Assignment Chapters 1 -8- Maths (CLASS XII)
•
1 like•1,282 views
This document lists 40 math assignment questions covering a range of calculus and algebra topics for Class 12. The questions involve evaluating integrals, differentiation, proving trigonometric and other mathematical identities, solving equations, finding increasing and decreasing intervals of functions, working with matrices, and more. The level of complexity ranges from straightforward computations to more conceptual proofs.
Report
Share
Report
Share
Download to read offline
![MATHS ASSIGNMENT (CHAPTER :- 1 – 8) CLASS – XII
4 MARKS
1. y = , show (x2
+ 1)2
y2 + 2x (x2
+ 1)2
y1 = 2.
2. Prove using properties :-
+ + +
+ + +
+ + +
= .
3. Evaluate :- ∫ ( )( )
dx
4. If (cos x)y
= (cos y)x
, find .
5. Prove :- = − .
6. A = R – {3}, B = R – {1}. f : A → B. f(x) = . Show that f is one – one & onto.
7. Prove :- ∫ √ + √ = √ .
8. If a + b + c ≠ 0 & = 0. Prove a = b = c
9. Evaluate :- ∫( − )√ − − dx.
10. Differentiate :- log (xsinx
+ cot2
x), w.r.t. x
11. Evaluate :- ∫ ( )( )
dx
12. Prove :- y = ( )
- x is an increasing function of x in [0, ]
13. Evaluate :- ∫ .
14. Differentiate :- tan w.r.t. x
15. If x + + √ + = . = ( )
.
16. If A =
−
, find k : A2
= 8A + kI .
17. If f(x) =
| |
≠
=
. check the continuity at x = 0.
18. If y = ecos x
, prove y2 + sin x y1+ y cos x = 0.
19. Evaluate :- ∫ dx.
20. Prove :-
( + )
( + )
( + )
= 2abc (a + b + c)3
.
21. If + + = , Prove x2
+ y2
+ z2
+ 2xyz = 1.
22. Find equation of tangent to the curve x2
+ 3y = 3 which is 11 to line y – 4x + 5 = 0.
23. Find x :
−
−
=
− − −](https://image.slidesharecdn.com/assignmentchapter1-8maths-150822075840-lva1-app6891/85/Assignment-Chapters-1-8-Maths-CLASS-XII-1-320.jpg)
Recommended
Assignment (chapter 1 8) maths
This document provides the questions for a mathematics assignment covering chapters 1-8 of class 12. There are 40 questions in total, ranging from proving trigonometric identities and evaluating definite integrals to solving equations using matrices and checking continuity of functions. The questions cover a wide range of calculus, trigonometry and algebra topics.
Quadratic function and its graph using geogebra
This document discusses quadratic functions and how to graph them using Geogebra. A quadratic function is defined as a function of the form f(x) = ax^2 + bx + c, where a, b, and c are integers. The graph of a quadratic function is a parabola. Examples are given of graphing the quadratic functions f(x) = x^2, f(x) = 1/2x^2, and f(x) = 2x^2 - 4x - 6. Formulas are provided for calculating the vertex coordinates of a parabola based on the values of a, b, and D, where D is the discriminant. The shape of the parab
Quadratic Function by Jasmine & Cristina
Quadratic functions are polynomial functions of the form f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a is not equal to 0. The graph of a quadratic function is a parabola, which is a U-shaped curve that opens up or down depending on the sign of the a coefficient. Examples of quadratic functions are provided in standard form (f(x) = ax^2 + bx + c) and their corresponding graphs are shown to illustrate parabolic shapes. Real-world examples from nature are also given.
Quadratic functions and Equations.pdf
This document discusses quadratic functions and equations. A quadratic function is defined as f(x) = ax^2 + bx + c, where a ≠ 0. The graph of a quadratic function is a parabola. A quadratic equation is an equation of degree 2 in the form ax^2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. There are three methods for solving quadratic equations: factorizing the equation, completing the square, and using the quadratic formula. Factorizing and completing the square are demonstrated through examples.
Quadratic functions
The document discusses graphs of quadratic functions. It begins by reviewing that the graph of a quadratic function y=ax^2+bx+c is a parabola. It explains that the parabola opens up when a>0 and opens down when a<0. It then provides steps for graphing a quadratic function, which include determining the vertex coordinates using the formula x=-b/2a, sketching the axis of symmetry, and finding any intersections with the x-axis or y-axis. Examples of graphing specific quadratic functions are shown. The document concludes by providing exercises for students to practice graphing quadratic functions.
Chapters 1 8 ( 6 marks)
The document contains a list of 31 multi-part math problems involving matrices, integrals, functions, geometry, and equations. The problems cover topics like finding the product and inverse of matrices, evaluating definite integrals, finding maximums and minimums of functions, solving systems of equations using matrices, and calculating areas of geometric shapes.
Lecture 7 quadratic equations
The document discusses quadratic functions and how to graph them. It defines a quadratic function as a function of the form f(x) = ax^2 + bx + c, where a ≠ 0. It explains that the graph of such a function is a parabola, and provides steps to find characteristics of the parabola like the vertex, axis of symmetry, x-intercepts, and y-intercept in order to graph the function. Examples are included to demonstrate applying these steps to graph specific quadratic functions.
