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A teacher poses the following problem of algebra to her class: "Does the graph x = y2 ever intersect the graph of x = y2 + 2? What are the different ways you would use to test your conjecture? Would your conjecture hold true for other equations of the form x = y2 + b." Which of the following statement/statements is/are correct in the given context? (a) One of the learning outcomes of posing this question is comparison and analysis of quadratic equations. (b) Teacher should focus only on getting the solution that the two graphs will not intersect. (c) The teacher can assess the reasoning skills of students. (d) Such questions confuse the students and hence should be discouraged in a mathematics classroom. Choose the correct option:-

A teacher poses the following problem of algebra to her class: "Does the graph x = y2 ever intersect the graph of x = y2 + 2? What are the different ways you would use to test your conjecture? Would your conjecture hold true for other equations of the form x = y2 + b." Which of the following statement/statements is/are correct in the given context? (a) One of the learning outcomes of posing this question is comparison and analysis of quadratic equations. (b) Teacher should focus only on getting the solution that the two graphs will not intersect. (c) The teacher can assess the reasoning skills of students. (d) Such questions confuse the students and hence should be discouraged in a mathematics classroom. Choose the correct option:- Correct Answer (a) and (c)

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression. Quadratic equations are also a part of algebra. Key Points

The objective and reason behind the question posed by the teacher in the above example is 

  • Teachers can know if the students can apply the knowledge they gained in different situations.
  • One of the learning outcomes of posing this question is the comparison and analysis of quadratic equations.
  • The teacher can assess the reasoning skills of students.
  • Teachers can differentiate the students who learned the concept through understanding from the ones who learned through memorization.

Hence (a) and (c) are the correct options.Additional Information

On the other hand, the remaining two options are wrong as they indicate that such questions will confuse the students and teachers should only focus on the correct answers which are not the objectives of mathematics.

