics and circular models, related to angular / periodic data, have vide applications in various walks of life. Visualizing a circular model through THPD matrix the required computations on THPD matrices using single bordering and double bordering are discussed. It can be seen that every tridiagonal THPD leads to Cardioid model.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
ย
The document presents a new method called the Laplace Substitution Method (LSM) for solving partial differential equations involving mixed partial derivatives. LSM uses Laplace transforms to obtain an exact solution with less computation compared to other methods. The method is demonstrated on three examples, finding the exact solutions. However, LSM is not applicable when the general linear term Ru(x,y) is non-zero. LSM shows promise for solving equations that arise in various fields when Ru(x,y)=0.
A Study on Differential Equations on the Sphere Using Leapfrog Methodiosrjce
ย
In this article, a new method of analysis of the differential equations on the sphere using Leapfrog
method is presented. To illustrate the effectiveness of the Leapfrog method, an example of the differential
equations on the sphere has been considered and the solutions were obtained using methods taken taken from
the literature [17] and Leapfrog method. The obtained discrete solutions are compared with the exact solutions
of the differential equations on the sphere. Solution graphs for the differential equations on the sphere have
been presented in the graphical form to show the efficiency of this Leapfrog method. This Leapfrog method can
be easily implemented in a digital computer and the solution can be obtained for any length of time
Lesson 14: Derivatives of Logarithmic and Exponential FunctionsMatthew Leingang
ย
The document is a lecture on derivatives of exponential and logarithmic functions. It begins with announcements about homework and an upcoming midterm. It then provides objectives and an outline for sections on exponential and logarithmic functions. The body of the document defines exponential functions, establishes conventions for exponents of all types, discusses properties of exponential functions, and graphs various exponential functions. It focuses on setting up the necessary foundations before discussing derivatives of these functions.
This document discusses an introduction to modeling in engineering and kinematics. It begins by defining what an engineer is as someone who has graduated with an engineering degree and works in one of its various fields. It then outlines the course topics for Modeling in Engineering I, including scalar and vector kinematics, particle kinematics in 1D, 2D and 3D, derivatives, work and energy, and conservation of energy and momentum. The professor's goals for the course are to compile the content from the topics in a dynamic way and show applications of the concepts to help students learn.
This document is a master's thesis written in Chinese that investigates the existence and uniqueness of solutions to stochastic differential equations (SDEs) with Lรฉvy noise and non-Lipschitz coefficients. It introduces Lรฉvy processes and their properties, including the Lรฉvy-Itรด decomposition. It defines stochastic integration with respect to compensated Poisson processes and provides Itรด's formula for Lรฉvy diffusions. The thesis proves that if weak existence and pathwise uniqueness hold for an SDE with Lรฉvy noise, then it has a unique strong solution. It establishes conditions on the coefficients that ensure infinite lifetime and pathwise uniqueness of the solution.
Let f(x) = ๏ง
๏ท and g(x) = ๏ง
๏ท
๏จ 1๏ญ x ๏ธ
๏จ x ๏ธ
that fog is not defined.
19.
If f : A ๏ฎ B is bijective, then write n(A) in terms of n(B).
20.
If f : A ๏ฎ B is onto and n(A) = 5, n(B) = 3. Then write n(A).
SHORT ANSWER TYPE QUESTIONS (2 MARKS)
1.
Define reflexive, symmetric
Dialectica Categories and Cardinalities of the Continuum (March2014)Valeria de Paiva
ย
This document discusses Dialectica categories and cardinalities of the continuum. It begins by outlining Hilbert's program to provide secure foundations for mathematics through formalization. Gรถdel's incompleteness theorems showed this was impossible. Gรถdel then developed the Dialectica interpretation as a way to prove consistency of arithmetic. De Paiva later introduced Dialectica categories, which provide a model of linear logic. These categories, called PV, are useful for proving inequalities between cardinal characteristics of the continuum. The structure of PV is discussed, along with examples of objects in this category.
The concept of moments of order invariant quantumAlexander Decker
ย
The document summarizes key concepts related to moments of order invariant quantum Lรฉvy processes. It begins by defining order equivalence and order invariant distributions for discrete random variables. It then states that if the distributions are order invariant, the moments of their sums converge as the number of variables increases. Similarly, for order invariant quantum Lรฉvy processes, the document shows that limits exist for the moments and provides an expression involving these limits. It proves the existence of the limits for moments by induction on the length of index tuples.
This document discusses techniques for setting linear algebra problems in a way that ensures relatively easy arithmetic. Some key techniques discussed include:
1. Using Pythagorean triples and sums of squares to generate vectors with integer norms in R2 and R3.
2. Using the PLU decomposition theorem to generate matrices with a given determinant, such as ยฑ1, to avoid fractions.
3. Extending a basis for the kernel of a matrix to generate matrices with a given kernel.
4. Ensuring the coefficients for a Leontieff input-output model are nonnegative to generate a productive consumption matrix. Examples and Maple routines are provided.
This document provides an introduction to tensor notation and algebra. It defines scalars, vectors, and tensors, and how they transform under changes of reference frame. Vectors have direction and magnitude, and tensors generalize this to have multiple directions/indices. Tensors of different orders are discussed, along with common examples like the velocity gradient tensor. Frame rotations are described using orthogonal transformation matrices, and how vectors and tensors transform under these changes of basis.
This document discusses applications of vector spaces and subspaces in geomatics engineering. It begins with an introduction to linear algebra and its importance in engineering. Vector spaces are central to modern mathematics and linear algebra is widely used in abstract algebra and functional analysis. The document then lists the objectives of understanding the importance of applying linear algebra in geomatics engineering. It provides theoretical background on vector spaces and subspaces, discussing their properties and applications in science and engineering problems. Examples are given of using the Wronskian method to determine if sets of functions are linearly independent or dependent. The document concludes with two problems involving determining linear independence of functions using the Wronskian theorem.
We will discuss history and recent developments in the study of the phase structure of noncommutative scalar fields. Apart from the usual disorder and uniform order phases, the theory exhibits a third phase, which survives the commutative limit.
