CTET Paper 2 Maths & Science September 2016 (English-Hindi-Sanskrit) (Previous Year Paper)

Scaffolding is a technique to provide the right kind of support in the right amount at right time to increase the child’s competence. Scaffolding is a form of facilitation that facilitates learning.

• Scaffolding can be a pre-planned activity being applied when needed. It aims to transfer responsibility for learning from the facilitator to the learner.
• It suggests that students learn through contact with more capable members of society. The more capable member organizes activities so that the students participate in real activities at their own level of capability. The system of support is called a scaffold.
• Scaffolding allows students to perform tasks that would normally be slightly beyond their ability without assistance and guidance from the teacher. Scaffolding is an important characteristic of constructivist teaching and learning.
• Providing a half-solved example, pre-teach vocabulary, use of visual aids is some example of scaffolding.

NOTE: The other statements are examples of positive and negative motivation.

Hence, we can conclude that providing a half-solved example is a good example of 'scaffolding (learning of a problem-solving task till the student can do it by herself).

'Learning styles' represent those characteristics which determine and characterize a person's preferred approach to learning and its use in problem-solving. Different learners display different preferences in terms of their learning styles.

• Learning styles are relatively more stable, though the same learner may resort to the use of a different learning style in a particular situation. Learners may have their preferred cognitive style, the learning strategies or problem-solving strategies they use are situation and task-dependent
• Learning styles are thus relatively well-established response patterns in individuals compounded by one's learning and problem-solving processes.
• Variety of task and test based on learner’s needs and local conditions is an essential component of child-centered learning. To provide need-based experience to each child a teacher requires a variety of teaching-learning materials.
• For example, Individual Worksheets, Differentiated seatwork, Differentiated Home Assignments, Individual Learning Plan are some required tasks and tests.

Thus, it is clear that if your class has learners with different learning styles to assess them, you would give them a variety of tasks and tests.

When teachers provide instruction on concepts in various subjects, they are teaching students who already have some pre-instructional knowledge about the topic. Student knowledge, however, can be erroneous, illogical, or misinformed. These erroneous understandings are termed alternative conceptions or wrong concepts. 

Purpose of Alternative Conceptions:

• These concepts are a normal part of the learning process.
• Through this process, the teacher recognizes that children are capable of thinking and their thinking is different from that of adults.
• They naturally form ideas from our everyday experience, but not all the ideas we develop are correct concerning the most current evidence and scholarship in a given discipline.
• This helps the students to interpret new experiences through these erroneous understandings for being able to correctly grasp new information.
• The teacher used instructional strategies to be effective in achieving conceptual change and helping students leave their alternative conceptions.

Hence, we can conclude that nowadays there is a tendency to refer to 'wrong concepts' of children as 'alternative conceptions'. This could be attributed to the recognition that children are capable of thinking and their thinking is different from that of adults.

A teacher is not merely a disseminator of knowledge, rather plays a variety of roles. The teacher has to play diverse roles like a planner, facilitator, co-creator of knowledge, leader in the classroom and outside the classroom, manager, counselor, and apart from that, a true human being. Following are some roles of a teacher in a middle school classroom- 

• motivate learners to frame their own question about various observations,
• ask learners to interpret a situation in their own way and identify the probable solution of a problem with scaffolding by teachers,
• encourage learners to work in a group and also become an active member of the group,
• keep learners active and motivate them to observe, react and reflect continuously,
• help learners in evolving new knowledge using their previous knowledge through discussions, debates, inquiry, or experimentation.
• Trust Building, Diagnosing Institutional Conditions, Dealing with Processes, and Work Management are some other roles of teachers.
• using teaching aids to make learning effective and constructive.
• promote positive values like a feeling of cooperation, courtesy among students.
• Encouraging multiple perspectives and focusing on the multi-dimensional perspectives of learners.

​Hence, we can conclude that providing opportunities for discussion is one of the teacher's roles in a middle classroom.

Motivation is defined as the reason, incentive, enthusiasm, or interest that causes a specific action or certain behaviour. Motivation is an important element of self-understanding and learning.

It is simply the reason for an action and that which gives purpose and direction to behaviour. There are two primary types of motivation namely, intrinsic motivation and extrinsic motivation. 

Key Points

• Intrinsic Motivation: There is a high relationship between the activity to the goal. In such a situation, we say, the person is intrinsically motivated. Cognitivism holds the view that curiosity, interest, or a sense of accomplishment are sources of motivation that are intrinsic (internal) rather than responding to external forces.
• An intrinsically motivated activity will always be rewarded due to the direct relationship between the activity and the goal. This secures a continuous motivation to do the activity.
• The element of joy experienced in doing the activity actually sustains the activity. The pursuit of our hobbies which give us pleasure are also examples of intrinsic motivation.
• Intrinsic motivation remains constant due to the high relationship between the activity and the goal.
• An intrinsically motivated person will work on a solution to a problem because the challenge of finding a solution provides a sense of pleasure. In neither case does the person work on the task because there is some reward involved, such as a prize, a payment, or in the case of students, a grade.
• Set challenges, Interest, and Purpose are some methods to increase intrinsic motivation.

Hint

• Extrinsic motivation refers to a behaviour that is guided by earning rewards or avoiding punishment.
• External awards lead to temporary motivation.

​Hence, we can conclude that learning is effective only when the students have intrinsic motivation - a desire to learn from inside.

Learning begins at infancy and continues throughout life. Learning is a complex mix of intelligence, motivation, psychological factor. It is a process of continual adaptation to the environment and assimilation and accommodation of new information and knowledge to fit in with pre-existing knowledge structures. 

• Learning may be understood as essentially an active process which allows the individual to interact with the environment and gain enrichment of experience. It can also be defined as improvement in behavior, in that with time we usually become more proficient at whatever it is that we are learning.
• Learning must take serious account of social interaction and physical activity. Learning is intimately connected to desires, feelings, beliefs, identities, memberships, and social interactions.
• Previous learning of a related skill benefits the learner in subsequent learning. Students' prior knowledge influences their learning.
• A person's intentions to learn are engaged and the meaning of learning is configured through the process of becoming a full participant in a socio-cultural practice. This social process includes. indeed it subsumes the learning of knowledgeable skills. Learning, both outside and inside the school. advances through collaborative social interaction and the social construction of knowledge. It has been pointed out that throughout most of their lives people Learn and work collaboratively.
• Learning and Acquisition both terms are different. The acquisition is subconscious while learning is conscious and deliberate.

Hence, we can conclude that it is clear that learning is facilitated by social actions.

Learning in primary school:

• Children learn in different ways – some learn by seeing, some by hearing, some by reading, some by doing.
• And at this stage, children still learn through play. Plenty of unstructured, free play helps balance formal lessons at school. It also gives children a chance to unwind after the routines and rules of school.
• Children also learn by using objects in many different ways. When your child is experimenting, exploring and creating with a range of materials, they learn about problem-solving in situations where there are no set or ‘right’ answers.
• Children aren’t born with social skills – they have to learn them, just like they have to learn to read and write. Giving your child chances to play with other children is a great way for them to develop skills for getting on with others.
• Your child’s community connections can offer valuable learning experiences too. For example, visiting the local shops, parks, playgrounds and libraries or walking around your neighbourhood helps your child understand how communities work. As you and your child explore your community together, you can talk to your child about interesting things that you see or share things that you know make dialogue with them.
• If your family speaks a language other than English at home, this can be a great way for your child to grow up as a bilingual learner. Learning more than one language doesn’t harm or hold back children’s development. In fact, being a bilingual child can have a lot of advantages – for example, better reading and writing skills.
• When you know how your child learns best, you can help your child with all areas of learning. For example, if your child seems to learn best by seeing and doing but needs to write a story for school, they could make a comic strip to organise their ideas.

Important Points

Tips for learning at primary school:

Here are some practical tips for helping your primary school-age child learn:

• Show an interest in what your child is doing and learning by talking about school.
• Play rhyming games, letter games, and shape and number games with your child, and practise taking turns in games and activities.
• Use simple language, and play with words and word meanings – for example, you could clap out the syllables of words or play word association games.
• Keep reading to your child even when your child can read by themselves.
• Let your child hear and see plenty of new words in books, on TV or in general conversation, and talk about what the words mean.
• Make sure your child has time for  free, unstructured play.
• Help your child discover what they’re good at by encouraging your child to try plenty of different activities that involve dialogue with doing.

Development refers to an increase in structure for better and enhanced functioning of organs. The rate and speed of development may vary in individual cases but the sequence of development patterns is almost the same in all children.

Characteristics of Development

• Development describes the growth of humans throughout the lifespan, from conception to death. The student seeks to understand and explain how and why people change throughout life. This includes all aspects of human growth, including physical, emotional, intellectual, social, perceptual, and personality development, among others.
• Development is a life-long process that covers the entire spectrum of human life and occurs at a different rate among different individuals. There is a difference in the starting point and also in the rate of development of two different human beings. Each individual (child) is unique and develops in his/her own way. Thus the development is an individual process.
• Developmental changes do not always go forward in a straight line. While the development of different physical and mental traits is continuous, it is never uniform.
• Each individual continuously changes in his/ her own way, even when some appearance and behavior traits seem to remain constant.
• The levels of biological, psychological, and intellectual growth and integration may differ from person to person, yet there are no individuals whose bodily functions, mental abilities, or personality organization lack unification at any phase of development.

Hence, we can conclude that development occurs at a different rate among different individuals.

Childhood is this age span ranging from birth to puberty. The three stages of childhood are- 

• Early Childhood  (The Preschool Years) (2-6 years)
• Middle Childhood (The School Years) (6 to age 11)
• Later Childhood (11-14 years of age)

Important Points

Middle Childhood- The period extends from age 6 to age 11 years. During this time, the growth rate is slow but steady.

Characteristics of Middle Childhood: 

• During middle childhood, children learn the values of their societies. Thus, the primary developmental task of middle childhood could be called integration, both in tams of development within the individual and of the individual within the social context.
• Physical development during middle childhood is less dramatic than in early childhood or adolescence. Growth is slow and steady until the onset of puberty when individuals begin to develop at a much quicker pace.
• Middle childhood is a time when children gain enthusiasm for learning and work, for achievement becomes a motivating factor at this stage.
• Middle childhood is also a time when children develop competence in intentional and social relationships. Children have a growing pea orientation, yet they are strongly influenced by their family.
• Social skills are learned through peer and family relationships. provide a necessary foundation for the challenges of adolescence. Best friends are important at this age.
• Middle childhood is a joyful time of increased independence, and developing interests, such as sports. art, or music. There is more pressure on schools to recognize problems in eight-to eleven-year-olds and to teach children the social and life skills that will help them continue to develop into healthy adolescents.