5 work sheet( for manasthali) class 11
1. This document contains 12 math word problems divided across 5 worksheets. The problems cover topics like derivatives, limits, probability, complex numbers, trigonometry and sequences and series.
2. The document tests a variety of calculus, trigonometry and algebra skills through problems involving derivatives, limits, sums, probabilities, graphs and equations.
3. Many problems ask students to use concepts like derivatives, limits, sequences, series, trigonometric identities and equations to solve word problems step-by-step and demonstrate mathematical reasoning and problem solving abilities.
Recommended
Assignment (chapter 1 8) maths
This document provides the questions for a mathematics assignment covering chapters 1-8 of class 12. There are 40 questions in total, ranging from proving trigonometric identities and evaluating definite integrals to solving equations using matrices and checking continuity of functions. The questions cover a wide range of calculus, trigonometry and algebra topics.
Quadratic function and its graph using geogebra
This document discusses quadratic functions and how to graph them using Geogebra. A quadratic function is defined as a function of the form f(x) = ax^2 + bx + c, where a, b, and c are integers. The graph of a quadratic function is a parabola. Examples are given of graphing the quadratic functions f(x) = x^2, f(x) = 1/2x^2, and f(x) = 2x^2 - 4x - 6. Formulas are provided for calculating the vertex coordinates of a parabola based on the values of a, b, and D, where D is the discriminant. The shape of the parab
Quadratic Function by Jasmine & Cristina
Quadratic functions are polynomial functions of the form f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a is not equal to 0. The graph of a quadratic function is a parabola, which is a U-shaped curve that opens up or down depending on the sign of the a coefficient. Examples of quadratic functions are provided in standard form (f(x) = ax^2 + bx + c) and their corresponding graphs are shown to illustrate parabolic shapes. Real-world examples from nature are also given.
Quadratic functions and Equations.pdf
This document discusses quadratic functions and equations. A quadratic function is defined as f(x) = ax^2 + bx + c, where a ≠ 0. The graph of a quadratic function is a parabola. A quadratic equation is an equation of degree 2 in the form ax^2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. There are three methods for solving quadratic equations: factorizing the equation, completing the square, and using the quadratic formula. Factorizing and completing the square are demonstrated through examples.
Quadratic functions
The document discusses graphs of quadratic functions. It begins by reviewing that the graph of a quadratic function y=ax^2+bx+c is a parabola. It explains that the parabola opens up when a>0 and opens down when a<0. It then provides steps for graphing a quadratic function, which include determining the vertex coordinates using the formula x=-b/2a, sketching the axis of symmetry, and finding any intersections with the x-axis or y-axis. Examples of graphing specific quadratic functions are shown. The document concludes by providing exercises for students to practice graphing quadratic functions.
Chapters 1 8 ( 6 marks)
The document contains a list of 31 multi-part math problems involving matrices, integrals, functions, geometry, and equations. The problems cover topics like finding the product and inverse of matrices, evaluating definite integrals, finding maximums and minimums of functions, solving systems of equations using matrices, and calculating areas of geometric shapes.
Lecture 7 quadratic equations
The document discusses quadratic functions and how to graph them. It defines a quadratic function as a function of the form f(x) = ax^2 + bx + c, where a ≠ 0. It explains that the graph of such a function is a parabola, and provides steps to find characteristics of the parabola like the vertex, axis of symmetry, x-intercepts, and y-intercept in order to graph the function. Examples are included to demonstrate applying these steps to graph specific quadratic functions.
5 work sheet( for manasthali) class 11
1. This document contains 12 math word problems divided across 5 worksheets. The problems cover topics like derivatives, limits, probability, complex numbers, trigonometry and sequences and series.
2. The document tests a variety of calculus, trigonometry and algebra skills through problems involving derivatives, limits, sums, probabilities, graphs and equations.
3. Many problems ask students to use concepts like derivatives, limits, sequences, series, trigonometric identities and equations to solve word problems step-by-step and demonstrate mathematical reasoning and problem solving abilities.
April 9, 2015
The document discusses graphing quadratic functions. It begins with reviewing key concepts like the vertex and axis of symmetry and how the a, b, and c coefficients affect the graph. Examples are provided for determining the width, direction opened, and vertical shift based on these coefficients. The remainder of the document provides step-by-step examples of graphing quadratic functions by finding the axis of symmetry, vertex, y-intercept, and other points to plot the parabolic curve.
Quadratic function
The document discusses quadratic functions and their zeros. It provides examples of finding the zeros of quadratic functions by factoring, completing the square, and using the quadratic formula. It also gives examples of writing the equation of a quadratic function given its zeros or given properties like the vertex and y-intercept. Methods discussed include using the fact that the zeros are the roots of the corresponding equation, and substituting known point values into the quadratic formula.
Quadratic function
The document discusses quadratic functions and their key properties. It defines a quadratic function as a polynomial function of second degree whose graph is a parabola. The standard form of a quadratic function is given as f(x) = ax^2 + bx + c, where a, b, and c are constants and a cannot equal 0. It also discusses the vertex form of a quadratic function and how to find the vertex, x-intercepts, y-intercept, equation of the symmetry axis, and sketch the graph of example quadratic functions.