This is connected to the UV/IR mixing of the noncommutative theory. We will rewrite the fuzzy theory as a modified quartic
matrix model, with extra multitrace terms in the action and perform saddle point analysis of the theory. Our goal will be to locate the triple point of the theory and to reconstruct the numerically obtained phase diagram. This goal will be successfully reached at the end of the talk.
Abstract. This manuscript provides a brief introduction to Functional Analysis. It covers basic Hilbert and Banach space theory including Lebesgue spaces and their duals (no knowledge about Lebesgue integration is assumed).
This document discusses stochastic partial differential equations (SPDEs). It outlines several approaches that have been used to solve SPDEs, including methods based on diffusion processes, stochastic characteristic systems, direct methods from mathematical physics, and substitution of integral equations. It also discusses using backward stochastic differential equations to study SPDEs and introduces notation for the analysis of an Ito SDE with inverse time. The document is technical in nature and outlines the mathematical frameworks and equations involved in solving SPDEs through various probabilistic methods.
We make use of the conformal compactification of Minkowski spacetime M# to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime [M#]โ1 obtained via conformal inversion, so as to discuss a doubled compactified spacetime on which Maxwell fields may be defined. Identifying M# with the projective light cone in (4+2)-dimensional spacetime, we write two independent conformal-invariant functionals of the 6-dimensional Maxwellian field strength tensors - one bilinear, the other trilinear in the field strengths -- which are to enter general nonlinear constitutive equations. We also make some remarks regarding the dimensional reduction procedure as we consider its generalization from linear to general nonlinear theories.
This document discusses quantum chaos in clean many-body systems. It begins by outlining the topic and noting that quantum chaos fits into many-body physics and statistical mechanics. It then discusses how the quantum chaos conjecture relates semiclassical physics to many-body systems. Specifically, it discusses how quantum ergodicity, decay of correlations, and Loschmidt echo relate to the integrability-breaking phase transition in spin chains. It also briefly mentions how quantum chaos appears in non-equilibrium steady states of open many-body systems.
This document provides an introduction and overview of the mathematics textbook. It discusses the importance of mathematics education and outlines the goals and structure of the textbook. The textbook aims to help students learn mathematics fundamentals and apply them to problem solving. It contains 12 chapters covering topics like sets, sequences, algebra, matrices, coordinate geometry, and probability. For each chapter, the document lists the key concepts and learning outcomes. It encourages teachers to facilitate understanding and maximize learning from the textbook.
Pythagoras was a Greek mathematician born in 570 BC on the island of Samos. He traveled extensively in his youth to Egypt and Babylon to further his education. Pythagoras founded a school in Crotona, Italy called the Pythagorean school around 530 BC, where he taught his theories and beliefs. He is most famous for discovering 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. Pythagoras also believed in the transmigration of souls and was a vegetarian. He died around 495 BC leaving behind many mathematical and philosophical contributions.
The document provides study material for mathematics for class 10 students of Kendriya Vidyalaya Sangathan. It was prepared by the Patna regional office in accordance with instructions from KVS headquarters. The study material aims to help students understand concepts well and meet quality expectations. It was prepared under the guidance of the Deputy Commissioner with contributions from teachers of KV No. 2 Gaya.
This document provides a summary of computing technology and related sciences through history in 3 sentence summaries:
The earliest known computing devices were tally sticks used as notches carved on bones dating back 20,000 years, while copper was first used as a conductor for its properties around 10,000 years ago and megalithic structures from 5,000 BCE may have functioned as early calendars. Mathematical and scientific advances originated in ancient cultures including the earliest use of numbers in Sumerian cuneiform around 3000 BCE, Babylonian sexagesimal and Egyptian base-10 numeric systems, and Archimedes' invention of the positional decimal system. Key developments included the abacus used for calculation for millennia, Euclid's
Samacheer kalvi syllabus for 10th mathsSeeucom Sara
ย
This document provides the syllabus for Sets and Functions from the 10th standard Tamil Nadu state board curriculum. It outlines the key topics to be covered, including introduction to sets, operations on sets, properties of set operations, De Morgan's laws, functions, and cardinality of sets. The expected learning outcomes and number of periods allocated for each topic are also specified. Teaching strategies like using Venn diagrams, real-life examples, and pattern approaches are recommended to help students understand the concepts.
Ratios and proportions can be used to compare quantities. A proportion exists when two ratios are equivalent, meaning the quantities have an equal relationship. To check if two ratios form a proportion, you can use cross multiplication or the scale factor method. Cross multiplication checks if the products of the means and extremes are equal. The scale factor method identifies a common factor that makes the ratios equal when applied. Homework involves copying proportions and showing work checking for equivalency using these methods.
Ratios and proportions power point copyJermel Bell
ย
The ratio of pencils to pens is 2 to 3 or 2:3. This can be expressed as a fraction as 2/3. To write the ratio, we write the quantity of pencils first (the numerator) and the quantity of pens second (the denominator).
This document discusses an introduction to modeling in engineering and kinematics. It begins by defining what an engineer is as someone who has graduated with an engineering degree and works in one of its various fields. It then outlines the course topics for Modeling in Engineering I, including scalar and vector kinematics, particle kinematics in 1D, 2D and 3D, derivatives, work and energy, and conservation of energy and momentum. The professor's goals for the course are to compile the content from the topics in a dynamic way and show applications of the concepts to help students learn.
This document is a master's thesis written in Chinese that investigates the existence and uniqueness of solutions to stochastic differential equations (SDEs) with Lรฉvy noise and non-Lipschitz coefficients. It introduces Lรฉvy processes and their properties, including the Lรฉvy-Itรด decomposition. It defines stochastic integration with respect to compensated Poisson processes and provides Itรด's formula for Lรฉvy diffusions. The thesis proves that if weak existence and pathwise uniqueness hold for an SDE with Lรฉvy noise, then it has a unique strong solution. It establishes conditions on the coefficients that ensure infinite lifetime and pathwise uniqueness of the solution.
Let f(x) = ๏ง
๏ท and g(x) = ๏ง
๏ท
๏จ 1๏ญ x ๏ธ
๏จ x ๏ธ
that fog is not defined.