Note: Infancy stage starts from 0-2 years

Thus from the above-mentioned points, it is clear that Middle childhood is the period from 6 years to 11 years.

Some of the factors which might contribute to individual growth and development may include genetic makeup, constitutional factors such as health and energy, the environment of the home and school, etc.

Important Points

Environmental factors do play any role in shaping an individual since the growth of each individual is determined by his genetic makeup.

Key Points

Both genetic and environmental factors influence human growth and development. Every child acquires his genetic potential for a particular adult size and shape from his parents and realizes this potential when the environment supports the genetic model that regulates development.

• However, the ability of environmental influences to alter genetic potential depends on several factors including the time at which they occur; the strength, duration, and frequency of their occurrence, and the age and gender of the child.
• Growth is a product of continuous and complex interaction of heredity and environment. A considerable proportion of the mean differences in body size between the populations being observed are due to the effects of environmental conditions. Some of the differences between individuals within populations are also due to differences in environment.
• When environmental conditions improve the size of the child also improves. Many environmental factors influence the rate of growth but most of them hinge upon the level of nutrition besides infections from disease, socio-economic level, and family size, urbanization, climate, and seasonal effects, and psychosocial stress.

Hence, we can conclude that  the above statement is not correct since there have been several types of research to prove that environment can have a major influence on development.

Socialization is a process through which a human infant begins to acquire the necessary skills to perform as a functioning member of society. 

• The Process of socialization is the social development of the individual. It simply refers to acquire the socially approved ways of behavior, approved social roles, and developing social attitudes.
• It is the process of learning to become a member of society. It includes formal and informal education. Socialization is done by parents, teachers, peers, neighbors, educational and religious institutions.
• It refers to the process which transforms a quite helpless human infant into a self-aware, knowledgeable person who is skilled in the ways of their society’s culture.

Key Points

The different types of socialization are-

• Primary Socialization- Primary socialization is the most important feature in the process of socialization. It happens during infancy and childhood. The primary stage basically takes shape during infancy and childhood where basic knowledge and language or behavior are taught. This phase of socialization usually takes place within the family. During this phase, infants learn a language and certain basic socialization behavior forms of the family and the society in which she/he lives.
• Secondary Socialization- Secondary socialization occurs once the infant passes into the childhood phase and continues into maturity. During this phase more than the family, some other agents of socialization like the school and friends’ group begin to play a role in socializing the child. Different kinds of social interaction through these different agents of socialization help the child to learn the moral standards, customs, and principles of their society and culture.

Hence, we can conclude that socialization is a process through which a human infant begins to acquire the necessary skills to perform as a functioning member of society.

Swiss psychologist Jean Piaget was the most well-known and influential theorist for cognitive development. Piaget was interested in how children reacted to their environments. 

Key Points

The factors which Piaget considered essential for cognitive development are:-​

• Assimilation-It refers to the process by which new objects and events are grasped or incorporated within the scope of existing schemes or structures.
• Accommodation- It is the process through which the existing schemes or structure is modified to meet the resistance to straightforward grasping or assimilation of a new object or event.
• Biological maturity:-The basis of Piaget's classification of cognitive development is maturation. This acts as a biological base for cognitive development. Jackson says that some degree of maturation interacting with experience is necessary for movement into the next stage of cognitive development.
• Physical experience:-It is accepted that there can be no knowledge development without relating objects. within the environment. An individual acquires knowledge not by passively copying objects in the environment but by acting upon them. For example, when the child learns from the perceptual properties of objects, by noting their weight, color of the harness, it is physical experience or first-hand information.

Thus from the above-mentioned points, it is clear that according to Piaget, experience with the physical world plays an important role in influencing development.

Jean Piaget, a Swiss psychologist, has made a systematic study of cognitive development in his theory that is categorized into four stages. 

Key Points

The pre-operational stage (2 to 7 years)- The pre-operational child progresses in the abilities that had emerged towards the end of the sensory-motor stage. Thus we have with us the pre-operational child who is now capable of representing reality mentally and who also understands that objects, in reality, can be represented by words.​

• The child knows by this stage that the objects which are physically absent do exist.
• This stage begins around age two and lasts until approximately age seven. During this stage, the child learns to use the symbols of language.
• This is the ability to make one thing - a word or an object stand for something other than itself.
• Ability of goal-oriented behaviour: being able to carry out a sequence of motor movements directed towards achieving something.
• At the end of the sensorimotor stage, the child develops the ability of goal-oriented behaviour.

Important Points

The limitations of the pre-operational child are:

• Pre-operational thinking tends to be egocentric.
• Pre-operational thinking tends to focus on only one aspect or dimension of a problem at a time.
• Pre-operational thinking tends to involve ‘transductive reasoning’.
• The pre-operational child cannot understand relational terms.
• The child at this stage is not able to understand how things operate. internally or how things relate to one another.

Thus from the above-mentioned points, it is clear that the cognitive ability that comes in the pre-operational period is the ability of goal-oriented behaviour.

Additional Information

• The ability to take others' perspectives develops in the concrete operational stage.
• Hypothetico-deductive thinking develops in the formal operational stage.
• The ability for abstract thinking develops in the formal operational stage.

Together with the development of cognition and social skills, children develop along the dimension of moral values and reasoning. They learn the rules for right and wrong and understand other laws and rules. Jean Piaget and Lawrence Kohlberg’s theories are two popular theories of Moral Development.

Kohlberg's Stages of Moral Development: 

• Extending the idea of moral development proposed by Jean Piaget, Lawrence Kohlberg worked throughout his life to develop a complete theory of moral development.
• Using storytelling techniques, he conducted many studies on children. The stories of his studies usually revolve around some kind of moral dilemma.
• At the end of every story, he used to ask some questions from his participants (children) and analyzed their answers for underlining reasoning. Based on his studies, he proposed that moral development consists of six stages and these six stages can be further grouped into three levels. These three levels are as follows:
• Level-I: Pre-conventional Level- At this level, the child is not responsive to cultural rules and labels of good and bad, right or wrong but interprets these labels in terms of physical or hedonistic consequences of actions or in terms of physical powers of those who communicate the rules and labels. This level is further subdivided into two stages.
• Stage-I: The Punishment and Obedience Orientation- The physical consequences of an action determine whether the action is good or bad regardless of human value or the meaning of these consequences. Avoidance of punishment and deference to power are valued in their own right, not in terms of respect for the underlying moral order.
• Stage-2: Instrumental Relativist Orientation- Right action consists of that which instrumentally satisfies one's own needs and occasionally the needs of others. Human reactions are considered those of market place. Elements of fairness, reciprocity and equal sharing are present but they are always interpreted. Reciprocity is a matter of “you scratch my back and I will scratch yours”. There is no consideration of loyalty, gratitude, or justice.
• Level-II: Conventional Level- At this level maintaining the expectations of the individual, family, group, or nation is perceived of value in its own right regardless of the immediate and obvious consequences. The attitude is not only of personal expectations and social order but of loyalty to it of actively maintaining, supporting, and justifying the order and of identifying oneself with persons or groups involved in it. The following two stages constitute this level.

1. Stage 3: Good boy - Nice Girl Orientation- Good behaviour is that which pleases or helps others and is approved by them. Behaviour at this stage is frequently judged by intentions - "he means well", becomes important for the first time. One earns approval by being good to others.
2. Stage 4: The Law and Order Orientation- There is an orientation towards authority, fixed rules, and the maintenance of social order. Right behaviour consists of doing one's duty, showing respect for established or law authority, and maintaining given social order for its own sake.

• Level III: Post-conventional, autonomous or principled level- At this level, there is a clear effort to define moral values and principles that have validity and application apart from the authority of the groups or persons. This level also has two stages.

1. Stage 5: The Social Contract, Legalistic Orientation- At this stage right actions tend to be defined in terms of general individual rights and standards that have been critically examined and agreed upon by the whole society. Apart from what is constitutional and democratically agreed upon the right is a matter of personal values. The result is based upon a legal point of view but with an emphasis on the possibility of changing the law in terms of consideration of social utility (rather than freezing it in terms of stage law and order).
2. Stage 6: The Universal Ethical Principle Orientation- Right is defined by the decision of the conscience in accordance with self-chosen ethical principles appealing to logical comprehensiveness, universality, and consistency. These are universal principles of justice, the reciprocity, and quality of human rights, and respect for the dignity of human beings as individual persons.

From the above, we can conclude that in the Good boy and good girl orientation, one earns approval by being nice.

Vygotsky believed that children are active seekers of knowledge, but he felt, it was a collaborative effort of the child and the socio-cultural environment.

Key Points Vygotsky's sociocultural theory:

• According to him, infants are endowed with basic perceptual, attention, and memory processes which are common to other animals as well. These develop naturally in the first two years of life.
• However, once the child has acquired language skills and has become capable of mental representation, his ability to participate in social dialogue surrounding culturally important tasks is enhanced.
• This leads to the development of the ability of the child to converse with himself in a manner similar to conversing with others.
• As a result, the child's basic mental capacities are transformed into uniquely human higher cognitive processes.
• According to Vygotsky, children use private speech for self-guidance and self-direction.
• With age, however**, private speech becomes transformed into silent inner speech or verbal thought**.
• The origin of private speech is traced to social interaction between the child and more mature members of society.
• Vygotsky felt that through joint activities with more mature members of society, children come to master activities and think in ways that have meaning in their culture.

From the above, it is clear that the concept of 'private speech' of children as proposed by Vygotsky illustrates that children use speech to guide their own actions.

Lev Vygotsky, a Russian psychologist and a contemporary of Jean Piaget proposed a theory of cognitive development known as ‘Socio-Cultural Theory’. Vygotsky believes that social and cultural (language, customs, and practices, family, work, etc.) processes are important in the process of development. They say that children continuously learn in everyday engagements with peers and adults. And thinking and knowledge developed in this process of learning. This view of development is known as a socio-cultural perspective or social constructivism.