The Quadratic Function Derived From Zeros of the Equation (SNSD Theme)
Christian Jett Morales presents on the quadratic function derived from zeros of the function. The presentation includes:
- An introduction to deriving the quadratic function f(x) = ax^2 + bx + c from the zeros r1 and r2 of the function.
- Examples of deriving quadratic functions when given different zeros, such as 3/2 and -1, or 2+√3 and 2-√3.
- An activity for participants to practice deriving quadratic functions.
- A dedication to God and the presenter's teacher for the opportunity to create the presentation.
LESSON-Effects of changing a,h and k in the Graph of Quadratic Function
The document discusses transforming quadratic functions into vertex form and describes how changing the values of a, h, and k affects the graph of the function. It then has students work in groups to graph and describe quadratic functions based on given equations in order to understand how the vertex, opening direction, and any shifts in the vertex position are represented algebraically.
QUADRATIC FUNCTIONS
The document provides an overview of quadratic functions including definitions of key terms like quadratic function, parabola, quadratic equation, and vertex form. It discusses how to graph quadratic functions, solve quadratic equations using methods like the quadratic formula, and find the maximums and minimums of quadratic functions. It includes examples of using these techniques to solve word problems involving quadratic applications. The document aims to teach students about the basic concepts of quadratic functions.
Mathematics 9 Lesson 3: Quadratic Functions
This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
Quadratic Function by Robert & Phillip
A quadratic function is a polynomial function of the form f(x)=ax^2+bx+c, where a cannot equal 0. It is a second degree polynomial with the highest exponent being 2. Setting a quadratic function equal to 0 produces a quadratic equation, whose solutions are the roots of the equation. Quadratic functions are commonly used to model real world phenomena like projectile motion or profit functions and appear in nature as parabolic shapes.
Higher Maths 2.1.2 - Quadratic Functions
This document provides an overview of quadratic functions including:
- The graph of a quadratic function is a parabola.
- The general form of a quadratic function is f(x) = ax2 + bx + c.
- Key aspects that must be identified before sketching the graph are the nature of the turning point, y-intercept, x-intercepts, and axis of symmetry.
- Quadratic equations can be solved by factorizing, completing the square, or using the quadratic formula. The discriminant determines the nature of the roots.
3 Forms Of A Quadratic Function
The document discusses three forms of quadratic functions - standard form, vertex form, and intercept form - and provides examples of how to write quadratic functions in each form and the steps to graph each by finding the vertex, axis of symmetry, and intercepts. The standard form is ax^2 + bx + c, the vertex form is a(x-h)^2 + k, and the intercept form is a(x-p)(x-q), with each using different variables to indicate the features of the parabolic graph.
Integration
This document provides an overview of integration and how it relates to calculating areas under curves and between functions. Some key points covered include:
- Integration uses the concept of reverse differentiation to calculate the area under a function.
- The area under a function between two x-values a and b is calculated as the definite integral from a to b.
- Integrals may be used to find the area between two curves by subtracting their integrals between the intersection points.
- Integrals can represent either positive or negative areas depending on whether the area is above or below the x-axis.
Mcq for manavsthali( 7 worksheets)
The document contains a worksheet with multiple choice questions related to relations, functions, and matrices. Some questions test concepts like equivalence relations, inverse functions, and properties of matrices. The questions cover topics such as determining if a relation is reflexive, transitive, or symmetric; evaluating composite and inverse functions; finding the order and properties of matrices; and evaluating determinants.
Higher Maths 1.2.1 - Sets and Functions
The document discusses key concepts in set theory and functions, including:
- Sets can contain numbers, elements, and be represented using curly brackets.
- Venn diagrams use overlapping circles to show logical connections between sets.
- A function has a domain (input) and range (output), where each input is mapped to a unique output.
- Composite functions combine other functions by substituting one into another.
- Inverse functions reverse the input and output of a function if it exists.
- Common functions that can be graphed include linear, quadratic, trigonometric, cubic, exponential and logarithmic functions.
5.1graphquadratics
This document discusses quadratic functions and their graphs. It defines a quadratic function as having the form y = ax2 + bx + c. The graph of a quadratic function is a parabola, which has a vertex (lowest or highest point) and an axis of symmetry (vertical line through the vertex). It provides examples of graphing different quadratic functions using a graphing calculator and by hand, including how to find and plot the vertex and axis of symmetry.
Transforming Quadratic Functions from General Form to Standard Form
This document describes the process of transforming a quadratic function from general form to standard form. It shows the general forms of quadratic functions, and the three step process to transform them: 1) factor out the leading coefficient a, 2) complete the square, 3) factor and combine terms. It provides examples of applying these steps to functions like f(x) = x^2 - 8x + 3 and f(x) = 2x^2 + 5x - 1. Finally, it lists 5 additional quadratic functions to transform into standard form.
Quadratic equations and function
This document discusses quadratic equations and functions. It explains that a quadratic equation is an equation of degree 2 that can be written in standard form as ax2 + bx + c = 0. It provides examples of quadratic equations and shows how to write equations in standard form. The document also discusses several methods for solving quadratic equations, including factoring, graphing, completing the square, and using the quadratic formula. It introduces the square root principle for solving equations of the form x2 = a.