Related Questions

"Assessment techniques in Mathematics is an important factor that contributes to Mathematics anxiety among students". Which of the following is/are correct reasons for the given statement? (a) Assessment in Mathematics is done only to test if the student knows or does not know the answer. (b) Assessment in Mathematics is designed to test the student's capability of arriving at a unique answer using the correct procedures. (c) Assessment techniques in Mathematics focus on process of learning hence gives scope of discussing multiple ways of doing a problem.  (d) Assessment is focused on testing the memorisation of facts and formulae rather than concept learning.  Choose the correct option 
The Coordinator of an International Virtual Conference has planned six guest lectures on different areas-Cryptography, Fluid Dynamics, Big Data Analysis, Wavelet Theory, Differential Equations and Linear Algebra-to be organised only one on each day from Monday to Sunday.  Wavelet Theory should be organised immediately after Differential Equations.  Big Data Analysis should be organised on Wednesday and should not be followed by Linear Algebra.  Fluid Dynamics should be organised on Friday and there should be a gap of two days between Cryptography and Linear Algebra.  One day there will be no lecture (Saturday is not that day), and just before that day Linear Algebra will be organised. How many lectures are organised between Big Data Analysis and Wavelet Theory? 
A passage is given with five questions following it. Read the passage carefully and select the best answer to each question out of the given fouralternatives. Just as space permeates everything in the universe, love permeates every part, every aspect of creation. If there is one answer to the question, “How and why doesthis world exist?” the answer, in one word, is Love. Rather, the answer is Pure Love, since the word love has lost its meaning. Your very existence is an expression of pure unconditional love of the Source (you may call it Consciousness, Creator, God, Divine Self). This is the truth of your being.True love transcends both love and hatred. It is unconditional, unquestioning, boundless, unchanging love. It is overflowing love of the Source for the Source throughall of creation. True love is way beyond the personalized love that two or more individuals assert on one another. Personalized love, though apparently selfless, is rooted in desiresand conditional satisfaction. We have been brought up in a society that judges love based on conditions. We have been made to believe that we can receive love only when we fit into peoplesexpectations. If we are not good enough, we will be deprived of love. These beliefs have influenced the collective psyche of families, groups, communities, and societies since generations to such an extent that love has been reduced tofear of denial. We need to shift from the paradigm of false conditional love to the essence of pure unconditional love . The experience of true love comes with surrender of the false I, in letting go of the feeling of separateness. Without this sacrifice, it is not possible to attain divinelove. When this separate I is discarded, you embrace everything in oneness and catch a glimpse of pure love. True love can be experienced only through giving, not by demanding. People who exist in your life are not here to love you. They are here to remind you that you arethe Source of Love. By knowing that you are the Source of love, you can love yourself, instead of waiting to receive love from the world. Ask yourself, “Why do I need an agent to love myself?” Waiting for the world to love you, is like hiring an agent to love yourself! It is time for you to honor yourself as the Source of love. You have undertaken this human journey to realize and express the boundless love that you truly are. According to the passage, which of the following statement is not TRUE?
A passage is given with five questions following it. Read the passage carefully and select the best answer to each question out of the given fouralternatives. Just as space permeates everything in the universe, love permeates every part, every aspect of creation. If there is one answer to the question, “How and why doesthis world exist?” the answer, in one word, is Love. Rather, the answer is Pure Love, since the word love has lost its meaning. Your very existence is an expression of pure unconditional love of the Source (you may call it Consciousness, Creator, God, Divine Self). This is the truth of your being.True love transcends both love and hatred. It is unconditional, unquestioning, boundless, unchanging love. It is overflowing love of the Source for the Source throughall of creation. True love is way beyond the personalized love that two or more individuals assert on one another. Personalized love, though apparently selfless, is rooted in desiresand conditional satisfaction. We have been brought up in a society that judges love based on conditions. We have been made to believe that we can receive love only when we fit into peoplesexpectations. If we are not good enough, we will be deprived of love. These beliefs have influenced the collective psyche of families, groups, communities, and societies since generations to such an extent that love has been reduced tofear of denial. We need to shift from the paradigm of false conditional love to the essence of pure unconditional love . The experience of true love comes with surrender of the false I, in letting go of the feeling of separateness. Without this sacrifice, it is not possible to attain divinelove. When this separate I is discarded, you embrace everything in oneness and catch a glimpse of pure love. True love can be experienced only through giving, not by demanding. People who exist in your life are not here to love you. They are here to remind you that you arethe Source of Love. By knowing that you are the Source of love, you can love yourself, instead of waiting to receive love from the world. Ask yourself, “Why do I need an agent to love myself?” Waiting for the world to love you, is like hiring an agent to love yourself! It is time for you to honor yourself as the Source of love. You have undertaken this human journey to realize and express the boundless love that you truly are. Which of the following statement(s) is/are TRUE about pure love?
A passage is given with five questions following it. Read the passage carefully and select the best answer to each question out of the given fouralternatives. Just as space permeates everything in the universe, love permeates every part, every aspect of creation. If there is one answer to the question, “How and why doesthis world exist?” the answer, in one word, is Love. Rather, the answer is Pure Love, since the word love has lost its meaning. Your very existence is an expression of pure unconditional love of the Source (you may call it Consciousness, Creator, God, Divine Self). This is the truth of your being.True love transcends both love and hatred. It is unconditional, unquestioning, boundless, unchanging love. It is overflowing love of the Source for the Source throughall of creation. True love is way beyond the personalized love that two or more individuals assert on one another. Personalized love, though apparently selfless, is rooted in desiresand conditional satisfaction. We have been brought up in a society that judges love based on conditions. We have been made to believe that we can receive love only when we fit into peoplesexpectations. If we are not good enough, we will be deprived of love. These beliefs have influenced the collective psyche of families, groups, communities, and societies since generations to such an extent that love has been reduced tofear of denial. We need to shift from the paradigm of false conditional love to the essence of pure unconditional love . The experience of true love comes with surrender of the false I, in letting go of the feeling of separateness. Without this sacrifice, it is not possible to attain divinelove. When this separate I is discarded, you embrace everything in oneness and catch a glimpse of pure love. True love can be experienced only through giving, not by demanding. People who exist in your life are not here to love you. They are here to remind you that you arethe Source of Love. By knowing that you are the Source of love, you can love yourself, instead of waiting to receive love from the world. Ask yourself, “Why do I need an agent to love myself?” Waiting for the world to love you, is like hiring an agent to love yourself! It is time for you to honor yourself as the Source of love. You have undertaken this human journey to realize and express the boundless love that you truly are. What does source refers to in the last line of the second para of the passage?