Vygotsky's Theory:

• The interdependence of the individual's internal processes and the external social processes in learning and development is the main focus of Vygotsky's theoretical framework.
• Child's social situations of development influence qualitatively their perception, experience, appropriation, internalization understanding, and memory of interaction in and with their environment.
• Vygotsky considered this interdependence "as a process that is characterized by a unity of material and mental aspects, a unity of the social and the personal".
• According to Vygotsky**, learning cannot be separated from its social context**.
• Vygotsky argued that "the child is a part of the social situation, and the relation of the child to the environment and the environment to the child occurs through the experience and activity of the child himself; the forces of the environment acquire a controlling significance because the child experiences them" (Vygotsky, 1998,p.294)
• Key Principles:
• Society and the culture of the children play a vital role in the development of their cognition.
• The sign system or the language of the society works as a tool in gaining knowledge.
• Inputs from others and especially from more knowledgeable people and adults have the capacity to affect the development of cognition.

From the above, we can say that according to Vygotsky, learning cannot be separated from its social context.

John Dewey, an American philosopher has proposed the concept of 'Progressive Education' which emphasizes that learning takes place only through 'hands-on' approach so the students must interact with their environment to adapt and learn.

Progressive education:

• It is based on the belief that education should primarily serve the needs of children and focus on understanding, action and experience rather than rote knowledge and memorization.
• A free and democratic atmosphere should be provided in the classroom for the proper development of an individual.
• Democratic climate provides the child with maximum opportunities for interaction with other children in the class, with the teacher and with a variety of teaching-learning material.
• A democratic atmosphere in the class encourages the students to actively participate in the learning process.

Important Points

Progressive education entails that the classroom is democratic and there is space given to children for understanding as ​it: 

• emphasizes to enhance skills and understanding of the learners by engaging with the contents and experiences.
• promotes 'learning by doing' to make children self-reliant and productive to use their knowledge and talents effectively.
• ensures the active participation of students by working in a group and applying practical knowledge to complete an activity.

Thus, from-above-mentioned points, it is clear that progressive education entails that the classroom is democratic and there is space given to children for understanding.

Intelligence involves a number of abilities together. It is the ability to understand the incoming information and make sense out of it. It is the ability to acquire new skills and use the existing knowledge to complete a task or deal with a situation. Intelligence includes the capacity to understand novel stimuli, learning a language, and communicate with others, being aware of the environment, have the ability to reason, plan, and solve problems creatively. 

Key Points Howard Gardner Multi-Dimensional Intelligence

• Howard Gardener refuted the classic view of intelligence as a capacity for logical reasoning.
• He proposed that there is not one form of intelligence but a certain number of intelligences work together.
• According to him, intelligence is the “ability to solve problems or fashion products that are of consequence in a particular cultural setting or community” (1993).
• Initially, he proposed eight distinct types of intelligence namely, naturalist, spatial, musical, logical-reasoning, interpersonal, bodily-kinesthetic, linguistic, and intra-personal.
• Linguistic Intelligence
• This intelligence includes the ability to effectively use language to express oneself rhetorically or poetically, and as a means to remember information.
• Writers, poets, lawyers, and speakers are among those that Howard Gardner sees as having high linguistic intelligence.
• This area has to do with words, spoken or written.
• People with high verbal-linguistic intelligence display a facility with words and languages.
• They are typically good at reading, writing, telling stories, and memorizing words along with dates.
• They tend to learn best by reading, taking notes, listening to lectures, and discussing and debate.
• Those with verbal-linguistic intelligence learn foreign languages very easily as they have high verbal memory and recall, and an ability to understand and manipulate syntax and structure.
• Careers that suit those with this intelligence include writers, lawyers, policemen, philosophers, journalists, politicians, poets, and teachers.

From the above, sensitivity to the meaning and order of words and the varied uses of language illustrates a person with linguistic intelligence.

Vygotsky’s Sociocultural Theory of Learning:

• Vygotsky was a Russian psychologist who believed that social interactions play a key role in development.
• According to Lev Vygotsky, language development changes the nature of human thought.
• According to him, learning occurs when children interact with people and the environment.
• His greatest contribution was the emphasis on the role of sociocultural influences in our development.
• He asserted that the cognitive development of children is enhanced through social interaction with other people, particularly those who are more skilled.
• He explains this with the concept of the Zone of Proximal Development (ZPD), which refers to a range of tasks that a child can achieve only with assistance from a more skilled adult or peer called the More Knowledgeable Other (MKO). Adult assistance is provided wherever necessary which is called scaffolding.

Thus, language has an influence on our thought processes.

Gender Stereotyping refers to the relatively fixed and overgeneralized attitudes and behaviours that are considered normal and appropriate for a person in a particular culture based on his or her biological sex. For example, believing that certain acts are meant for boys only and certain things are for girls only. Note that:

• Gender stereotyping can limit the development of the natural talents and abilities of girls and boys, women and men, as well as their educational and professional experiences and life opportunities in general.
• Stereotypes about women result from deeply ingrained attitudes, values, norms, and prejudices against women.
• To avoid the situation of gender stereotype, a family should start involving boys into household chores that were mainly concerned with girls traditionally which gave rise to gender biasing and stereotyping.
• Therefore, "to bridge the gap of gender stereotypes, girls should be asked to help in works outside the home too as well as boys to help inside the home".

Hence, we conclude that the above statement shows gender stereotype.

Individual difference: Every child is unique and different from others. It should be kept in mind that learners possess different abilities, personalities, and belong to different backgrounds. So, the stimulus needs of every learner will be different. 

Key Points The following are its characteristics.

• It stands for those differences which in their totality distinguish one individual from another.
• Everyone has different Learning Style, Aptitude, Attitude, Personality, and Emotional Intelligence, motor abilities, social atmosphere,  etc
• Children vary in their cognitive, affective & psychomotor styles and hence they differ in their thinking, reasoning, expressing, performing, etc.

Hence, we can conclude that both statements are true regarding individual differences in the classroom.

Assessment is integral to the teaching-learning process which helps in facilitating student learning and improving instruction. It is a process of collecting relevant information on student learning.

• The continuous assessment focuses on informal and a combination of both formative and summative.
• It refers to all-around development including both scholastic and co-scholastic aspects of a child's development.

Paper-pencil tests: The formal paper-pencil tests do not provide all information about the student. 

• Tests of paper and pencil assessment types are customarily used to assess cognitive objectives.
• There are important instructional objectives that cannot be appropriately assessed by paper and pencil tests.
• These paper and pencil tests have failed to promote and measure higher-level thinking and problem-solving skills.
• The current educational practice relies heavily on paper and pencil tests as the sole criterion for measuring educational effectiveness. Assessment leads to decision making.
• There are important instructional objectives that cannot be appropriately assessed by the paper-and-pencil test. It involves objectives associated with the subject matter process. or product.
• Paper-pencil tests assess only that which is memorized or that which is of cognitive origin.

Hence, we can conclude from the above-mentioned points, it is clear that assessment by only paper-pencil tests limits assessment.

Inclusive Education means education for all children in school. It refers to the inclusion of all children in the education system, regardless of their differences and disabilities.

• Hearing impairment refers to hearing loss that prevents a person from totally receiving sounds through the ear. If the loss is mild, the person has difficulty hearing faint or distant speech.

Key Points

If a teacher has a 'hearing impaired' child in her middle school class. She needs to make the child sit at a place from where she can see the teacher's lips and facial expressions clearly. 

Strategies for teaching Hearing Impaired child

• It is not possible to establish enough special schools to accommodate every hearing impaired\child. The other alternative is to use the already existing infrastructure in the general stream and integrate the hearing impaired children into the mainstream of education.
• Generally, hearing impaired children are as intelligent as children with normal hearing. Given timely help, these children can get successfully integrated into the educational system.
• Children with hearing impairment find it difficult to have focussed listening for every word which is spoken. Children with hearing impairment find it difficult to have focussed listening for every word which is spoken.
• Children are often comfortable with signs, and to facilitate them to understand the message, one may use signs freely. Once the child has understood the word or sentence, you may not need to use signs. Do encourage your child to speak words. You may repeat the word.

We can conclude that teacher can make the child sit at a place from where she can see the teacher's lips and facial expressions clearly.

The disadvantaged child is one who is from a socially and economically backward section of the community, who cannot profit from school because of deprivation of one sort or another. Such children show cumulative academic deficits, a high dropout rate, and a progressive decline in intellectual functioning. 

Key Points

The interventions for children belonging to socially and economically backward section have to be based on the intensive micro-planning that address the needs of every child. Some of the suggestions for the inclusion of backward children in school are:

• Establishing norms of behaviour within the school for teachers, school staff, and students.
• Timely detection of the forms of discrimination practised in a particular context by either teachers or school staff or students. This is not an easy task as many forms of discrimination have become part of accepted behaviour, go unnoticed, and unchallenged by the majority.
• The teacher is a key figure in the school to ensure inclusion. But his/her role in this process has been largely neglected so far.
• A teacher should adapt different pedagogy as per the needs of every child in the classroom.
• Sensitization of teachers from the stage of pre-service training onwards, developing special modules for use in teacher education and training programs.
• Co-curricular activities, such as sports, music, and drama which tend to break social barriers among children need to be encouraged.
• They have remained a hugely neglected area and would be an important strategy for increasing the interaction of children as well as allowing children from varied backgrounds to exhibit their talents and get recognition.

Hence, we can conclude that a teacher can effectively respond to the needs of the children from 'disadvantaged sections' of society by adapting her pedagogy to the needs of every child in the classroom.

Learning disability refers to a neurological disorder that causes cognitive impairment. Dyslexia, dysgraphia, dyscalculia, etc are the most common learning disability.

Important Points

Learning disability:

• Learning disability is intrinsic and due to central nervous system dysfunction.
• It is a variable state which can be addressed by appropriate comprehensible input.
• It can't be attributed to cultural deprivation as it can present in children of any culture.
• It can't be attributed to educational deprivation as it can also present in children with average or above-average IQ.

Key Points

The characteristics of the learning disabled children are:

• Learning disabled children are normal in intellectual functioning.
• Learning disabled children face problem in a few area of learning, not in all.
• Learning disability mainly lies in their way of learning and in their perceptual systems.
• Learning disabled children show problems in sustaining attention, got easily distracted and have a poor fine-gross motor skills.
• Learning disabled children are often several years behind their peers in reading, fluency and spelling, letter, number, etc.

Hence, it is clear that children with learning disability struggle with some aspects of learning.