Add Math(F4) Quadratic Function 3.1
The document discusses quadratic functions, including how to recognize a quadratic function based on its standard form, how to plot graphs of quadratic functions based on either tabulated values or a given function, and examples of determining if a function is quadratic and plotting quadratic graphs. Key aspects covered are the standard form of a quadratic function as f(x) = ax^2 + bx + c where a ≠ 0, recognizing quadratic functions, tabulating x and f(x) values for a given quadratic function, and using Geometer's Sketchpad software to plot the graphs.
Quadratic functions
The document discusses quadratic functions and their graphs. It defines quadratic functions as functions of the form f(x)=ax^2+bx+c, where a is not equal to 0. The graph of a quadratic function is a parabola with certain characteristics: it is symmetrical about an axis of symmetry and has a vertex which is either a maximum or minimum point. The axis of symmetry is the line x=0 for functions of the form f(x)=ax^2 and the vertex is at (0,0). For functions of the form f(x)=ax^2+k, the graph is a translation of f(x)=ax^2, so the vertex is (0,k) and the
Assignment (chapter 1 8) maths
This document provides the details of a mathematics assignment consisting of 40 questions with 4 marks each. The questions cover various topics in calculus, trigonometry, matrices and determinants. Some example questions are:
1) Find dy/dx if y = tan−1[√1+x2 + √1−x2/√1+x2 − √1−x2]
2) Evaluate: ∫(x2 + 5x)dx from 1 to 3 as limit of sum
3) Prove that: |(b + c)2 ba ca| = 2abc(a + b + c)3
4) Solve the system of equations: x + 2y
Class 12 practice paper
This document contains a mathematics sample paper with 29 questions across 4 sections - A, B, C and D. The questions cover a wide range of mathematics topics including calculus, algebra, trigonometry, matrices, probability, linear programming, and geometry. The paper is designed to test students' mathematical skills and knowledge over 3 hours with the maximum marks being 100.
Chapters 1 8 ( 6 marks)
The document contains a list of 31 multi-part math problems involving matrices, integrals, functions, geometry, and equations. The problems cover topics like finding the composition and inverse of functions, evaluating definite integrals, solving systems of equations using matrices, finding maximums and minimums, and proving geometric properties.
Chapters 1 8 ( 6 marks)
The document contains a list of 31 multi-part math problems involving matrices, integrals, functions, geometry, and equations. The problems cover topics like finding the product and inverse of matrices, evaluating definite integrals, finding maximums and minimums of functions, solving systems of equations using matrices, and calculating areas of geometric shapes.
More Related Content
What's hot
April 9, 2015
The document discusses graphing quadratic functions. It begins with reviewing key concepts like the vertex and axis of symmetry and how the a, b, and c coefficients affect the graph. Examples are provided for determining the width, direction opened, and vertical shift based on these coefficients. The remainder of the document provides step-by-step examples of graphing quadratic functions by finding the axis of symmetry, vertex, y-intercept, and other points to plot the parabolic curve.
Quadratic function
The document discusses quadratic functions and their zeros. It provides examples of finding the zeros of quadratic functions by factoring, completing the square, and using the quadratic formula. It also gives examples of writing the equation of a quadratic function given its zeros or given properties like the vertex and y-intercept. Methods discussed include using the fact that the zeros are the roots of the corresponding equation, and substituting known point values into the quadratic formula.
Quadratic function
The document discusses quadratic functions and their key properties. It defines a quadratic function as a polynomial function of second degree whose graph is a parabola. The standard form of a quadratic function is given as f(x) = ax^2 + bx + c, where a, b, and c are constants and a cannot equal 0. It also discusses the vertex form of a quadratic function and how to find the vertex, x-intercepts, y-intercept, equation of the symmetry axis, and sketch the graph of example quadratic functions.
The Quadratic Function Derived From Zeros of the Equation (SNSD Theme)
Christian Jett Morales presents on the quadratic function derived from zeros of the function. The presentation includes:
- An introduction to deriving the quadratic function f(x) = ax^2 + bx + c from the zeros r1 and r2 of the function.
- Examples of deriving quadratic functions when given different zeros, such as 3/2 and -1, or 2+√3 and 2-√3.
- An activity for participants to practice deriving quadratic functions.
- A dedication to God and the presenter's teacher for the opportunity to create the presentation.
LESSON-Effects of changing a,h and k in the Graph of Quadratic Function
The document discusses transforming quadratic functions into vertex form and describes how changing the values of a, h, and k affects the graph of the function. It then has students work in groups to graph and describe quadratic functions based on given equations in order to understand how the vertex, opening direction, and any shifts in the vertex position are represented algebraically.
QUADRATIC FUNCTIONS
The document provides an overview of quadratic functions including definitions of key terms like quadratic function, parabola, quadratic equation, and vertex form. It discusses how to graph quadratic functions, solve quadratic equations using methods like the quadratic formula, and find the maximums and minimums of quadratic functions. It includes examples of using these techniques to solve word problems involving quadratic applications. The document aims to teach students about the basic concepts of quadratic functions.