19.
If f : A ๏ฎ B is bijective, then write n(A) in terms of n(B).
20.
If f : A ๏ฎ B is onto and n(A) = 5, n(B) = 3. Then write n(A).
SHORT ANSWER TYPE QUESTIONS (2 MARKS)
1.
Define reflexive, symmetric
Dialectica Categories and Cardinalities of the Continuum (March2014)Valeria de Paiva
ย
This document discusses Dialectica categories and cardinalities of the continuum. It begins by outlining Hilbert's program to provide secure foundations for mathematics through formalization. Gรถdel's incompleteness theorems showed this was impossible. Gรถdel then developed the Dialectica interpretation as a way to prove consistency of arithmetic. De Paiva later introduced Dialectica categories, which provide a model of linear logic. These categories, called PV, are useful for proving inequalities between cardinal characteristics of the continuum. The structure of PV is discussed, along with examples of objects in this category.
The concept of moments of order invariant quantumAlexander Decker
ย
The document summarizes key concepts related to moments of order invariant quantum Lรฉvy processes. It begins by defining order equivalence and order invariant distributions for discrete random variables. It then states that if the distributions are order invariant, the moments of their sums converge as the number of variables increases. Similarly, for order invariant quantum Lรฉvy processes, the document shows that limits exist for the moments and provides an expression involving these limits. It proves the existence of the limits for moments by induction on the length of index tuples.
This document discusses techniques for setting linear algebra problems in a way that ensures relatively easy arithmetic. Some key techniques discussed include:
1. Using Pythagorean triples and sums of squares to generate vectors with integer norms in R2 and R3.
2. Using the PLU decomposition theorem to generate matrices with a given determinant, such as ยฑ1, to avoid fractions.
3. Extending a basis for the kernel of a matrix to generate matrices with a given kernel.
4. Ensuring the coefficients for a Leontieff input-output model are nonnegative to generate a productive consumption matrix. Examples and Maple routines are provided.
This document provides an introduction to tensor notation and algebra. It defines scalars, vectors, and tensors, and how they transform under changes of reference frame. Vectors have direction and magnitude, and tensors generalize this to have multiple directions/indices. Tensors of different orders are discussed, along with common examples like the velocity gradient tensor. Frame rotations are described using orthogonal transformation matrices, and how vectors and tensors transform under these changes of basis.
This document discusses applications of vector spaces and subspaces in geomatics engineering. It begins with an introduction to linear algebra and its importance in engineering. Vector spaces are central to modern mathematics and linear algebra is widely used in abstract algebra and functional analysis. The document then lists the objectives of understanding the importance of applying linear algebra in geomatics engineering. It provides theoretical background on vector spaces and subspaces, discussing their properties and applications in science and engineering problems. Examples are given of using the Wronskian method to determine if sets of functions are linearly independent or dependent. The document concludes with two problems involving determining linear independence of functions using the Wronskian theorem.
We will discuss history and recent developments in the study of the phase structure of noncommutative scalar fields. Apart from the usual disorder and uniform order phases, the theory exhibits a third phase, which survives the commutative limit.
This is connected to the UV/IR mixing of the noncommutative theory. We will rewrite the fuzzy theory as a modified quartic
matrix model, with extra multitrace terms in the action and perform saddle point analysis of the theory. Our goal will be to locate the triple point of the theory and to reconstruct the numerically obtained phase diagram. This goal will be successfully reached at the end of the talk.
Abstract. This manuscript provides a brief introduction to Functional Analysis. It covers basic Hilbert and Banach space theory including Lebesgue spaces and their duals (no knowledge about Lebesgue integration is assumed).
This document discusses stochastic partial differential equations (SPDEs). It outlines several approaches that have been used to solve SPDEs, including methods based on diffusion processes, stochastic characteristic systems, direct methods from mathematical physics, and substitution of integral equations. It also discusses using backward stochastic differential equations to study SPDEs and introduces notation for the analysis of an Ito SDE with inverse time. The document is technical in nature and outlines the mathematical frameworks and equations involved in solving SPDEs through various probabilistic methods.
We make use of the conformal compactification of Minkowski spacetime M# to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime [M#]โ1 obtained via conformal inversion, so as to discuss a doubled compactified spacetime on which Maxwell fields may be defined. Identifying M# with the projective light cone in (4+2)-dimensional spacetime, we write two independent conformal-invariant functionals of the 6-dimensional Maxwellian field strength tensors - one bilinear, the other trilinear in the field strengths -- which are to enter general nonlinear constitutive equations. We also make some remarks regarding the dimensional reduction procedure as we consider its generalization from linear to general nonlinear theories.
This document discusses quantum chaos in clean many-body systems. It begins by outlining the topic and noting that quantum chaos fits into many-body physics and statistical mechanics. It then discusses how the quantum chaos conjecture relates semiclassical physics to many-body systems. Specifically, it discusses how quantum ergodicity, decay of correlations, and Loschmidt echo relate to the integrability-breaking phase transition in spin chains. It also briefly mentions how quantum chaos appears in non-equilibrium steady states of open many-body systems.
This document provides an introduction and overview of the mathematics textbook. It discusses the importance of mathematics education and outlines the goals and structure of the textbook. The textbook aims to help students learn mathematics fundamentals and apply them to problem solving. It contains 12 chapters covering topics like sets, sequences, algebra, matrices, coordinate geometry, and probability. For each chapter, the document lists the key concepts and learning outcomes. It encourages teachers to facilitate understanding and maximize learning from the textbook.
Pythagoras was a Greek mathematician born in 570 BC on the island of Samos. He traveled extensively in his youth to Egypt and Babylon to further his education. Pythagoras founded a school in Crotona, Italy called the Pythagorean school around 530 BC, where he taught his theories and beliefs. He is most famous for discovering 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. Pythagoras also believed in the transmigration of souls and was a vegetarian. He died around 495 BC leaving behind many mathematical and philosophical contributions.
The document provides study material for mathematics for class 10 students of Kendriya Vidyalaya Sangathan. It was prepared by the Patna regional office in accordance with instructions from KVS headquarters. The study material aims to help students understand concepts well and meet quality expectations. It was prepared under the guidance of the Deputy Commissioner with contributions from teachers of KV No. 2 Gaya.