A passage is given with five questions following it. Read the passage carefully and select the best answer to each question out of the given fouralternatives. Just as space permeates everything in the universe, love permeates every part, every aspect of creation. If there is one answer to the question, “How and why doesthis world exist?” the answer, in one word, is Love. Rather, the answer is Pure Love, since the word love has lost its meaning. Your very existence is an expression of pure unconditional love of the Source (you may call it Consciousness, Creator, God, Divine Self). This is the truth of your being.True love transcends both love and hatred. It is unconditional, unquestioning, boundless, unchanging love. It is overflowing love of the Source for the Source throughall of creation. True love is way beyond the personalized love that two or more individuals assert on one another. Personalized love, though apparently selfless, is rooted in desiresand conditional satisfaction. We have been brought up in a society that judges love based on conditions. We have been made to believe that we can receive love only when we fit into peoplesexpectations. If we are not good enough, we will be deprived of love. These beliefs have influenced the collective psyche of families, groups, communities, and societies since generations to such an extent that love has been reduced tofear of denial. We need to shift from the paradigm of false conditional love to the essence of pure unconditional love . The experience of true love comes with surrender of the false I, in letting go of the feeling of separateness. Without this sacrifice, it is not possible to attain divinelove. When this separate I is discarded, you embrace everything in oneness and catch a glimpse of pure love. True love can be experienced only through giving, not by demanding. People who exist in your life are not here to love you. They are here to remind you that you arethe Source of Love. By knowing that you are the Source of love, you can love yourself, instead of waiting to receive love from the world. Ask yourself, “Why do I need an agent to love myself?” Waiting for the world to love you, is like hiring an agent to love yourself! It is time for you to honor yourself as the Source of love. You have undertaken this human journey to realize and express the boundless love that you truly are. According to the passage, whom to honour as the source of love?
Classroom environment plays an important role in overcoming mathematics anxiety among learners. Which of the following statements / situations are indicative of a mathematics classroom free from fear and anxiety among learners? (a) A sense of failure in mathematics among majority of students. (b) Product oriented assessment aiming at ranking students on the basis of correct answer given. (c) Students posing and solving problems related to their daily lives. (d) Teacher engaging meaningfully with every child in the class. Choose the appropriate option.
Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. What is the average weight of new students added? I. In a class 60% students are male and there average weight is 15 kg more than the female students, 9 males and 6 new female students joined the class and the average weight of the class increased by 0.84 II. Total male students in the class is 12 more than female students adding 9 male students to the class increases the average weight of male students by 1 kg and adding 6 female students increases the average weight of female students by 0.6.
Read the passage carefully and select the best answer to each question out of the given four alternatives. One should consciously engage in activities that will nourish your soul. Just as we nourish the body, we need to nurture the soul to connect to the creative power ofthe universe and to manifest joy in our lives. Often, we forget to address the soul, lost as we are in a jungle of material and sensual pleasures. But the more youembrace what feeds your soul, the happier you become. So if you want to enjoy the abundance of life, engage in what enriches your soul. Nurturing the soul is allabout finding calm amidst chaos. There are a number of practices that empower people towards this end including silent contemplation, various forms of meditation,yoga and tai chi However, the rigor and discipline involved in the pursuit of such practices often seems to discourage people. Add to this, the temptations of thematerial world that leave little time and motivation for anyone to pursue the spiritual path. Poet Walt Whitman declared: “Whatever satisfies the soul is truth”. Thegood news is that simple, everyday activities can also nutrify the soul — like spending time in the midst of nature, dancing in the rain or just putting thoughts onpaper. Do whatever is calming and pleases you. Creative pursuits are particularly appealing as inside each one of us, there is an artist craving for release andawaiting an opportunity for expression. One of the ways to indulge the artist within is to get started with the practice of any one or more of the creative art formssuch as music, singing, dancing, acting, drawing, painting, sculpting, poetry, fiction or essay writing. When you engage in such soul nourishing activities, all thought and energy gets focused toward goal accomplishment. At this point, you will find that even unknownforces of the universe are conniving to assist you in your amateurish but sincere attempts. As you progress, you are motivated to do better. You touch and access afaculty, a part of you that you never knew existed. Your inner artist is unleashed, baring the beauty of your soul that has found a fond medium of expression. Forinstance, a sculptors soul is seen in his artwork; a musicians in his compositions; an actors in his acting, a painters in his paintings and so on. It is immaterialwhether your effort is an immaculate artwork or just a clumsy attempt by a layperson. The idea is to try, be inspired and to create giving free rein to the mind. AsMichelangelo remarked: “I saw the angel in the marble and carved until I set him free”! What can you infer from Michelangelos statement - "I saw the angel in the marble and carved until I set him free"?
Read the passage carefully and select the best answer to each question out of the given four alternatives. One should consciously engage in activities that will nourish your soul. Just as we nourish the body, we need to nurture the soul to connect to the creative power ofthe universe and to manifest joy in our lives. Often, we forget to address the soul, lost as we are in a jungle of material and sensual pleasures. But the more youembrace what feeds your soul, the happier you become. So if you want to enjoy the abundance of life, engage in what enriches your soul. Nurturing the soul is allabout finding calm amidst chaos. There are a number of practices that empower people towards this end including silent contemplation, various forms of meditation,yoga and tai chi However, the rigor and discipline involved in the pursuit of such practices often seems to discourage people. Add to this, the temptations of thematerial world that leave little time and motivation for anyone to pursue the spiritual path. Poet Walt Whitman declared: “Whatever satisfies the soul is truth”. Thegood news is that simple, everyday activities can also nutrify the soul — like spending time in the midst of nature, dancing in the rain or just putting thoughts onpaper. Do whatever is calming and pleases you. Creative pursuits are particularly appealing as inside each one of us, there is an artist craving for release andawaiting an opportunity for expression. One of the ways to indulge the artist within is to get started with the practice of any one or more of the creative art formssuch as music, singing, dancing, acting, drawing, painting, sculpting, poetry, fiction or essay writing. When you engage in such soul nourishing activities, all thought and energy gets focused toward goal accomplishment. At this point, you will find that even unknownforces of the universe are conniving to assist you in your amateurish but sincere attempts. As you progress, you are motivated to do better. You touch and access afaculty, a part of you that you never knew existed. Your inner artist is unleashed, baring the beauty of your soul that has found a fond medium of expression. Forinstance, a sculptors soul is seen in his artwork; a musicians in his compositions; an actors in his acting, a painters in his paintings and so on. It is immaterialwhether your effort is an immaculate artwork or just a clumsy attempt by a layperson. The idea is to try, be inspired and to create giving free rein to the mind. AsMichelangelo remarked: “I saw the angel in the marble and carved until I set him free”! What activities can nutrify soul?