Mathematics 9 Lesson 3: Quadratic Functions
This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
Quadratic Function by Robert & Phillip
A quadratic function is a polynomial function of the form f(x)=ax^2+bx+c, where a cannot equal 0. It is a second degree polynomial with the highest exponent being 2. Setting a quadratic function equal to 0 produces a quadratic equation, whose solutions are the roots of the equation. Quadratic functions are commonly used to model real world phenomena like projectile motion or profit functions and appear in nature as parabolic shapes.
Higher Maths 2.1.2 - Quadratic Functions
This document provides an overview of quadratic functions including:
- The graph of a quadratic function is a parabola.
- The general form of a quadratic function is f(x) = ax2 + bx + c.
- Key aspects that must be identified before sketching the graph are the nature of the turning point, y-intercept, x-intercepts, and axis of symmetry.
- Quadratic equations can be solved by factorizing, completing the square, or using the quadratic formula. The discriminant determines the nature of the roots.
3 Forms Of A Quadratic Function
The document discusses three forms of quadratic functions - standard form, vertex form, and intercept form - and provides examples of how to write quadratic functions in each form and the steps to graph each by finding the vertex, axis of symmetry, and intercepts. The standard form is ax^2 + bx + c, the vertex form is a(x-h)^2 + k, and the intercept form is a(x-p)(x-q), with each using different variables to indicate the features of the parabolic graph.
Integration
This document provides an overview of integration and how it relates to calculating areas under curves and between functions. Some key points covered include:
- Integration uses the concept of reverse differentiation to calculate the area under a function.
- The area under a function between two x-values a and b is calculated as the definite integral from a to b.
- Integrals may be used to find the area between two curves by subtracting their integrals between the intersection points.
- Integrals can represent either positive or negative areas depending on whether the area is above or below the x-axis.
Mcq for manavsthali( 7 worksheets)
The document contains a worksheet with multiple choice questions related to relations, functions, and matrices. Some questions test concepts like equivalence relations, inverse functions, and properties of matrices. The questions cover topics such as determining if a relation is reflexive, transitive, or symmetric; evaluating composite and inverse functions; finding the order and properties of matrices; and evaluating determinants.
Higher Maths 1.2.1 - Sets and Functions
The document discusses key concepts in set theory and functions, including:
- Sets can contain numbers, elements, and be represented using curly brackets.
- Venn diagrams use overlapping circles to show logical connections between sets.
- A function has a domain (input) and range (output), where each input is mapped to a unique output.
- Composite functions combine other functions by substituting one into another.
- Inverse functions reverse the input and output of a function if it exists.
- Common functions that can be graphed include linear, quadratic, trigonometric, cubic, exponential and logarithmic functions.
5.1graphquadratics
This document discusses quadratic functions and their graphs. It defines a quadratic function as having the form y = ax2 + bx + c. The graph of a quadratic function is a parabola, which has a vertex (lowest or highest point) and an axis of symmetry (vertical line through the vertex). It provides examples of graphing different quadratic functions using a graphing calculator and by hand, including how to find and plot the vertex and axis of symmetry.
Transforming Quadratic Functions from General Form to Standard Form
This document describes the process of transforming a quadratic function from general form to standard form. It shows the general forms of quadratic functions, and the three step process to transform them: 1) factor out the leading coefficient a, 2) complete the square, 3) factor and combine terms. It provides examples of applying these steps to functions like f(x) = x^2 - 8x + 3 and f(x) = 2x^2 + 5x - 1. Finally, it lists 5 additional quadratic functions to transform into standard form.
Quadratic equations and function
This document discusses quadratic equations and functions. It explains that a quadratic equation is an equation of degree 2 that can be written in standard form as ax2 + bx + c = 0. It provides examples of quadratic equations and shows how to write equations in standard form. The document also discusses several methods for solving quadratic equations, including factoring, graphing, completing the square, and using the quadratic formula. It introduces the square root principle for solving equations of the form x2 = a.
Add Math(F4) Quadratic Function 3.1
The document discusses quadratic functions, including how to recognize a quadratic function based on its standard form, how to plot graphs of quadratic functions based on either tabulated values or a given function, and examples of determining if a function is quadratic and plotting quadratic graphs. Key aspects covered are the standard form of a quadratic function as f(x) = ax^2 + bx + c where a ≠ 0, recognizing quadratic functions, tabulating x and f(x) values for a given quadratic function, and using Geometer's Sketchpad software to plot the graphs.