​ 

Some Disabilities in Brief:

Creative expression provides the richest opportunities for individual expression and growth. The child must be free of teacher control and direction to accomplish this.

Creative thinking aims at novelty in the first instance rather than truth. Because it aims at novelty, it necessarily has to be different from the conventional modes of thinking. Hence, creative thinking is labeled in psychology as divergent thinking. 

Some of the ways to promote creative thinking or divergent thinking are- 

• to ask students to raise questions instead of requiring them to answer questions we pose,
• to ask students to observe the everyday world around them and raise questions about it,
• to ask them to identify suitable problems. where they can apply their knowledge and think of different ways to solve a problem.
• to adopt the discovery model of teaching wherever this is possible, offering successive clues to the answer,
• to orient them to lateral thinking.

Hence, we can conclude that teachers can encourage children to think creatively by asking them to think of different ways to solve a problem.

Philosophical Perspectives of children with special needs

Inclusion is a philosophy or concept that aims at fostering mutual respect among people and their different ways of life. The institution changes its philosophy, its curriculum, its structure to accommodate the different needs of the individuals.

• Inclusion does not stem from the rhetoric of tolerance, or of celebrating unity in diversity, of seeing commonalities among individuals. It does not see the individual separate from her or his political, social-economic, religious, gendered, and disabled background.
• Every student has a right to be educated among normal students in a normal setting without any discrimination.
• In the inclusive classroom, each student gets access to knowledge, skills and information, which improve available choices to all children and we do not necessarily limit ourselves to knowledge domain, but rather include the affective domain, and the attitudinal domain as well.
• The individual in an inclusive institution is not “existing in a vacuum”, but is in a sociocultural context. Inclusive schools or setups facilitate an environment where everyone works together creatively so that each student participates, learns, and benefits.
• Inclusive schools see diversity as the reality as they accommodate students from different ethnic groups, language groups, cultures, family situations, and social and economic backgrounds with different interests and purposes for learning and different abilities and styles of learning.
• The fundamental principle of the inclusive school is that all children should learn together, where possible and that ordinary schools must recognize and respond to the diverse needs of their students, while also having a continuum of support and services to match these needs.

Hence, we can conclude that children with special needs have the right to inclusive education and study in regular schools.

The learner-centred approach of teaching puts learners in the centre and gives primacy to children's experiences and needs.

It strongly believes that when children are given the freedom to work at their own pace, they develop the ability to assimilate the concepts efficiently.

Important Points

Characteristics of the learner-centred approach:

• It stresses the importance of enquiry, observation and investigation.
• It takes into account learner's capabilities, capacities and learning styles.
• It uses methods like experiential learning, problem-solving, concept mapping and creative writing.
• It emphasizes to provide ample opportunities to the children to foster their own strategy of learning to perform a task.
• In this method, teachers facilitate students as a facilitator by providing with proper environment and materials to learn at their own pace.
• Students work in flexible, cooperative groupings to solve problems and analyze texts to demonstrate an understanding of a task.

Hence, it could be concluded that learner-centred approach means methods where learners own initiative and efforts are involved in learning.

Additional Information

Conditioning is the process of modifying one’s behavior with the help of some preparation or training. Behaviourism theory is an idea which states that learning takes place owing to conditioning. There are two types of conditioning:

• Classical conditioning
• Operant conditioning.

Important Points 

• ​Classical conditioning is a basic form of learning in which a previously neutral stimulus comes to elicit a given response. On the other hand, Operant conditioning is a form of learning in which the correct response is reinforced and becomes more likely to occur. In operant conditioning, the rewarding of the desired response is known as reinforcement.
• Classical conditioning gets its name from the fact that it is the kind of learning situation that existed in the early "classical" experiments of Ivan Pavlov (1849-1936). Classical Conditioning is also sometimes called respondent conditioning.
• Operant conditioning is a process through which organisms learn to repeat behaviors that produce positive outcomes or avoid or escape from the negative outcomes. It occurs when we make conscious choices.
• Skinner defined reinforcement as any operation or action that increases the rate of response.
• In operant conditioning, the behavior is controlled by the central nervous system while in classical conditioning the behavior is controlled by the automatic nervous system two principles of operant conditioning are called shaping and chaining.
• Shaping is a process of learning a new behavior in which successively closer approximation of the desired behavior is reinforced, that is the organism will be rewarded for each small step towards targeted behavior.
• Any complex behavior or skill is the chain of many steps. The process of chaining involves breaking a task into small steps and then teaching these steps in sequence or chain.
• In chaining, only the targeted behavior is rewarded, i.e., once the trainee accomplishes the last step he will be rewarded.

NOTE:

• Imitation is one of the important methods based on social learning theory, which could be applied in learning many skills.
• Rote Memorization leads to temporary learning and does not makes learning effective.

Hence, we can conclude that Conditioning is central to learning.

Children's knowledge often involves systematic errors and misconceptions. Constructivism alone accounts for their formation. The formation of personal constructs, misconceptions, and errors will become obvious to you. 

Constructivist theory is compatible with the interactional and cultural emphasis of theorists like Vygotsky and Piaget. 

• According to the great psychologist Piaget's theory that learning and cognitive development in terms of structures like individual schema and mental processes like organization and adaptation (assimilation and accommodation).
• The learner with the help of these structures and processes constructs knowledge himself/herself. So the learner through active is alone in this process of knowledge construction.
• In the words of Piaget (1980) himself " Education, for most people, means trying to lead the child to resemble the typical adult of his society (whereas) for me, education means making creators, even if there aren't many of them, even if one's creations are limited by comparison with those of others."
• Social constructivism regards knowledge as a social construct and prioritizes the social aspects of learning and cognitive development. Some of these social aspects are language, culture, everyday practices, material objects, interpersonal interaction, peer interaction, tools, and symbols.

Hence, we can conclude that In a constructivist classroom as envisioned by Piaget and Vygotsky, learning is constructed by the students themselves who play an active role.

The nature of Mathematics includes mathematical ideas that progress from concrete to abstract; grow from particular to general and its knowledge is conceptual as well as procedural. Students are exceptionally blessed with the higher-level thinking abilities of creativity and problem-solving. Such activities require the use of already stored information along with the information concurrently received from the environment. 

• Problem-solving includes higher-order thinking skills such as visualization, association, abstraction, comprehension, manipulation, reasoning, analysis, synthesis, generalization.

Key Points

If a teacher asks "Two complementary angles are in the ratio 2 : 3. Find these angles."  

• Here, the children are faced with the problem of drawing the angle. In order to find the solution, the children have used their previous knowledge, a few mental calculations, and reasoning while measuring different angles and measurement, created a few relations like complimentary/supplementary, equated a few formulas, and finally succeeded in finding the solution to the problem i.e. drawing the angle.
• As teachers, we should be aware of the fact that students make use of various processes to arrive at solutions to the problems that they encounter, and such a process is considered to be the key processes in mathematical reasoning. Technically, we name these processes as generalizations, conjectures, counterexamples, hypotheses, and proofs. These are the key processes used to build and validate mathematical knowledge.

Thus from the above-mentioned points, it is clear that the above problem from the NCERT textbook of Class VII refers to higher-order thinking as it demands the interpretation of given information, its analysis, and its use in getting the desired information.

Mathematics is the study of numbers, shapes, quantities, and patterns. Mathematics is the ‘queen of all sciences’ and its presence is there in all the subjects. It acts as the basis and structure of other subjects.

Proof of a Mathematical Statement consists of a sequence of statements, each statement being justified with a definition or an axiom or a proposition that is previously established by the method of deduction using only the allowed logical rules. Thus, each proof is a chain of deductive arguments each of which has its premises and conclusions.

Important Points

Proof by contradiction:

• This method is called proof by contradiction. It is also called reductio ad absurdum (a Latin phrase) because it relies on reducing a given assumption to an absurdity.
• Here, we start with the assumption that the given statement is false. By rules of logic, we arrive at a conclusion contradicting the assumption, and hence it is inferred that the assumption is wrong and hence the given statement is true.
• In this method, to prove q is true, we start by assuming that q is false (i.e., ~ q is true). Then, by a logical argument we arrive at a situation where a statement is true as well as false, i.e., we reach a contradiction r ∧ ~ r for some statement that is always false. This can only happen when ~ q is false also. Therefore, q must be true.
• Prove that there is no rational number whose square is 2. For this, we begin by assuming that q is a rational number whose square is 2 and ended up with the conclusion that the square of q (rational number) is not 2.

Additional Information

• Proof by induction:- In this method of proof, examples, and steps are taken to prove a statement without the help of any theorem. In this method, the proof is made by way of induction.
• Direct proof: In this method, a given statement or equation can be proved directly from examples. By using hypothetical values, figures or data, the direct proof method can be used to prove the Sum of two even integers is always even. Example: 2 + 4 = 6. Here, we have taken 2 even numbers 2 and 4 and get result 6 which is again an even number.
• Counter positive proof:- In this method of proof, inferences are used in proofs for some given conditional statements. The contrapositive of a conditional can be formed by interchanging the conclusion and the hypothesis and then negating both of them.

Thus from the above-mentioned points, it is clear that this type of proof is proof by contradiction.

Key Points

• If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. This statement is a theorem.
• Theorem is said to be proposition that is not self-evident but that can be proved from accepted premises and so is established as a law or principle.
• There are many properties of a parallelogram. We draw a parallelogram and draw both its diagonals intersecting at the point. Measure the lengths of these lines. We observe that the mid-point of the diagonals. Repeat this activity with some more parallelograms.
• Each time we will find that the mid-point of both the diagonal. We can use the previous concept like length, mid-points etc. Hence we can prove this theorem by accepted premises.

Representation in mathematics typically involves visual or symbolic methods to illustrate numbers, relationships, or data. 

Key Points

'Representation' in Mathematics refers to:

• Expressing the number sequence through geometrical pattern: This involves using visual or spatial arrangements to illustrate number sequences. For example, representing the sequence of triangular numbers using a pattern of dots arranged in a triangle.
• Expressing the relation between two variables as an equation: This involves using algebraic notation to describe how two variables are related. For example, the equation y=2x+3y=2x+3 y = 2x + 3

y=2x+3 represents a linear relationship between xx x

x and yy y

y.

• Expressing the given data through graphs: This involves using graphical methods, such as bar graphs, line graphs, or pie charts, to visually represent data. Graphs make it easier to see patterns, trends, and relationships in the data.