This document provides a summary of computing technology and related sciences through history in 3 sentence summaries:
The earliest known computing devices were tally sticks used as notches carved on bones dating back 20,000 years, while copper was first used as a conductor for its properties around 10,000 years ago and megalithic structures from 5,000 BCE may have functioned as early calendars. Mathematical and scientific advances originated in ancient cultures including the earliest use of numbers in Sumerian cuneiform around 3000 BCE, Babylonian sexagesimal and Egyptian base-10 numeric systems, and Archimedes' invention of the positional decimal system. Key developments included the abacus used for calculation for millennia, Euclid's
Samacheer kalvi syllabus for 10th mathsSeeucom Sara
ย
This document provides the syllabus for Sets and Functions from the 10th standard Tamil Nadu state board curriculum. It outlines the key topics to be covered, including introduction to sets, operations on sets, properties of set operations, De Morgan's laws, functions, and cardinality of sets. The expected learning outcomes and number of periods allocated for each topic are also specified. Teaching strategies like using Venn diagrams, real-life examples, and pattern approaches are recommended to help students understand the concepts.
Ratios and proportions can be used to compare quantities. A proportion exists when two ratios are equivalent, meaning the quantities have an equal relationship. To check if two ratios form a proportion, you can use cross multiplication or the scale factor method. Cross multiplication checks if the products of the means and extremes are equal. The scale factor method identifies a common factor that makes the ratios equal when applied. Homework involves copying proportions and showing work checking for equivalency using these methods.
Ratios and proportions power point copyJermel Bell
ย
The ratio of pencils to pens is 2 to 3 or 2:3. This can be expressed as a fraction as 2/3. To write the ratio, we write the quantity of pencils first (the numerator) and the quantity of pens second (the denominator).
Circle - Tangent for class 10th students and grade x maths and mathematics st...Let's Tute
ย
Circle - Tangent for class 10th students and grade x maths and mathematics.Lets tute is an online learning centre. We provide quality education for all learners and 24/7 academic guidance through E-tutoring. Our Mission- Our aspiration is to be a renowned unpaid school on Web-World.
Top 10 math professor interview questions and answersjessicacindy3
ย
In this file, you can ref interview materials for math professor such as types of interview questions, math professor situational interview, math professor behavioral interviewโฆ
The document discusses linear inequalities with one variable. It provides examples of inequalities such as 2x - 1 > 3 and 2x - 3 > 4x + 5. It then shows how to determine the solution set of each inequality by manipulating and solving the inequalities. Finally, it provides three practice problems for finding the solution set of additional inequalities.
MIT Math Syllabus 10-3 Lesson 9: Ratio, proportion and variationLawrence De Vera
ย
Ratio is an indicated quotient of two quantities that can be expressed as a fraction. A proportion is a statement that indicates the equality of two ratios. There are three main types of variation: direct variation, where y varies directly with x; inverse variation, where y varies inversely with x; and joint variation, where z varies jointly as two other variables.
This document discusses ratios, rates, proportions, and how to use them to solve real-life problems. It provides examples of how to:
- Write ratios comparing two numbers or quantities
- Calculate rates when the numerator and denominator are in different units
- Use unit analysis to determine the correct units for rates and proportions
- Set up and solve proportions using the reciprocal and cross product properties
Chapter 3. linear equation and linear equalities in one variablesmonomath
ย
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 โค 40
3) Isolate x by undoing the operations
4) Write the solution set
The solution is 0 โค x โค 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 โ 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.
This document discusses algebraic expressions and terms. An algebraic term is the product of unknowns and numbers, with the coefficient being the other factors. Like terms have the same unknowns, while unlike terms do not. To multiply algebraic terms, multiply the signs, coefficients, and unknowns. To divide terms, write as a fraction and simplify by cancelling common unknowns in the numerator and denominator. An algebraic expression is a combination of terms using addition and subtraction.
This document discusses different types of angles including acute, obtuse, right, and straight angles. It defines an angle as being formed by two rays sharing an endpoint called the vertex. Angles are measured in degrees, with acute angles between 0-90 degrees, obtuse angles between 90-180 degrees, right angles equal to 90 degrees, and a straight angle equaling 180 degrees. It includes examples of each type of angle and encourages identifying them in a game.
The document discusses linear functions and graphs. It explains that linear graphs form straight lines and linear expressions only contain one variable with no exponents. It also defines slope as the rate of incline or decline of a line and discusses how to find the slope and y-intercept of a linear equation in slope-intercept form. Finally, it provides an example of using a linear equation to generate a table of x-y points and graph those points on a line.
This document discusses various theorems and properties related to triangles. It explains the Basic Proportionality Theorem, also known as Thales' Theorem, which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. It also covers similarity criteria like AAA, SSA, and SSS. The Area Theorem demonstrates that the ratio of areas of similar triangles equals the square of the ratio of corresponding sides. Additionally, it proves Pythagoras' Theorem, which relates the sides of a right triangle, and its converse. In summary, the document outlines key triangle theorems regarding proportional division, similarity, areas, and the Pythagorean relationship between sides.
1. The document is a model question paper with 3 sections containing multiple choice and long answer questions on mathematics.
2. Section A contains 15 multiple choice questions worth 1 mark each. Section B contains 10 long answer questions worth 2 marks each. Section C contains 9 long answer questions worth 5 marks each and 1 compulsory question.
3. The questions cover topics in algebra, trigonometry, geometry, sequences and series, and probability.
This document outlines the course structure for mathematics in Class X. It is divided into two terms, with marks allocated to different units in each term. The first term covers number systems, algebra, geometry, trigonometry and statistics. The second term continues instruction in algebra, geometry and trigonometry, and also covers probability, coordinate geometry and mensuration. Key concepts taught include polynomials, linear and quadratic equations, trigonometric ratios and identities, similarity and congruence, areas of plane figures, and surface areas and volumes of solids. Recommended textbooks and resources are also listed.