Quadratic functions
The document discusses quadratic functions and their graphs. It defines quadratic functions as functions of the form f(x)=ax^2+bx+c, where a is not equal to 0. The graph of a quadratic function is a parabola with certain characteristics: it is symmetrical about an axis of symmetry and has a vertex which is either a maximum or minimum point. The axis of symmetry is the line x=0 for functions of the form f(x)=ax^2 and the vertex is at (0,0). For functions of the form f(x)=ax^2+k, the graph is a translation of f(x)=ax^2, so the vertex is (0,k) and the
What's hot (18)
The Quadratic Function Derived From Zeros of the Equation (SNSD Theme)
The Quadratic Function Derived From Zeros of the Equation (SNSD Theme)
LESSON-Effects of changing a,h and k in the Graph of Quadratic Function
LESSON-Effects of changing a,h and k in the Graph of Quadratic Function
Transforming Quadratic Functions from General Form to Standard Form
Transforming Quadratic Functions from General Form to Standard Form
Similar to Assignment Chapters 1 -8- Maths (CLASS XII)
Assignment (chapter 1 8) maths
This document provides the details of a mathematics assignment consisting of 40 questions with 4 marks each. The questions cover various topics in calculus, trigonometry, matrices and determinants. Some example questions are:
1) Find dy/dx if y = tan−1[√1+x2 + √1−x2/√1+x2 − √1−x2]
2) Evaluate: ∫(x2 + 5x)dx from 1 to 3 as limit of sum
3) Prove that: |(b + c)2 ba ca| = 2abc(a + b + c)3
4) Solve the system of equations: x + 2y
Class 12 practice paper
This document contains a mathematics sample paper with 29 questions across 4 sections - A, B, C and D. The questions cover a wide range of mathematics topics including calculus, algebra, trigonometry, matrices, probability, linear programming, and geometry. The paper is designed to test students' mathematical skills and knowledge over 3 hours with the maximum marks being 100.
Chapters 1 8 ( 6 marks)
The document contains a list of 31 multi-part math problems involving matrices, integrals, functions, geometry, and equations. The problems cover topics like finding the composition and inverse of functions, evaluating definite integrals, solving systems of equations using matrices, finding maximums and minimums, and proving geometric properties.
Chapters 1 8 ( 6 marks)
The document contains a list of 31 multi-part math problems involving matrices, integrals, functions, geometry, and equations. The problems cover topics like finding the product and inverse of matrices, evaluating definite integrals, finding maximums and minimums of functions, solving systems of equations using matrices, and calculating areas of geometric shapes.
April 10, 2015
The document discusses graphing quadratic functions. It begins with reviewing key concepts like the vertex and axis of symmetry. The effects of the a, b, and c coefficients on the parabola are explained. Examples are provided to show how changing these values affects the width, direction opened, and vertical translation of the graph. The class will graph various quadratic functions by finding the axis of symmetry, vertex, y-intercept, and other points to plot the parabola. Students are assigned class work problems to graph quadratic functions and show their work.
Tema Numeros Reales
This document provides an overview of sets and set operations including:
- Four ways to define sets: by listing elements, with a condition, Venn diagrams, or verbal description
- Examples of set operations like union, intersection, complement, and difference
- Examples of how to express sets using these operations
- Diagrams explaining set relationships and operations
The document is a reference for the basic concepts and notation of sets and set operations in mathematics. It includes examples and exercises to demonstrate expressing sets in different ways using operations like union, intersection, complement, and difference.
Function
FUNCTION
A function is a set of ordered pairs which relates two sets such that to each element of one set there is only one element of the second set
Mathsclass xii (exampler problems)
The document provides a summary of Chapter 1 and Chapter 2 from a Class XII Maths textbook. Chapter 1 discusses relations and functions, including whether certain binary operations are commutative, evaluating functions, and determining if functions are injective or surjective. Chapter 2 covers inverse trigonometric functions, including evaluating various inverse trig expressions and proving identities about inverse trig functions.
Maths important questions for 2018
This document contains questions related to relations and functions, inverse trigonometric functions, and matrices and determinants. It includes 1 mark, 2 mark, 4 mark, and 6 mark questions on these topics that would be expected for an exam in 2018. The questions cover key concepts like equivalence relations, one-to-one and onto functions, evaluating inverse trigonometric functions, solving inverse trigonometric equations, properties of matrices including determinants, and solving matrix equations.
Maths imp questions for 2018
This document contains questions related to relations and functions, inverse trigonometric functions, and matrices and determinants. It includes 1 mark, 2 mark, 4 mark, and 6 mark questions. The questions cover topics such as equivalence relations, one-to-one and onto functions, composition of functions, inverse functions, inverse trigonometric functions, properties of matrices including symmetric, skew-symmetric and singular matrices, and evaluating determinants.
Assignment chapters 3 to 7
1. This document contains mathematics questions on matrices and determinants ranging from 1 to 6 marks. Questions involve finding determinants, inverses, solving systems of equations using matrices, properties of determinants, and continuity and differentiability.
2. The document is divided into sections on 1, 2, 4 and 6 mark questions related to matrices and determinants as well as questions on continuity and differentiability ranging from 2 to 4 marks.
3. The questions cover a wide range of matrix and calculus concepts and techniques including finding determinants, inverses, solving systems of equations, properties of determinants, continuity, differentiation, mean value theorem, Rolle's theorem and related calculus topics.
Função quadrática
The document is about quadratic polynomial functions and contains the following information:
1. It discusses investigating relationships between numbers expressed in tables to represent them in the Cartesian plane, identifying patterns and creating conjectures to generalize and algebraically express this generalization, recognizing when this representation is a quadratic polynomial function of the type y = ax^2.
2. It provides examples of converting algebraic representations of quadratic polynomial functions into geometric representations in the Cartesian plane, distinguishing cases in which one variable is directly proportional to the square of the other, using or not using software or dynamic algebra and geometry applications.