Hint

• Expressing an important geometrical result as a theorem: It refers to stating a mathematical result or fact, such as a theorem, rather than a method of representation. A theorem is a proven statement about mathematical concepts, not a representation of data or relationships.

Hence, the correct answer is expressing an important geometrical result as a theorem.

Mathematics learning can be pleasurable in adopting a variety of ways like performing learner-friendly activities, games, preparation of models and charts, participation in quizzes and exhibitions, collecting and responding to puzzles and riddles. 

• Some basic ways related to the learning of mathematics during the early stages of school learning are manipulation of objects, performing meaningful tasks in the real-life situations, representation in multiple ways, evolving and using alternative strategies and problem-solving and problem posing.

Key Points

In NCERT exemplar book lots of unit end activities are given. The main aims of this-

• It can be helpful for sharing one’s representation with others in the class helps to explore different approaches for elaborating the process or procedures and to develop multiple representations.
• Children can learn most of the basic concepts of mathematics being engaged in activities that give them pleasure.
• Every child loves to play games with other children and these games that may be the perfect medium for learning several mathematical concepts.
• These activities enhance the skills like operations on numbers, spatial thinking and measurement.
• Each individual will perceive the same object in a unique way. Communication is possible only to the extent that two perceivers have similar purposes, assumptions and experience.

Thus from above-mentioned points, it is clear that the objectives of such tasks giving at the end of the chapter are to help all learners with different learning styles and to enhance spatial orientation.

Methods are the ways/styles of the transaction of content in the classroom for effective learning. In the learning- centred approaches the focus is how students construct their own knowledge on the basis of their prior experience. 

Key Points

Project Work in Mathematics-

• The project-based learning is a learner-centred method in which the students are challenged to do something by themselves outside the realm of normal classwork.
• Project-based learning is an individual or group activity that goes on over a period of time, resulting in a product, presentation, or performance.
• A project of mathematics contains rich activities, active participation, freedom to students and correlation with other subjects.
• It promotes inquiry skills, enhances problem-solving skills and establishes interdisciplinary linkages.
• The project based learning followed the following steps- 
• Providing situations
• Choosing and purposing
• Planning for the project
• Executing the project
• Judging the project
• Recording the project

Thus from above-mentioned points, it is clear that Projects make scoring easy in Mathematics is not true.

In your day-to-day life, you must have seen several kinds of tables consisting of numbers, figures, names, etc. These tables provide ‘Data’. Data is a collection of numbers gathered to give some information. They are collected from a variety of sources.

Data representation and Data interpretation: Data Interpretation should be done honestly and integrally without any biased manipulation of data.  This means that you need to report your research honestly and that this applies to your methods, your data, your results, and whether you have previously published any of it. One should not make up any data, including extrapolating unreasonably from some of your results or do anything which could be construed as trying to mislead anyone. It is better to undersell than exaggerate your findings. You should aim to avoid bias in any aspect of your research, including design, data analysis, interpretation, and peer review. 

The following techniques can be beneficial for data representation and data interpretation-

• Direct Personal Investigation-
• know the local conditions, customs, and tradition
• Indirect Oral Investigation-
• information is collected hm a witness or from a third party who are directly or indirectly related to the problem and possess sufficient knowledge.
• Use of Local Reports-
• use of local newspaper, magazines, and journals by the investigators
• Questionnaire method- 
• It involves the preparation of a list of questions relevant to the inquiry and presenting them in the form of a booklet, often called a questionnaire

Thus from the above-mentioned points, it is clear that Debate is not an appropriate activity for 'data representation and data interpretation'.

Calculation : 

x = 2/3 and y = 3/4

x - y = 2/3 - 3/4 = (8 - 9)/12 = -1/12

∴ (x - y)^-1 = -12

x^-1 = 3/2 and y^-1 = 4/3

x^-1 - y^-1 = 3/2 - 4/3 = (9 - 8)/6 = 1/6

Then, the rational number between (x - y)^-1 and x-1 - y^-1 = (-12 + 1/6)/2 = (1 - 72)/12 = -71/12

Additional Information

 A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero. For example 2, 6/5, -9/12, etc.

Rational number between two numbers a and b = (a + b)/2.

Calculation : 

0.001 + 1.01 + 1.001 - (1.03 × 0.1) + (1.11 ÷ 0.1) + x = 1.4 × (1/10)-1 

⇒ 2.012 - 0.103 + 11.1 + x = 1.4 × 10

13.112 - 0.103 + x = 14

13.009 + x = 14

∴ x = 14 - 13.009 = 0.991

3(5x - 7) - 4(8x - 13) = 2 (9x - 11) - 17

Calculations:

3(5x - 7) - 4(8x - 13) = 2 (9x - 11) - 17

⇒ 15x - 21 - 32x + 52 = 18x - 22 - 17

⇒ -17x + 31 = 18x - 39

⇒ 18x + 17x = 31 + 39

⇒ 35x = 70

⇒ x = 70/35

⇒ x = 2

$\frac{7x -5}{11x-9}$ = $\frac{{7×2 -5}}{{11× 2}-9}$

⇒ (14 - 5) ÷ (22 - 9)

⇒ 9/13

∴ The required value is 9/13

Given:

$\frac{\sqrt{1058}×\sqrt{648}}{x} = 18$

Formula required:

$\sqrt[2]{a} = a^{1/2}$

$\sqrt[n]{a} = a^{1/n}$

$a^m \times a^n = a^{m + n}$

a^-m = 1/a^m

Calculation:

$\frac{\sqrt{2 × 529} × \sqrt{2 × 324}}{x} = 18$

$\Rightarrow \frac{\sqrt{2 × 529 × 2× 324}}{18} = x$

$⇒ x = \frac{\sqrt{2^2 × 23^2 × 18^ 2}}{18}$

⇒ x = (2² × 23² × 18²)^1/2 ÷ 18

⇒ x = 2 × 23 × 18 ÷ 18

⇒ x = 46

∴ The required value is 46

Given:

$\sqrt[3]{500} × \sqrt[3]{3456} = 40 × A$

Formula required:

$\sqrt[2]{a} = a^{1/2}$

$\sqrt[3]{a} = a^{1/n}$

$a^m \times a^n = a^{m + n}$

a-m = 1/am

calculations:

 ⇒$\sqrt[3]{500 × 3456}$ = 40 × A

⇒  $\sqrt[3]{5 × 5 × 5 × 4 × 4 × 4 × 6 × 6× 6 }$ = 40 × A

⇒ $\sqrt[3]{5^3× 4^3 × 6^3}$ = (5³ × 4³ × 6³)^1/3 = 40 × A

⇒ 5 × 6 × 4 = 40 × A

⇒ A = 3

∴ The value of A is 3

Given:

$\left(\frac{2}{9}\right)^{3} \times \left(\frac{4}{81}\right)^{-6} = \left(\frac{2}{9}\right)^{2m-1}$

Formula required:

$\sqrt[2]{a} = a^{1/2}$

$\sqrt[3]{a} = a^{1/n}$

$a^m \times a^n = a^{m + n}$

a-m = 1/am

Calculations:

$\frac{4}{81} = (\frac{2}{9})^2$

[(2/9)²]^-6 = (2/9)^-12

$(\frac{2}{9})^3 \times (\frac{2}{9})^{-12} = (\frac{2}{9})^{2m-1}$

⇒ 3 - 12 = 2m - 1

⇒ 2m = 3 - 12 + 1

⇒ 2m = - 8

⇒ m = - 8/2

Hence, m = - 4

∴ The value of m is -4

Given :  x = 597 × 1022 + 73.5 × 1021 

Calculation

 x = 597 × 1022 + 73.5 × 1021

= 597 × 10 × 10²¹ + 73.5 × 10²¹

= 5970 × 10²¹ + 73.5 × 10²¹

= (5970 + 73.5) × 10²¹ = 6043.5 × 10²¹ = 6.0435 × 10²⁴

On comparing it with the standard form of x which is x = 6.0435 × 10^m  we get

m = 24

Calculation

$2m - {1\over 2m } = 2$

Dividing by 2 both sides

⇒ $m - {1\over 4m} = 1$ 

On squaring both sides we get,

$(m - {1 \over 4m} )^2$ = $m^2 + {1\over 16m^2} - {1\over2} = 1$

⇒ $m^2 + {1\over 16m^2} = 1 + {1\over2} = {3\over2}$

So, $m^2 + {1\over16m^2} = {3\over2} = 1{1\over2}$

Additional Information

Formula for (a - b)² = a² + b² - 2ab

Formula used:

(a + b)2 = a2 + b2 + 2ab

a2 - b2 = (a + b)(a - b)

Calculation

$x^4 + 4$

Adding and subtracting 4x² we get,

$x^4 + 4 = x^4 + 4 + 4x^2 - 4x^2$

 $(x^2 + 2)^2 - (2x)^2$

∴ $(x^2 + 2)^2 - (2x)^2$ = $(x^2 + 2 - 2x)(x^2 + 2 + 2x)$

So, $x^2 - 2x + 2$ is a factor of $x^4 + 4$

Given:

The mean of the five observations = 11

Number of observations = 5

The observations = x, x + 2, x + 4, x + 6, x + 8

Formulae required:

Mean or Average = Sum of observations ÷ Number of observations

Calculations:

Sum of observations = x + x + 2 + x + 4 + x + 6 + x + 8

⇒ 5x + 20 = 5(x + 4)

Mean = [5(x + 4)] ÷ 5

⇒ 11 = x + 4

⇒ x = 7

First three observations =  x + x + 2 + x + 4

Sum of three observations = 3x + 6

⇒ 3(x + 2)

The number of observations = 3

Mean of first three observations = [3(x + 2)] ÷ 3

⇒ x + 2 = 7 + 2

⇒ 9

∴ The mean of first three observations is 9

Alternate Method

Average/mean = (x1 + xn)/2  whrere x1 is first number and xn is the last number with common difference between consecutive numbers

Mean = (x + x + 8)     (∵ x1 = x,  xn = x + 8)

⇒ (2x + 8) ÷ 2 = 11

⇒ [2(x + 4)] ÷ 2 = 11

⇒ x + 4 = 11

⇒ x = 11 - 4

⇒ x = 7

Average of three observations = (x + x + 4) ÷ 2 

⇒ 2(x + 2)/2 = (x + 2) 

⇒ (7 + 2) = 9          (∵ x = 7)

∴ The mean of first three observations is 9

Given:

The bag has red marbles = 5

The bag has green marbles = 4

The bag has blue marbles = 3

Concept used:

The probability formula is used to compute the probability of an event to occur. To recall, the likelihood of an event happening is called probability.