This document provides a syllabus for mathematics courses at the secondary and higher secondary levels. Some key points:
- The syllabus builds upon concepts from previous grades in a continuous manner from classes 9 to 12.
- It is designed to be taught in approximately 180 hours to allow sufficient time for exploration and understanding of concepts.
- Areas like proofs and mathematical modeling are introduced gradually from classes 9 to 12 since they are new concepts.
- The syllabus covers topics like number systems, algebra, trigonometry, coordinate geometry, geometry, mensuration, statistics and probability.
- Specific concepts outlined for each class include polynomials, linear equations, quadratic equations, trigonometric ratios and identities.
This document provides an index and overview of a mathematics question bank and worksheets for Class 10. It contains chapters on real numbers, polynomials, linear equations, quadratic equations, arithmetic progressions, triangles, coordinate geometry, trigonometry, applications of trigonometry, circles, constructions, areas related to circles, surface areas and volumes, statistics, and probability. Each chapter includes multiple choice question worksheets and practice questions. Key formulas and concepts are provided for real numbers. The document is dedicated to the author's late father and prepared by M.S. KumarSwamy, a teacher of mathematics.
The document discusses an inquiry lab activity that investigates which three pairs of corresponding parts can be used to show that two triangles are congruent. The activity involves copying and arranging sides and angles of triangles on paper to form new triangles. This allows students to determine if triangles are congruent based on different combinations of corresponding parts. The activity aims to show that two triangles can be proven congruent without demonstrating that all six pairs of corresponding parts are congruent.
Real world applications of trigonometry ppm42watts
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This unit teaches students how to apply trigonometry concepts like trig identities, inverses, and right triangle trigonometry to solve real-world measurement problems. Students will learn to measure objects in nature, man-made structures, and historical objects. They will also use trig functions to model real-life situations and create a project using trigonometry to measure a real object, which they will present to the class. The goal is for students to understand how trigonometry applies to measuring the physical world.
The document discusses key concepts related to sets. It defines what a set is and the different ways of representing sets. It describes types of sets such as empty, finite, infinite and singleton sets. It explains the concepts of subset, equal sets, power set and different set operations like union, intersection, difference and complement. It provides properties and laws related to these set operations including commutative, associative and De Morgan's laws. It also discusses different types of intervals on the number line.
This document defines vectors and scalar quantities, and describes their key properties and relationships. It begins by defining physical quantities that can be measured, and distinguishes between scalar and vector quantities. Scalars have only magnitude, while vectors have both magnitude and direction. The document then provides a more rigorous definition of vectors as quantities that remain invariant under coordinate system rotations or translations. It describes how to represent and transform vectors between different coordinate systems. Vector addition, subtraction, and multiplication operations like the scalar and vector products are defined. Derivatives of vectors are also discussed. Examples of velocity and acceleration vectors in uniform circular motion are provided.
The document outlines the syllabus for mathematics in classes 9 and 10. It includes 6 units for class 9 (Number Systems, Algebra, Coordinate Geometry, Geometry, Mensuration, Statistics and Probability) and 7 units for class 10 (Number Systems, Algebra, Coordinate Geometry, Geometry, Trigonometry, Mensuration, Statistics and Probability). The objectives of teaching mathematics are to consolidate skills, develop logical thinking, apply knowledge to solve problems, and develop interest in the subject. Assessment includes pen and paper tests, portfolios, and practical lab activities.
CBSE Math 9 & 10 Syllabus - LearnConnectEdLearnConnectEd
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The document outlines the syllabus for mathematics in classes 9 and 10. It includes 6 units for class 9 (Number Systems, Algebra, Coordinate Geometry, Geometry, Mensuration, Statistics & Probability) and 7 units for class 10 (Number Systems, Algebra, Coordinate Geometry, Geometry, Trigonometry, Mensuration, Statistics & Probability). The objectives are to consolidate mathematical knowledge and skills, develop logical thinking and the ability to apply concepts to solve problems. Assessment includes pen and paper tests, portfolios and practical lab activities.
This document contains 29 geometry problems from Romanian textbooks for 9th and 10th grade students, compiled and solved by Florentin Smarandache. The problems cover a range of topics in geometry including properties of angles, triangles, polygons, circles, areas, and constructions. Smarandache compiled these problems during his time teaching mathematics in Romania and Morocco between 1981-1988. He provides solutions to each problem at the end of the document to serve as an educational aid for mathematics students and instructors.
A talk presented at the University of New South Wales on the occasion of Ian Sloan's 80th birthday, remembering our work together and thinking about how math is used in science.
The document provides information about the revised mathematics syllabus for classes 9-10 in India. Some key points:
- The syllabus was revised in accordance with the National Curriculum Framework of 2005 and recommendations from experts to meet the needs of all students.
- At the secondary level, mathematics aims to help students apply algebraic and trigonometric concepts to solve real-life problems.
- The syllabus covers topics like number systems, algebra, geometry, trigonometry, mensuration, statistics, and coordinate geometry.
- Teaching methods should include activities using concrete materials, models, and experiments to make mathematics engaging and applicable.
The document discusses group theory and its applications in physics. It begins by introducing symmetry groups that are important in physics, including translations, rotations, and Lorentz transformations. It then discusses the use of group theory in formulating fundamental forces and the Standard Model of particle physics. The document provides definitions of group theory concepts like groups, operations, identity, and inverse. It explains how group theory provides a mathematical framework for describing physical symmetries.
The purpose of this communication is to generalize the theorem of Pythagoras using the corresponding area formulas for different geometric figures used in experience; the aim is to look at the possibility of Demosthenes this relationship using different geometric figures squared, showing how calculators can be used to explore the situation and give account of the difficulties that students with geometric concepts.
marathon class 10 maths cbse all firmulas.pptxKarvin4
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This document contains a summary of the key chapters and concepts covered in the Term 1 Complete Maths course, including:
1. Real numbers, polynomials, pairs of linear equations in two variables, triangles, coordinate geometry, trigonometry, areas related to circles, and probability.
2. The chapters describe important formulas, definitions, theorems, examples and questions. Concepts covered include HCF, LCM, quadratic equations, similarity, Pythagoras theorem, trigonometric ratios, and probability calculations.