3. It discusses characterizing the coefficients of quadratic functions, constructing their graphs in the Cartesian plane, and determining their zeros (
Assignments for class XII
The document defines matrices and their properties, including symmetric, skew-symmetric, and determinant. It provides examples of solving systems of equations using matrices and their inverses. It also discusses properties of determinants, including properties related to symmetric and skew-symmetric matrices. Inverse trigonometric functions are defined, including their domains, ranges, and relationships between inverse functions using addition and subtraction formulas. Sample problems are provided to solve systems of equations and evaluate determinants.
Class XII CBSE Mathematics Sample question paper with solution
Class XII CBSE Mathematics Sample question paper with solutionPratima Nayak ,Kendriya Vidyalaya Sangathan
The document is a sample question paper for Class XII Mathematics. It consists of 3 sections - Section A has 10 one-mark questions, Section B has 12 four-mark questions, and Section C has 7 six-mark questions. All questions are compulsory. The paper tests concepts related to matrices, trigonometry, calculus, differential equations, and vectors. Internal choices are provided in some questions. Calculators are not permitted.Grph quad fncts
The document discusses graphing quadratic functions. It defines a quadratic function as f(x) = ax^2 + bx + c where a, b, and c are real numbers and a is not equal to 0. The graph of a quadratic function is a parabola that is symmetrical about an axis. When the leading coefficient a is positive, the parabola opens upward and the vertex is a minimum. When a is negative, the parabola opens downward and the vertex is a maximum. Standard forms for quadratic functions and methods for finding characteristics like the vertex, axis of symmetry, and x-intercepts from the equation are also presented.
17 integrals of rational functions x
This document discusses integrating rational functions. It begins by defining rational functions as functions of the form P(x)/Q(x) where P and Q are polynomials. It states that integrating rational functions involves decomposing them into simpler fractions using the Rational Decomposition Theorem. Examples are then provided to demonstrate how to decompose rational functions and integrate each term using substitution.
Assignment of class 12 (chapters 2 to 9)
This document contains questions from the topics of inverse trigonometry, matrices and determinants, and continuity and differentiability from Class XII Mathematics. For inverse trigonometry, there are 1 mark, 2 mark and 4 mark questions testing concepts like principal values, evaluating inverse trig expressions, and proving trigonometric identities. For matrices, there are 1 mark, 2 mark, 4 mark and 6 mark questions on topics such as matrix operations, determinants, and solving systems of equations using matrices. For continuity and differentiability, there are 2 mark, 4 mark questions involving checking continuity, evaluating derivatives, applying mean value and Rolle's theorems.
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...
My dear Students,
Wishing you all happy SHIVRATRI. & ALL THE BEST IN YOUR ANNUAL EXAMS-2014
Here I have uploaded II- P.U.C MATHEMATICS MODEL QUESTION PAPER FOR the year 2014 Which i have designed according to New syllabus of CBSE. I hope this model paper will be helpful to all the students who are writing annual exams on 18-March-2014.
wish you all the best
Regards,
A. NAGARAJ
Director-Faculty
Shree Susheela Tutorials
BAGALKOT-587101
mob: 9845222682
Chapter 1 (math 1)
This document provides a summary of precalculus concepts including:
1. Functions and their graphs including function definitions, transformations, combinations, and compositions of functions.
2. Trigonometry including trigonometric functions, graphs of trigonometric functions, and trigonometric identities.
3. Graphs of second-degree equations including circles, parabolas, ellipses, and hyperbolas.
The document contains examples and explanations of key precalculus topics to serve as a review for a Math 131 course. It covers essential functions like polynomials, rational functions, and transcendental functions. It also discusses trigonometric functions and their graphs along with transformations of functions.
Tutorial 1.pdf
This document contains 20 questions related to discrete mathematics concepts such as sets, relations, functions, and Venn diagrams. The questions cover topics like finding the cardinality of sets, set operations like union and intersection, proving functions are bijective, describing equivalence relations and partial orders, and composition of functions. Students will discuss their answers to these questions during tutorial sessions on February 20th and 22nd, 2023.
Similar to Assignment Chapters 1 -8- Maths (CLASS XII) (20)
Class XII CBSE Mathematics Sample question paper with solution
Class XII CBSE Mathematics Sample question paper with solution
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...
More from Poonam Chopra
SURFACE CHEMISTRY
1. Adsorption is the accumulation of molecules on the surface of a solid or liquid. It occurs due to intermolecular interactions between the adsorbate (gas or solute) and adsorbent (solid or liquid).
2. There are two types of adsorption - physical adsorption (physisorption) which involves weak van der Waals forces, and chemical adsorption (chemisorption) which involves chemical bonding.
3. Factors that affect adsorption include the nature of the adsorbent and adsorbate, surface area, pressure, and temperature. Freundlich and Langmuir isotherms describe the relationship between amount adsorbed and pressure
Solid (CLASS XII)
This document discusses different types of solids and their properties. It describes amorphous solids as having atoms arranged irregularly without a characteristic shape, and crystalline solids as having atoms arranged regularly in defined planes. Amorphous solids are isotropic while crystalline solids are anisotropic. Crystalline solids have sharp melting points and cleavage planes, while amorphous solids soften over a range of temperatures and have irregular surfaces when cut. The document also discusses the unit cell and space lattice of crystalline solids.