Formulae required:

Probability P(A) = the number of favourable outcomes/total number outcomes

Calculations:

The total number of marbles = 5 + 4 + 3

⇒ 12

Non- green marble = not green 

The non-green marbles in a bag = total marbles - green marbles

⇒ 12 - 4 = 8

Probability of non-green marble = 8/12

⇒ 2/3

∴ The probability that it is a non-green marble is 2/3

Given : 

AB × BA = BCB and A ≠ B ≠ C

Calculation

A and B cannot take the same value as A ≠ B

So, let A = 1 and B = 2

Then, AB × BA = 12 × 21 = 252

⇒ BCB = 252 

∴ C = 5 

A = 1, B = 2 and C = 5

∴ A + B + C = 1 + 2 + 5 = 8

Given : 

Number of faces of polyhedra = x

number of vertices of polyhedra = y

Number of edges of polyhedra = z

Using Formula : F + V - E = 2

Calculation

x + y - z = 2

⇒ x - 2 = z - y

Additional Information

 Polyhedron : A polyhedron is a 3-dimensional solid made by joining together polygons.

If we know about the number of faces and the vertex of a polyhedron, the number of edges can be calculated using the ‘polyhedron formula’ or ‘Euler’s formula’.

 F + V - E = 2

where F, V, and E represents the number of faces, edges and vertices of the polyhedron respectively.

Given:

Ravi purchased two articles each article cost = Rs. 1,500

When he sold,

Gain on first article = 6% 

Loss on second article = 4%

Calculations:

Selling  price of first article = 1500 + 1500 × 6/100

⇒ 1500× (1 + 6/100) = 1500 × ( 100 + 6) ÷ 100

⇒ 15 × 106 = 1590

Selling  price of second article = 1500 - 1500 × 4/100

⇒ 1500 × (1 - 4/100) = 1500 × ( 100 - 6) ÷ 100

⇒ 15 × 96 = 1440

The total cost price = cost price of first article + cost price of second article

⇒ 1500 + 1500 = 3000

The total selling price = selling price of first article + selling price of second article 

⇒ 1590 + 1440 = 3030

The total cost difference of selling price and cost price whole transaction = total selling price - total cost price 

⇒ 3030 - 3000 = 30

Profit = (30/3000) × 100   (∵ selling price > cost price)

⇒ (1/100) × 100 = 1%

∴ The total transaction gain 1%

2) 

3) 

Sum of all four angles of a quadrilateral =360° 

In this case, ∠ A + ∠ B + ∠ C = 75° + 150° + 140° = 365° > 360°

Concept 

Complementary angles are those angles whose sum is 90º 

Supplementary angles are those whose sum is 180º

Calculation

x is equal to its complement 

⇒ x + x = 90º 

2x = 90º

⇒ x = 45º

y is equal to its supplement 

⇒ y + y = 180º

2y = 180º

⇒ y = 90º

so, 2x + 3y = 2 × 45º + 3 × 90º = 90º + 270º = 360º

Concept 

Measure of each interior angle of a regular polygon with 'n' sides = 180°(n - 2)/n

Calculation

Interior angle = 180°(n - 2)/n = 108º

⇒ 180ºn - 360º = 108ºn

⇒ (180º - 108º)n = 360º

⇒ 72º × n = 360º

∴ n = 360º/72º = 5

Concept 

Area of quadrilateral = Sum of areas of two triangles formed by one diagonal

Area of triangle = 1/2 × base × height

Calculation

Area of quadrilateral ABCD = Area of Δ ABD + Area of Δ BCD

= (1/2 × 40 × 16) + (1/2 × 40 × 12) = 320 + 240 = 560 cm²

So, area of quadrilateral ABCD = 560

Given:

The measurement of each sheet of paper is 22 cm and 28 cm.

If one sheet rolled out into a cylinder through its length thus,

The height of the cylinder, h = 22 cm, and the area of the base = 28 cm

The height of the cylinder, h = 28 cm, and the area of the base = 22 cm

Formula required:

Circumference of base = 2πr

Volume of cylinder = π r²h

Concept used:

In this particular question, there are two sheets of dimensions 22 m × 28 m

Here two cases arise 

Case 1

When rotated along the side 28 cm then the perimeter will be 28 cm and the height will be 22 cm

Case 2

When rotated along the side 22 cm then the perimeter will be 22 cm and the height will be 28 cm

Calculations:

Circumference of cylinder1 = 2 π r₁

2 π r1 = 28 cm

⇒ 2 × π × r1 = 28

⇒ r1 = 28 / 2π 

⇒ r1 = 14/π 

Volume of cylinder 1 = π r1²h

π r1²h = π × (14/π) × (14/π) × 22

⇒ 1372 cm³

If other sheet rolled out into a cylinder through its width thus, the height of the

cylinder, h = 28 cm, and the perimeter of the base = 22 cm

Circumference of cylinder 2 = 2 π r₂

2 π r2 = 22 cm

⇒ 2 × π × r2 = 22 cm

⇒ r2 = 7/2  cm 

Volume of cylinder 2 = π r2²h

π r₂²h = π × (7/2) × (7/2) × 28

⇒ 1078 cm³

Hence, the difference of volume = (1372 – 1078) cm³ = 294 cm³

∴ The required difference = 294 cm³

Calculation:

Let the radius of the circle be 'r'

Let the side of the square be 'a'

According to the question,

The perimeter of circle = The perimeter of the square

⇒  2 π r = 4a

⇒ r = 4a/2π 

⇒ r = 2a/π 

Area of square = a²

Area of circle =  π r²

 The ratio of the area of the square to that of the circle  = a² ÷ π r²

⇒ a² ÷ [π (2a/π)²] = π /4

∴ The ratio of the area of the square to that of the circle is π ∶ 4

Mathematics is the study of numbers, shape, quantity, and patterns. The nature of mathematics is logical and it relies on logic and connects learning with learners' day-to-day life.

• Teaching methods of mathematics include problem-solving, lecture, inductive, deductive, analytic, synthetic, heuristic and discovery method. Teacher adopts any method according to the needs and interests of students.

Key Points

Anisha is using deductive logic.

Deductive Method: The deductive method is based on deduction. At first, the rules are given and then students are asked to apply these rules to solve more problems.

• It begins with general premises and through logical argument, comes to a specific conclusion.
• For example, while teaching mathematics, the teacher introduces a theory and explains the rules of the theory and the formula, and the students are asked to solve problems using the given formula.
• Deductive approach proceeds from-
• General to specific
• Unknown to know
• Complex to simple
• Formula to example

In the above example Anisha proves it by taking the case n i.e, she uses the method from unknown to known.

Thus it is clear that Anisha is using deductive logic.

Additional Information

Inductive Method: Inductive approach is based on the process of induction. It is a method of constructing a formula with the help of a sufficient number of concrete examples. 

• Induction means to provide a universal truth by showing, that if it is true for a particular case.
• Inductive approach proceeds from-
• Particular to general
• Known to unknown
• Simple to complex
• Example to formula

Teaching-learning materials (TLMs) are, therefore, tools, which are used by teachers to help learners to learn concept with ease and efficiency. The role of TLMs in the classroom is to make learning real, practical and fun for children. Teachers use TLMs to illustrate or reinforce a skill, fact or idea. TLMs also help in bringing novelty and freshness in classroom teaching as it relieves learners from anxiety, fear and boredom.

Key Points

Information and communication technology (ICT) has brought new possibilities in the classroom. Internet and interactive multimedia are of great significance for teaching. It needs to be effectively integrated into the formal classroom activities for enriching the content and quality of teaching and learning. For this, the teachers need to prepare themselves to keep pace with the application of technology in the classroom. Computers have already come into the classrooms of many schools and in near future, most schools would have such facilities available for students.

• Game-based learning is a teaching method in which students investigate relevant aspects of games in a learning environment created by teachers. Teachers and students work together to bring depth and perspective to the game-playing experience.
• Points systems, badges, leaderboards, discussion boards, quizzes, and classroom response systems are all part of game-based learning.
• The child is allowed complete freedom and is provided with all necessary amenities in this method. Games-based learning makes learning more engaging, provides better learning outcomes, and makes the learning process more enjoyable, result-oriented, and less boring.
• Games involving factorization of numbers or formation of new shapes by joining 2D shapes etc, enhance students' ability to learn concepts is improved since they can investigate, observe, and infer at their own pace.

Thus from the above-mentioned points, it is clear that using technology-based games involving factorization of numbers or formation of new shapes by joining 2D shapes, etc. enhances students ability to understand the concepts better as they are able to explore, observe and infer at their own pace.

Mathematics is a deductive system in which one starts from some definitions, some undefined terms and some self-evident truths (which may be based on experience) called axioms. Writing proofs in geometry implies argument or justification of statements.

Key Points

• As in all mathematical theories, Euclid built a theory involving some abstract objects and relationships between them. Some of the objects are undefined, for example, 'point', 'line', etc. Others are defined in terms of these objects. Of course, the effort is to keep the number of undefined terms to a minimum.
• Each theorem in Euclid's geometry is proved from some preceding results. Of course, he started with a set of five assumptions about the undefined terms, which are the axioms or postulates of the theory. Any set of statements can be laid down as postulates so long as they do not lead to any logical contradictions or inconsistencies. Obviously, the fewer the postulates, the better. Mathematicians try to derive more and more theorems from fewer and fewer postulates.

Thus from the above-mentioned points, it is clear that writing proofs in geometry imply argument or justification of statements.

Field trip refers to a learning approach that ensures the active involvement of learners in the learning process by taking them to a certain place where they can earn knowledge by engaging with real situations. 

Key Points

Field trips are useful in Science for empirical evidence (information obtained through observation and experimentation) as it:

• reinforces experiential and contextual learning.
• provides an active learning experience to learners.
• involves learners in both group and self-directed activities.
• links classroom learning to life outside school or with the real-world.
• gives students a lot of opportunities for observation and exploration.
• enhances the process skills of students, can be used for assignments and projects for formative assessment and provides concrete experiences to students.

Hence, we conclude that objectives A, B and C can be attained through the field trip.

The nature of assessment in science is not something entirely different from other subjects but it has certain distinctive characteristics, which have been drawn from the objectives of teaching-learning in science. 