3. Key formulas introduced are for distance, midpoint, section, centroid, area of circle/sector/segment, trig ratios, and probability. Examples are provided to demonstrate solving pairs of linear
This document provides the weekly syllabus for mathematics for class 10 for the 2011-2012 school year. It is divided into two terms, with the first term covering chapters on numbers, algebra, geometry, trigonometry, and statistics. The second term covers additional chapters on algebra, geometry, mensuration, trigonometry, coordinate geometry, and probability. Each week outlines the chapter, examples, and activities to be covered. Suggested activities are also provided to assess students for formative assessments.
The document outlines the syllabus for Class IX mathematics for the academic session 2011-2012. It is divided into two semesters. The first semester covers chapters on number systems, polynomials, coordinate geometry, introduction to Euclid's geometry, lines and angles, triangles, and Heron's formula. The second semester covers chapters on linear equations in two variables, quadrilaterals, areas of parallelograms and triangles, circles, constructions, statistics, probability, and surface areas and volumes. Mental maths practice is scheduled every Monday based on the concerned topic. Related activities are provided at the end of each chapter.
This document provides a weekly syllabus distribution for the mathematics subject for Class VIII during the 2011-2012 school year. It was prepared by three mathematics teachers under the guidance of the District Deputy Education Officer and school principal. The syllabus covers 14 chapters taught over 39 weeks, including topics on rational numbers, linear equations, squares and square roots, data handling, algebraic expressions, and mensuration. Time is allotted each week for exercises, chapter summaries, and suggested hands-on activities relating to the topics. Revision sessions are scheduled prior to exams in December and March.
The document is a weekly syllabus for 7th class mathematics provided by the Directorate of Education, Government of NCT Delhi for the 2011-2012 academic year. It outlines the chapters, topics, and exercises to be covered over each month and week from April to March. Key chapters include integers, fractions, data handling, simple equations, geometry topics like lines and angles, symmetry, and visualizing solid shapes.
The document provides a weekly syllabus for 6th class mathematics covering April 2011 to December 2011. It includes 5 chapters to be covered each month with topics like numbers, operations, fractions, decimals, measurement, symmetry, algebra and data handling. Each topic is broken down into sections and exercises to be completed over multiple class days with mental math problems and activities interspersed.
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A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
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The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
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(๐๐๐ ๐๐๐) (๐๐๐ฌ๐ฌ๐จ๐ง ๐)-๐๐ซ๐๐ฅ๐ข๐ฆ๐ฌ
๐๐ข๐ฌ๐๐ฎ๐ฌ๐ฌ ๐ญ๐ก๐ ๐๐๐ ๐๐ฎ๐ซ๐ซ๐ข๐๐ฎ๐ฅ๐ฎ๐ฆ ๐ข๐ง ๐ญ๐ก๐ ๐๐ก๐ข๐ฅ๐ข๐ฉ๐ฉ๐ข๐ง๐๐ฌ:
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๐๐ฑ๐ฉ๐ฅ๐๐ข๐ง ๐ญ๐ก๐ ๐๐๐ญ๐ฎ๐ซ๐ ๐๐ง๐ ๐๐๐จ๐ฉ๐ ๐จ๐ ๐๐ง ๐๐ง๐ญ๐ซ๐๐ฉ๐ซ๐๐ง๐๐ฎ๐ซ:
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Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
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Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the bodyโs response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
1. DIRECTORATE OF EDUCATION
Govt. of NCT Delhi
WEEKLY SYLLABUS
2011 - 2012
Subject - Mathematics
Class - X
UNDER THE GUIDANCE OF
Mr. Khan Chand Mrs. Savita Drall
Dy. Director of Education Principal
Central / Jhandewalan, S.K.V. Mata Sundri
School
Delhi- 6 New Delhi -1
Prepared By
Ms. Mamta (TGT Maths) Abdul Salim (TGT-
Maths)
RSKV No. 2, Jama Masjid (2127017) GGSS Kalan Mahal
(2127027)
Delhi- 6 Delhi -2
11
2. SYLLABUS OF MATHEMATICS AS PER CCE GUIDELINES
CLASS โ X
First Term Marks : 80 Marks
Unit
I Number System (Real Numbers) 10
II Algebra (Polynomials Pair of Liner 20
Equation in two variables)
III Geometry (Triangles) 15
V Trigonometry (Introduction to 20
Trigonometry, Trigonometric
identity)
VII Statistics 15
Total 80
Second Term Marks : 80 Marks
Unit
II Algebra (Contd.) Quadratic 20
Equation Arithmetic Progression
III Geometry (Contd.) Circles, 16
Construction.
IV Mensuration (Area related to 20
circles. Surface Area & Volume)
V Trigonometry (Contd.) Heights and 08
Distances)
VI Co-ordinate Geometry 10
VII Probability 06
Total 80
12
3. WEEK WISE DISTRIBUTION OF SYLLABUS FOR 2011-2012
MATHEMATICS (CLASS โ X)
WEEK/ NO. OF
CHAPTER /
DATES WORKING DETAILS
TOPIC
(Mon-Sat) DAYS
01.04.11 to 2 Chapter-6 Introduction, Examples of similar triangles, Basic
02.04.11 Triangles Proportionality Theorem (with proof)
04.04.11 to 5 Chapter-6 Ex 6.1, Ex 6.2
09.04.11 Triangles (Motivate) : If in two triangles, corresponding angles are
equal, then their corresponding sides are in the same ratio (or
proportion) and hence the two triangles are similar.
(Motivate): If in two triangles, side of one triangle are
proportional to (i.e. in the same ratio of) the side of the other
(Mental- triangle then their corresponding angle are equal and hence
Maths) the two triangles are similar.
(Motivate): If one angle of a triangle is equal to one angle of
the other triangle and the sides including then angles are
proportional, then the two triangles are similar.
Practical Activity : To verity the result of BPT
YUVA : 3.1 Attitude is everything.