IP Sample paper 2 Class XI
This document contains a sample paper for Class 11 with questions in Informatics Practices (065) subject. It has 7 sections with multiple choice and written response questions related to programming concepts in Java and SQL queries. The questions cover topics like loops, conditional statements, variables, data types, database concepts like tables, queries, DML commands, data manipulation etc.
Sample Paper 2 Class XI (Computer Science)
This document contains a sample paper for Class 11 Computer Science with 7 questions covering topics like characteristics of computers, operating systems, data vs information, RAM vs ROM, loops, arrays, functions, structures, unions, and different types of errors. The paper has 70 total marks and is focused on testing knowledge of basic C++ programming concepts through multiple choice and code writing questions.
Sample Paper Class XI (Informatics Practices)
This document contains a sample paper for Class 11 Informatics Practices with 7 questions covering topics like operating systems, compilers vs interpreters, databases, programming, SQL, and e-commerce/e-governance. The questions range from short answer and code writing to longer explanations. Some questions have multiple parts requiring different concepts to be tested. This sample paper evaluates students on their understanding of key foundational digital literacy and computer science concepts.
Computer Science Sample Paper 2015
This document provides a sample paper for Class XII Computer Science. It includes two sections - Section A focused on C++ programming and Section B focused on Python programming. Each section contains multiple questions testing concepts like functions, classes, inheritance, file handling, arrays, and sorting/searching algorithms. Students are required to attempt either Section A or B, along with the compulsory Section C. The questions range from writing and analyzing code snippets to higher-level conceptual questions.
More from Poonam Chopra (7)
Recently uploaded
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Temple of Asclepius in Thrace. Excavation results
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Leveraging Generative AI to Drive Nonprofit Innovation
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh
How to deliver Powerpoint Presentations.pptx
"How to make and deliver dynamic presentations by making it more interactive to captivate your audience attention"
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
Hindi varnamala | hindi alphabet PPT.pdf
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Topic : Bed making
Subject : Nursing Foundation
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Physical pharmaceutics notes for B.pharm students
Recently uploaded (20)
B. Ed Syllabus for babasaheb ambedkar education university.pdf
B. Ed Syllabus for babasaheb ambedkar education university.pdf
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
spot a liar (Haiqa 146).pptx Technical writhing and presentation skills
spot a liar (Haiqa 146).pptx Technical writhing and presentation skills
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Assignment Chapters 1 -8- Maths (CLASS XII)
- 1. MATHS ASSIGNMENT (CHAPTER :- 1 – 8) CLASS – XII 4 MARKS 1. y = , show (x2 + 1)2 y2 + 2x (x2 + 1)2 y1 = 2. 2. Prove using properties :- + + + + + + + + + = . 3. Evaluate :- ∫ ( )( ) dx 4. If (cos x)y = (cos y)x , find . 5. Prove :- = − . 6. A = R – {3}, B = R – {1}. f : A → B. f(x) = . Show that f is one – one & onto. 7. Prove :- ∫ √ + √ = √ . 8. If a + b + c ≠ 0 & = 0. Prove a = b = c 9. Evaluate :- ∫( − )√ − − dx. 10. Differentiate :- log (xsinx + cot2 x), w.r.t. x 11. Evaluate :- ∫ ( )( ) dx 12. Prove :- y = ( ) - x is an increasing function of x in [0, ] 13. Evaluate :- ∫ . 14. Differentiate :- tan w.r.t. x 15. If x + + √ + = . = ( ) . 16. If A = − , find k : A2 = 8A + kI . 17. If f(x) = | | ≠ = . check the continuity at x = 0. 18. If y = ecos x , prove y2 + sin x y1+ y cos x = 0. 19. Evaluate :- ∫ dx. 20. Prove :- ( + ) ( + ) ( + ) = 2abc (a + b + c)3 . 21. If + + = , Prove x2 + y2 + z2 + 2xyz = 1. 22. Find equation of tangent to the curve x2 + 3y = 3 which is 11 to line y – 4x + 5 = 0. 23. Find x : − − = − − −
- 2. 24. Evaluate :- ∫ dx. 25. Prove : ∫ = . 26. Using property of determine. Prove : + + − − − + + − − − + + = 2 (a + b) (b + c) ( c + a) 27. Solve for x : + = 28. Evaluate :- ∫ . 29. Prove : √ − + sin = √ − . 30. Show that the relation R in set R of real numbers, defined as R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive. 31. Using elementary operation find A-1 , A = . 32. Show that the curve 2x = y2 & 2xy = k cut at right angles if k2 = 8. 33. Find if y = – . 34. Evaluate : ∫ ( ) , ( ) = | | + | + | + | + | . 35. Find the intervals in which f(x) = sin x + cos x, 0 ≤ ≤ is strictly increasing or decreasing. 36. Show that the relation R on z defined by (a, b) ∈ R a – b is divisible by 5 is an equivalence relation. 37. Solve by matrix method :- x + 2y + 5z = 10, x – y – z = -2, 2x + 3y – z = -11. 38. Evaluate :- ∫ . 39. If y = Aemx + Benx , show that y2 – (m + n) y1 + mny = 0. 40. Evaluate : ∫ + as limit of sum.