Key Points

The following tools and techniques have been suggested for assessment as a secondary level in science. 

• Project work-
• In the process, the students learn fundamental principles of science, methods, and processes of science, and are exposed to the phases involved in a scientific investigation
• Practical Record-
• We monitor the learner's progress through written tests and practical examinations as well as their practical record in their practical notebooks. Written tests may be unit tests, weekly tests, monthly tests, and terminal tests. Assessment of all such tests will facilitate us in the monitoring of learners' progress.
• Quiz-
• It expands a person’s horizon of knowledge, sharpens memory, and prompts spontaneous communication. It is of equal interest to the participants and to the spectators.
• Field trips-
• The field trip is an educational activity that gives an outdoor experience that cannot be provided in the classroom. It helps to relate concepts of science learned in the classroom with real life and with the environment.
• Roleplays-
• Roleplay among students develops the skills to handle social and scientific interactions. It builds confidence and communication skills among students.
• Portfolios-
• Student portfolio provides evidence of students’ knowledge, skills, and attitudes. It is a documentation of the student's growth. Portfolios are portraits of the students during a term or throughout the year.
• Anecdotes-
• The anecdotal record refers to a written description of a child’s progress that a teacher keeps on a day-to-day basis. It provides observational narrative records of significant incidents in a child’s life.

Thus from the above-mentioned points, it is clear that practical records are most appropriate to assess the experimental skills of students in a science classroom.

Science is a powerful way of investigating and understanding the world. Therefore, the teaching-learning of science must enable children to examine and analyse their everyday experiences. 

Key Points

The skills developed in the students through the above activity are-

• Children raise questions, form hypothesis and test them, record observation, collect, organise and record data, manipulate materials and examine their innovative ideas.
• Children get the opportunity to share their ideas and findings with their peers and adults.
• Students develop the ability to inquire, explain, analyse, and interpret scientific processes and phenomena more than their ability to recall specific facts.
• For example, experimenting with objects to see how the water flow and how the refill deviate the path of water etc. the learners are engaged in finding out how the world around them works.
• They learn through observation and interaction with the environment around, nature, things and people both through action and languages.
• This will promote challenging and allow independent thinking, and multiple ways of being solved encourage independence, creativity and self-discipline in learners.
• It will promote experimentation, ability to think logically and rationally and maybe her attitude of inquiry and interest in science.

Thus from above-mentioned points, it is clear that the skills developed in the students through this activity are observation, experimentation and creativity.

Science is dynamic, expanding body of knowledge covering ever-new domains of experience. It is an organized system of knowledge that is based on inquiry born out of natural curiosity, logical reasoning, and experimentation. It is this organized knowledge with inquiry, logical reasoning, and experimentation as its central themes, that we call science. Science may rightly be said to be a domain of inquiry. 

Key Points

Nature of science- 

• Science is a particular way of looking at nature.
• Science is a rapidly expanding body of knowledge
• One of the most important characteristics of science is that even the most established theories can be modified, or even abandoned if new experimental results do not fit into the existing theories.
• Science is always tentative-
• Even the most established and universal laws of science are always regarded as provisional, subject to modification in the light of new observations, experiments, and analyses.​
• Science is a truly international enterprise.

Thus from the above-mentioned points, it is clear that the statement 'Even the most established and universal laws of science are always regarded as provisional, subject to modification in the light of new observations, experiments, and analyses is correct about the nature of science.

We, in our daily lives, use energy from various sources for doing work. We use diesel to run our trains. We use electricity to light our street-lamps. Or we use energy in our muscles to cycle to school. 

• By this standard, children are aware of what constitutes energy, energy is what we used in making food, for travel, etc.
• What we need to do now is to develop their ideas to save energy. We would start by analyzing what we have been using and the energy sources our friends are using.
• Children understand energy better through the activities given in the text.
• They are also expected to make a list of energy sources and what they use and also find out their ingredients and their sources.
• The child should also investigate whether the sources are conventional or non-conventional.
• For this, we should ask a student to write Write at least five ways to save energy, Make a model/project to depict energy-saving, and encourage students to save energy in various ways in their lives. Also, ask them to tell their friend about energy saving.

Thus from the above-mentioned points, it is clear that options B, C, and D are correct.

Concept:

• The solar system consists of nine planets which is as shown in below diagram.
• The time period of a planet to revolve around the sun is directly proportional to the distance from the sun.
• If a planet is far from the sun, the time taken to make a complete revolution is comparatively more than which is close to the sun

Conclusion:

The planets nearer to Sun as compared to earth are Mercury and Venus.

These two planets hence will have a shorter time period of revolution. 

The correct option is Mercury and Venus.

Additional Information

Concept:

Melting Point:

Melting point is the temperature at which the solid converts into liquid. 

Metals usually have higher melting point as compared to non - metal.

Explanation:

If an element have lesser temperature than melting point, it will be in solid. 

Given melting points

Alumunium 666 °C

Iron 1535 °C

Sulphur 113 °C

So, Below 666 °C, Alumunium will be solid. 

So, AI and Fe are solids at 200 °C. is the correct option.

Considering other option

Fe, S and AI are solids at 200 °C

• This is wrong, as for sulphur the melting point is 113 °C. So, it will be liquid.

Only S is solid at 200 °C

• S is liquid at  200 °C as he melting point is 113 °C.
• Only Fe is solids at 200 °C
• This is also wrong because  Aluminium (AI) is also solid.

Concept:

Electric Current and voltage:

• The rate of flow of charge is called electric current.
• For electric current to flow, there should be a potential difference between the two points.
• Potential difference is work done in moving a unit positive charge from one point to another.

Electric Circuit:

• The electric circuit is the path of the current.
• It contains a battery, connecting wires, and electrical devices like a bulb, fan etc.

Ohms Law:

The potential difference (V) is the product of current and resistance at a particular temperature.

V = IR

V is voltage, I is current, R is resistance.

Resistance is the ability to resist the flow of current. 

Explanation:

Given,

• The positive terminal of a battery V is connected to a bulb B1.
• It is connected to resistor R and another Bulb B₂.
• Now, by Ohms Law, when the resistance will increases, the current will decrease.
• Bulbs are also having resistance.
• So, the net resistance will be increasing if the R will increase.
• If R is increased, the current will decrease and hence less current will be drawn.
• So, if the current is less, both bulbs will be dimmer.
• Power in the bulb is given as P = I² R.
• So, if I decrease, P will also decrease.

Correct option is 'both B1 and B2 will become dimmer.'

Concept:

Thermometer: ​

• A device that measures the temperature is called a thermometer.
• A thermometer is based on the principle of thermal expansion.
• Mercury, liquid metal with high density is used.
• More the heat more will be the expansion.

Conclusion:

Statement A Says, The range of the clinical thermometer is from 35°C to 42°C. This is correct as the body temperature is usually around this.

Statement B says the range of laboratory thermometer is usually from 10° C to 110° C. This is wrong as the range is -10° C to 110° C. 

Statement A and is correct but Statement B is false

CONCEPT:

• Cyclone: A cyclone is a rotating low-pressure weather system with inward-spiralling winds, which spins clockwise in the southern hemisphere and anticlockwise in the northern hemisphere.
• The eastern coastal states are Tamil Nadu, Andhra Pradesh, Orissa and West Bengal.
• The western coastal states are Gujarat, Maharashtra, Goa, Karnataka and Kerala.
• The 4 union territories lying on the coast-line are Daman & Diu, Puducherry, Lakshadweep Islands and the Andaman & Nicobar Islands.

EXPLANATION:

• Puri is most likely to be affected by a cyclone because the east coast is more prone to cyclones and puri is situated on the East coast of India.

The reason is more prone to the cyclone is:

• The temperature and salinity of the Bay of Bengal are more than the Arabian sea.
• Prevailing of Easterly Subtropical Jetstream.
• The Bay of Bengal is very active during the end of the monsoon (Oct to Dec) because a lot of freshwater mixes in it via great rivers Ganga Brahmaputra etc.

NOTE: Porbandar, Mumbai, and Goa are situated on the western coast of India. Only Puri is situated on the eastern coast of India.

Concept:

The movement of energy from one place to another is called energy transfer. Heat transfer mainly takes place due to temperature differences.

There are three modes of Heat transfer.

The fundamental modes of heat transfer are:

Conduction

• Conduction is the method of transfer of heat within a body or from one body to the other by molecules vibrating at their mean positions.
• The bodies through which the heat transfers must be in contact with each other.
• Conduction occurs usually in solids where molecules in the structure are held together strongly by intermolecular forces of attraction amongst them and so they only vibrate about their mean positions as they receive heat energy and thus pass it to the surrounding molecules through the vibration.

Convection:

• Convection is the mode of heat transfer which occurs mostly in liquids and gases.
• In this method, heat transfer takes place through the actual motion of matter from one place within the body to the other.

Radiation

• Radiation is a form of heat transfer.
• It does not require any medium and can be used for the transfer of heat in a vacuum as well.
• This method uses electromagnetic waves which transfer heat from one place to the other.

Explanation:

• The air near a heat source gets hot and rises. the air from the sides comes in to take its place.
• This process is convection.
• The hot air is having a lower density.
• When heated it rises.
• After rising, the area remains vacant.
• The vacant space is filled by a convection current of air from the cooler area.

So, the correct option is convection.

Concept:

• Force: A force is something that changes the state of rest or motion of a body.
• It causes the body to start moving if it is at rest or stops if it is in motion or deflects from the initial path.
• Force is a vector quantity having SI unit Newton (N) and dimension (MLT-1).
• Newton’s First Law: It states that a body continues in its state of rest or uniform motion in a straight line until and unless an unbalanced force acts on it.
• Newton’s First Law is also known as the law of inertia.
• Inertia is the property of the inability of a body to change its position of rest or uniform motion in a straight line.
• It is valid only in an inertial frame.
• Newton’s Second law of motion: The rate of change of momentum of a body is directly proportional to the resulting force acting on  a body

Mathematically

 $\vec F \propto \frac{{d\vec P}}{{dt}};or;\vec F = m \times a$

• Newton’s Third law of motion: According to this law, for every action, there is an equal and opposite reaction.
• When two bodies A and B exert force on each other, the force by A on B is (i.e., action represented by FAB) is equal and opposite to force by B on A (i.e., Reaction FBA).

That is  FAB = - FBA

• These forces are called action-reaction force but we cannot say the particular force is action and the other one is a reaction.
• Action and reaction always act on different bodies.