11.04.11 to 4 Chapter 6 Ex. : 6.3
16.04.11 Triangle (with proof) : The ratio of the areas of two similar triangles is
equal to the square of the ratio of their corresponding sides,
(Mental- Ex. 6.4
Maths) Yuva : 3.2 Choice, Not Chance, Determines Destiny
18.04.11 to 5 Chapter 6 Ex. 6.4 (continued),
23.04.11 Triangles
(motivated) if a perpendicular is drawn from the vertex of the
13
4. right triangle to the hypotenuse then triangles on both sides of
the perpendicular are similar to the whole triangle and to each
other.
(with proof) In a right triangle the square of the hypotenuse is
(Mental-
equal to the sum of the squares of the other two sides.
Maths)
(with proof) In a triangle, If square of one side is equal to the
to the sum of the squares of the other two sides, then the angle
opposite to the first is a right angle.
Yuva : Ex.6.5 Road Safety and US
25.04.11 to 6 Chapter โ 2 Zeros of a polynomial and geometrical meaning of the zeroes
30.04.11 Polynomials of a polynomial Ex. 2.1 Relationship between zeroes and co-
efficient of a polynomial with real co-efficient, Ex. 2.2.
Division Algorithm with real Co-efficient, Ex - 2.3
Practical Activity : To verify the result of Pythagoras
Theorem
Yuva : 3.6 if there was a bomb threat.
Chapter โ 3 Ex. 3.1 Geometrical representation of different possibilities of
n
Pair of liner solution consistency / inconsistency graphical method of sol
eqn in two of a pair of liner equation Ex. 3.2
variables
Mental-Maths Suggest Activity for FAI : 1st MCQ type questions (10
marks)
2nd: Evolution of activity in marks lab (10 marks)
02.05.11 to 6 Chapter โ 3 Ex. 3.2 (Continued). Algebraic method of solving of liner
07.05.11 Pair of liner equations โ substitution method ex. 3.3
eqn in two
variables.
Yuva : 3.3 My principle are my strength !
14
5. Practical Activity : Based on consistency / inconsistency
(Mental system of linear equation.
Maths) 3rd Suggestive activity for FAI (10 marks)
Worked / Assignment based on Chapter III
09.05.11 to 2 Chapter โ 3 Ex. 3.3 (continued)
10.05.11 Pair of liner
eqn in two
variables
11.05.11 to SUMMER VACATIONS
30.06.11
4th Suggestive Activity for FAI (Project/ Models / Charts) (10
marks)
1. Introduction and family of โs
2. Concept of congruency with the help of figures.
3. Number System
4. To prove (a + b)2 = a2 + b2 + 2ab
5. To prove (a + b)3 = a3 + b3 + 3a2b + 3ab2
6. Biography of any one Mathematician
7. Importance of Maths in daily life.
8. Know about circle
9. Use of Graphs in sports.
10. Use of statistics in daily life.
01.07.11 to 2 Chapter โ 3 Elimination method โ Ex. 3.4
02.07.11 Pair of linear
eqn in two
variables
04.07.11 to 5 Chapter โ 3 Ex. 3.4 (Continued). Cross multiplication method:
09.07.11 Pair of linear Ex. 3.5
eqn in two
15
6. variables
(Mental
Maths) Yuva : 3.4 I admire u because ...........
11.07.11 to 6 Chapter โ 3 Equation reducible to a liner equations in two variables Ex.
16.07.11 Pair of linear 3.6
eqn in two
variables
(Mental-
YUVA : 3.9 I too have rights !
Maths)
18.07.11 to 6 Chapter - I Eulid's division leema - finding HCF and LCM of number
23.07.11 Real Number Ex.-1.1, fundamental theorem of arithmetic Ex. 1.2, Theorem
1.3 and proofs of results - irrationality of โ2, โ3, โ5, Ex. 1.3
Decimal expansion of rational number in terms of terminating
/ non terminating recurring decimal Ex. 1.4
(Mental
1st Suggestive activity of FA 2 : Class Test of lesson I. (10
Maths)
marks)
Yuva (3.10) Every Drop is precious.
25.07.11 to 6 Chapter โ 8 Trigonometric ratios of a acute angle of a right angled triangle
30.07.11 Introduction Ex. 8.1
to Trigonometric ratios of some specific angles, value (with
trigonometry proof) of the trigonometric ratios of 300, 450 and 600 โ Ex. 8.2
Yuva : 3.11 End it, before it ends US !
(Mental-
Suggestive Activity in Maths Lab
Maths)
Making of Clinometer
2nd Suggestive Activity of FA 2: - Oral test based on
trigonometry formula (Max. marks 10)
01.08.11 to 6 Chapter โ 8 Ex. 8.2 (Contd.) Trigonometric Ratios of complementary
06.08.11 Introduction angles Ex. 8.3
to Yuva : 3.12 : Towards zero waste
Trigonometry
16
7. (Mental- 3rd suggestive activity for-FA2
Maths) 2nd UNIT TEST (Max. Marks : 10)
08.08.11 to 5 Chapter โ 8 Trigonometric Identities, Proof and application of the identity
13.08.11 Introduction Sin2 A + Cos2 A=1, Ex : 8.4
to
Trigonometry
Yuva : 3.13 Empowered to save power.
(Mental-
Maths)
15.08.11 to 5 Chapter โ 8 Ex. 8.4 (continued)
20.08.11 Introduction
to Introduction, Mean of Grouped Data Ex. 14.1)
Trigonometry
Chaptr-14 Yuva : Meditation and Pre-Examination stress (3.5)
Statistics
(Mental-
Maths)
22.08.11 to 5 Chapter 14 Mode of Grouped Data Ex 14.2, Median of Grouped Data Ex.
27.08.11 Statistics 14.3
(Mental-
Maths) Yuva : 10.1 : Idgah
4th Suggestive activity of FA2
Group Activity related to statistics
29.08.11 to 5 Chapter 14 Ex 14.3 (contd.) graphical representation of cumulative
03.09.11 Statistics frequency distribution - Ex 14.4
(Mental-
Maths) Yuva : 10.2 : Hasty - Tasty Funky Noodles
05.09.11 5
to10.09.11 REVISION
12.09.11 FIRST C.C.E.P.
17
8. 13.09.11 to 5 REVISION
17.09.11
19.09.11 to
27.09.11 1ST SEMESTER EXAM
28.09.11 to
29.09.11 To show the Answer sheet
30.09.11 OPEN-DAY
01.10.11 Noting the result in teacher's Diary and mark the week
students.
03.10.11 to AUTUMN BREAK
06.10.11
07.10.11 to 1 Chapter-12 Perimeter and area of the circle Ex 12.1
08.10.11 Area related
to circle
10.10.11 to 5 (Mental - Area of sector and segment of a circle Ex. 12.2
15.11.11 Maths)
Chapter : 12 Yuva : Flying high the kite of hope.
Area related
to circle (10.3)
17.10.11 to 6 Chapter : 12 Area of combination of plane figures : Ex. 12.3
22.10.11 Area related
to circle. Yuva (10.4) : Keeping healthy.
(Mental -
Maths) Suggestive activity : For FA 3
To prepare a worksheet by paper cutting and pasting based on
area related to circle (10 marks)
24.10.11 to 4 Chapter : 13 Introduction, Surface area of combination of solids..
29.10.11 Surface Area
and volume Ex. 13.1
31.10.11 to 6 Chapter : 13 Volume of the combination of solids and conversion of solids
05.11.11 Surface Area from one shape to another (Ex. 13.2, Ex. 13.3)
and volumes
(Mental Yuva : (10.8): I too will work for a clean and safe
18
9. Maths) environment (school)
2nd Suggestive Activity for FA:3 (10 marks). Worksheet/
Assignment related to formulas of surface area and volume,
area related to circle.
Suggestive Maths - Lab Activity:
1. To find the relation between volume of a care and cylinder.
2. To make the right circular cylinder with the help of
rectangular sheet and verify the result of curved surface area
of cylinder by folding rectangular sheet length wise and
breath wise.
07.11.11 to 3 Chapter - 13 Frustum of a cone Ex. 13.4
12.11.11 Surface area
and volumes 3rd Suggestive Activity for FA 3 (10 marks)
(Mental - Any activity/assignment/project based on Frustum.
Maths)
14.11.11 to 6 Chapter : 10 Introduction, Targets to a circle (with proof): The tangent at
19.11.11 Circles any point of a circle is perpendicular to the radius through the
point of contact
(with proof): The length of tangents drawn from an external
(Mental
Maths) point to a circle are equal Ex. 10.1, Ex. 10.2
4th suggestion activity for FA 3 (10 marks)
To verify the result that the length of tangents drawn from as
external point to a circle are equal by taking circles of
different radius with the help of paper - folding.
Yuva : (10.10) "If there were no rights...! (P.M.I.)
21.11.11 to 6 Chapter: 9 Introduction, heights and distances, simple and believable
26.11.11 Some problems on height and distance problems should not involve
applications more than two right triangles. Angle of elevation/depression
of o o o
Trigonometry should be only 30 , 45 , 60 Ex 9.1
(Mental- Yuva : (10.7) : A strange race.
Maths)
28.11.11 to 6 Chapter - 7 Introduction, Distance Formula, Section formula Ex. 7.1, Ex.
Co-ordinate
19
10. 03.12.11 Geometry. 7.2
(Mental - Yuva : There are so many jobs to choose from.
Maths)
05.12.11 to 4 Chapter - 7: Area of triangle Ex. 7.3
10.12.11 Co-ordinate
Geometry Yuva : I can improve my performance in the coming board
exams.
1st Suggestive Activity for FA4
Assignment based on lesson co-ordinate geometry (Max.
Marks : 10)
12.12.11 SECOND C.C.E.P.
13.12.11 to 5 Chapter: 5 Introduction to A.P., nth terms of an A.P. Ex. 5.1 , Ex. 5.2
17.12.11 Arithmetic
progression Suggestive Maths Lab Activity:
(Mental
Maths) To verify that the given sequence is an arithmetic progression
by paper cutting and pasting method.
Yuva : 10.12 Our prized possession.
19.12.11 to 6 Chapter : 5 Ex. 5.2 (contd.) sum of first n terms Ex. 5.3
24.12.11 Arithmetic
Progression Suggestive Maths Lab Activity
(Mental
Maths) 1. To verify that the sum of first a natural number is n (n+1)/2
by graphical method:
2. To verify that the sum of first n odd natural numbers is n2
by an activity method.
2nd Suggestive Activity for FA4 (10 Marks)
Any two activity can be taken based on arithmetic
progression by paper cutting and pasting
25.12.11 to WINTER BREAK
15.01.12
3rd Suggestive Activity for FA4 can be given as
(10 marks)
Prepared a cross-word based on any two chapters.
20
11. 16.01.12 to 6 Chapter : 4 Standard form of quadratic equation - Ex 4.1 solution of a
21.01.12 Quadratic quadratic equation by factorization method Ex. 4.2
equation
(Mental - Yuva : Understanding my parents.
Maths)
23.01.12 Chapter : 4 Solution of a quadratic equation by completing the square,
Quadratic and by using quadratic formula, relationship between
to equation
discriminate and nature of roots Ex. 4.3 Ex. 4.4
28.01.12 (Mental -
Maths) Yuva : (6.3) : (What is right, what is wrong) ?
4th Suggestive Activity for FA 4: 10 marks
M.C.Q/U.T./Class Test based on quadratic eqn.
30.01.12 to 6 Chapter - 11 Division of a line segment in a given ratio (Internally).
04.02.12 Construction Tangent to a circle from a point outside it, construction of a
(Mental triangle similar to a given triangle. Ex. 1.1, Ex. 11.2
Maths)
Yuva : 3.4: I admire U because.........
06.02.12 to 5 Chapter - 15 Simple Problems on single event Ex. 15.1
11.02.12 Probability Yuva : 3.5 Meditation and Pre-examination stress.
(Mental
Maths)
13.02.12 to 6 Revision
18.02.12 For the students opted board as well as school based
examination.
20.02.12 to 5 Revision
25.02.12
27.02.12 to 6 Revision
03.03.12
05.03.12 to 4 Revision
10.03.12
12.03.12 to ANNUAL EXAMINATION
24.03.12
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