Explanation:

According to Newton’s Third law:

• Newton's third law explains the nature of the force.
• When two bodies experience some force between them each body exerts the force on the other body.
• There is no single force between them Force always act in pair.
• The force by the first body on the second body is called action force (F₁₂).
• The second body also applies an equal and opposite force on the first body is called reaction force (F₂₁).
• From Newton's law,
• F12 = - F21
• The negative sign indicates that the two forces act opposite to each other.

 

• Let a book lie on the table.
• The weight of the book W acts vertically downward.
• It is the action force applied by the book on the table.
• But because of this force whether the book moves down. No.
• It means the resultant force on the book-table system is zero.
• It is possible only when the table applies an equal and opposite reaction force R on the book and R = - W
• This proves that action and reaction forces are equal and opposite.

Every action is equal and opposite on different objects

So, the Action (Weight) and reaction (normal) forces act on the object book.

Concept:

Winnowing:

• It is an ancient agricultural method used to separate the grain from the straw.
• It is also used to remove pests from stored grain.
• Husk from wheat grains is separated from heavier seeds of grain by the process of winnowing.
• Winnowing is used to separate heavier and lighter components of a mixture by wind or by blowing air.

Sieving:

• Sieving allows the fine flour particles to pass through the holes of the sieve while the bigger impurities remain on the sieve.
• In a flour mill, impurities like husk and stones are removed from wheat before grinding it. Usually, a bagful of wheat is poured on a slanting sieve.

Filtration:

• Filtration can be used to separate components of a mixture of an insoluble solid and a liquid.
• It is the process of separating suspended solid particles from the fluid either by chemical or physical processes.

Explanation:

• Husk is separated from heavier seeds of grain by winnowing - Correct
• Difference in the size of particles in a mixture is utilized to separate them by the process of sieving and filtration - Correct.

Concept:

Pressure: 

• The pressure is the physical quantity which is defined as the force acting per unit of area.

$P = \frac{F}{A}$

• P is pressure, F is force, A is an area.
• The SI unit of Pressure is Pascal.

Pressure by Liquid

• The liquid exerts pressure on the walls of its container.
• Equal pressure is applied at equal height in all directions by the liquid.

Pascal's Law:

• Pascal's principle states that pressure applied to fluids is equally transmitted in all directions, to all parts of the fluid, and to all parts of a container.
• The increase in pressure at one point of the enclosed liquid in an equilibrium of rest is transmitted equally to all other points of the liquid and also to the walls of the container, provided the effect of gravity is neglected.

Conclusion:

• The pressure at a point is equally transmitted in all directions.

Concept:

Image formation by Plane mirror

• The plane mirror always forms a virtual image of a real object. The virtual images can’t be formed on a screen.
• The size of the image formed by a plane mirror is equal to the size of the object.
• The distance between object and mirror is the same as the distance between the mirror and the image.
• The image is laterally inverted, which means the left-right inversion.
• For example, the left hand of the object will appear on the right side of the image.

​Explanation:

So, 

• Statement A is false, as image size is equal to object size.
• Statement B is true, as the distance between image and mirror is the same as the distance between object and mirror.
• Statement C is true, as the image is laterally inverted.
• Statement D is true, as the image is virtual.

B,C and D are tue.

Concept:

• On the basis of the number of cells, organisms can be divided into two types 1. Unicellular Organisms 2. Multicellular organisms

1. Unicellular organisms/Single-celled organism are made up of a single cell only. Ex- Amoeba, Paramecium, Euglena, Yeast, etc.
2. Multicellular organisms are made up of many cells. Ex- animals, plants, etc.

• Multicellular organisms exhibit different levels of body organization like cellular, tissue. organ & organ system level of body organisation

Explanation:

• Among the given options embryo is multicellular, the rest of the three are single-celled or unicellular.

Justification:

• The paramecium is a ciliated protozoan. It comprises a single cell only.
• The egg of a hen is single-celled, however, it becomes multicellular after hatching.
• A zygote is a structure formed after the fusion of male & female gametes, it is single-celled only.
• The zygote differentiates to form the multicellular embryo. The embryo further differentiates to form the entire body of the organism.

Concept:

The changes occurring in the environment can be divided into two types - Physical changes & Chemical changes.

Physical change -

• Properties such as shape, size, colour and state of a substance are called its physical properties. A change in which a substance undergoes a change in its physical properties is called a physical change. A physical change is generally reversible.

Chemical change -

• A change in which one or more new substances are formed is called a chemical change. A chemical change is also called a chemical reaction.
• The chemical change is irreversible.

Explanation:

• A - When food gets spoiled, it produces a foul smell because of the microbial growth, which results in discolouration & change in food's quality.
• B - A slice of apple acquires brown colour when kept out for some time because the apple contains iron and when it is cut with the knife the iron present in the apple reacts with the atmospheric oxygen to form iron oxide. This represents an oxidation reaction.
• C -  When an ant bites, calamine is used to ease the irritation on the skin because the ant's bite contains an acid that gets neutralised when rubbing with the basic calamine. This represents a neutralisation reaction.
• All three points represent a chemical change.

Concept:

Metals:

• The elements readily form positive ions (cations) are called metals.​
• Metals are usually solid, a good conductor of heat and electricity, malleable, ductile, sonorous, and have good tensile strength.
• Sodium, Potassium, Magnesium, Iron, Copper, Silver etc are few examples of metals.
• ​Metals react with oxygen to form their respective metal oxides, this reaction goes in the manner given by the general equation.

​Metal + oxygen → Metal oxides

• To test the acidity and basicity of these metal oxides, they are made with water and then react with water and then tested with litmus paper.
• A basic solution turns litmus to blue whereas an acidic solution turns blue litmus to red.
• Metals produce basic oxides when dissolved in water.

Non-Metal:

• The physical properties of non - metals are the opposite of metals. For example, They are insulators, have lower tensile strength, dull appearance.
• They form negative ions by accepting or gaining electrons.
• Generally, the Oxides of non-metals are acidic in nature.

Explanation:

Magnesium ribbon gives magnesium oxide when burnt in the air. The ribbon burns with bright white light or white flame.

• When magnesium metal burns it reacts with oxygen present in the air to form a compound called magnesium oxide.
• This is an exothermic reaction and intense heat is produced.
• The reaction produces white powder or white ash as magnesium oxide.
• The balanced chemical equation is,

​2Mg(s) + O2(g) → 2MgO(s) + Energy

• This white ash is Magnesium oxide and it can be given as

Mg + O2 → 2MgO

• When this White ash (Magnesium oxide) is dissolved in water (H2O) it gives Magnesium Hydroxide.

MgO + H2O → Mg(OH)2

• When magnesium ribbon is burnt in the air, then it from MgO. This MgO when dissolving in water forms Mg(OH)2 which is basic in nature (pH = 10.1).

So, this solutions blue litmus remains blue, whereas the red litmus turns blue.

​

Important Points

• Non-metallic oxides are acidic in nature and metal oxides are basic in nature by usual convention.
• Some metal oxides, for example, oxides of aluminium and zinc show both acidic and basic nature. Such oxides are called amphoteric oxides.

Additional Information

• The scale to decide the acidity and basicity is the pH scale.
• It is a scale from 0 to 14. 0 for most acidic, 14 most basic, and 7 is neutral.
• The pH scale is determined by the presence of hydrogen ion H+ concentration in the aqueous solution. The more its concentration more acidic the solution will be.
• The basic solution has more OH - ion concentration than H+ ion.

Concept:

Metal reactivity series:

• The metals are arranged in reactivity order that is known as the metal reactivity series.
• The more reactive metals are present at the top of the series whereas the less active metals are put at the end of the series.
• The metal reactivity series is as follows-

​

Importance of the series-

• The metal activity series is used to predict displacement reactions.
• Metals that are above hydrogen in the series can displace hydrogen from acids.
• Metals that are below hydrogen in the series cannot displace hydrogen from the acids
• Metals that are higher in the activity series can displace metals that are lower to them from their salts.

Explanation:

For example, zinc can displace copper from a solution of copper sulfate because zinc is above copper in the activity series.

• Since copper is less reactive than zinc, so it cannot displace zinc from its salt solution.
• Copper is less reactive than zinc and so placed below zinc in the reactivity series of metals.
• A less reactive metal cannot displace a more reactive metal from its salt solution.

​Hence, copper cannot displace zinc from its salt solution the reason is copper is less reactive than zinc.

Explanation:

• Bacteria can be harmful in many ways. Some of the bacteria cause diseases in human beings, plants and animals.
• Such disease-causing bacteria are called pathogenic bacteria.
• Tuberculosis, pneumonia and Typhoid are diseases caused by bacteria.
• TB (tuberculosis):
• It is caused by the bacteria ''Mycobacterium tuberculosis''.
• It attacks the lungs however, the bacterium can also affect other body organs like the spine & brain.
• The major symptoms are Heavy coughing, chest pain, fever & chills.
• Typhoid: 
• It is caused by the pathogenic bacteria Salmonella typhi
• It is spread through contaminated food and water.
• It generally enters the small intestine and then migrates or moves to other organs through blood.
• The symptoms include Constant high fever (39oC to 40oC), Stomach pain, Constipation, Loss of appetite & Weakness.
• Pneumonia:
• It is caused by Bacteria like Streptococcus pneumoniae and Haemophilus influenzae.
• It infects the alveoli (air-filled sacs) of the lungs. As a result of the infection, the alveoli get filled with fluid leading to severe problems in respiration.
• The symptoms of pneumonia include fever, chills, cough and headache.
• In severe cases, the lips and fingernails may turn grey to bluish in colour.

Additional Information

Explanation:

The correct match is - a - iii, b - ii, c - iv, d - i

• Aspergillus:
• It is a Fungus genus that belongs to the class Ascomycetes or the sac fungi.
• It includes several species like A. Proliferans, A. Fumigatus, A.Flavus & A. Niger
• ​Lactobacillus: 
• Lactobacillus is a gram-negative bacteria.
• It promotes the formation of curd. It multiplies in milk and converts it into curd.
• Paramecium:
• The paramecium is a ciliated protozoan.
• It comprises a single cell only.
• Spirogyra:
• Spirogyra is a free-floating green algae. It belongs to the Chlorophyta kingdom.
• Spirogyras are filamentous algae that consist of thin unbranched chains of cylindrical cells.