CTET Paper 2 Maths & Science 1st Jan 2022 (English-Hindi) (Previous Year Paper)

Critical period: There are some periods in the life of the child that are crucial for development and learning. 

• A critical period is one when the child is maturational ready to acquire a skill. During this period the child must have favourable experiences, which will help her to acquire the skill. If the favourable experiences come after the critical period is over, the child finds it difficult to learn.

Key Points

• A critical or sensitive period is that time period in life when an environmental influence has its greatest impact on the development of the child.
• During these periods if the child has favourable experiences, her development will be fostered. If in these periods experiences are unfavourable, development suffers.
• During this period, specific experiences affect the development of the child more than they do at other times.
• Such periods are critical for development because during these periods the child is ready to learn a particular skill.
• At times, the damage done because of unfavourable experiences may be irreversible. These periods when a child is particularly sensitive to the conditions in her environment are referred to as critical periods or sensitive periods.
• Thus, the Sensitive period’ in child development is referred to as the optimal period for the development of specific capabilities.

Additional Information

• There are critical periods in prenatal development as well. It has been observed that the first three months of pregnancy are by and large critical for most body systems and exposure to harmful environmental factors during these months can cause major developmental defects.

Development: The term 'development' refers to a progressive series of changes that occur in an orderly, predictable pattern as a result of maturation and experience.

Key PointsDevelopment is always in a sequence:

• Every living being followed a pattern of development. A child also develops in an orderly sequence that is almost similar in all children.

Each stage of development leads to the next; for instance, all children first learn to sit without support before they learn to stand up.

Cephalocaudal:

• One of the sequential patterns of development relates to the two directions in which development takes place. Normally, the development of the upper portions of the body precedes the development of the lower portions. This is known as the 'cephalocaudal' or "head to toe" sequence.
• This means that improvements in the structure and function of a child's body come first in the head region, then in the trunk and last in the leg region. This growth pattern helps to explain why children sit before they can stand and crawl before they can walk.

Thus, Cephalo – Caudal principle of development states that development proceeds from head to toe.

Additional Information 

• Secondly, the development moves from the centre line of the body outward towards the distant or peripheral parts referred to as 'proximodistal' or 'near to far'.

Thus, Cephalo – Caudal principle of development states that development proceeds from head to toe.

Any development process proceeds through some stages and each development stage differs from the other.

Each stage of development has its characteristics. The transition from one stage to the next is gradual rather than sudden. 

• Infancy Birth to 2 years
• Early childhood 2 years to 6 years
• Later childhood 6 years to 12 years
• Adolescence 12 years to 18 years

Key Points

• Adolescence is a phase of the life of a person when he is no more a child and not yet an adult. Life is full of tremendous energy. Curiosity and experimentation at one time pave the path to success and at other, may cause uncertainty.
• Thought becomes abstract and idealistic. This is a critical time in life because the experiences, knowledge, and skills acquired in adolescence have important implications in adulthood.

 Thus, it concludes that Thought becomes abstract and idealistic during the period of Adolescence.

Important Points 

• Infancy: Development is an ongoing process. It starts from the birth of the child and goes up to death.
• At birth, the proportions of the body are very different from those of the adult. Infants, during the first two weeks, are called neonates.
• Early childhood: Early childhood is generally referred to as the preschool period. During the period between two and six years, children enlarge the scope of their behavior. By the time a child is three years old, positive emotions like love and affection are shown.
• In the pre-school period, mental/intellectual development is characterized by the rapid expansion of cognitive abilities. Children become more curious and eager to seek information, keep it in order and use it.
• Late Childhood: Physical growth during late childhood occurs faster than at any other time since infancy. Older children in late elementary and early middle school find it hard to adjust to their changing bodies and may feel self-conscious, and fearful that everyone is staring at them.
• It is important at this time for the parents to be available to talk to their preteens about any questions troubling them. During this time, children are attending school and are becoming more active. Several important physical changes happen as a child moves through this stage.

Piaget (1896 – 1980) was born in Switzerland. He was a student of biology, and also had a keen interest in psychology and philosophy. His interest in the study of cognition evolved while working in a laboratory.

Key PointsProcesses central in Cognitive Development: Piaget’s theory has three central concepts –

• Schemes for an organization: Piaget proposed that people are born with a tendency to organize their thinking into schemes (schema). These schemes are psychological (mental) categories in which people organize knowledge. These schemes develop and become more complex with experience as one grows from an infant to an adult.
• For example: Suppose Raman, a child in his early childhood, sees a dog for the first time? When does he first time see a dog does he ‘know’ that the animal he sees is a dog? He does not, however, his experience of observing the dog for the first few times, helps him in developing a scheme for understanding dogs.

Thus, rearranging schemas, and linking them with other schemas to create a strongly interconnected cognitive system in Piaget’s theory is referred to as Organization.

Additional Information Adaptation: 

• Adaptation, as you may have studied in Biology, is a process through which living beings adjust to their environment.
• Two basic processes are involved in adaptation: assimilation and accommodation. Assimilation takes place when people try to understand something new by fitting it into what we already know. Accommodation occurs when a person must change existing schemes to respond to a new situation.

 Equilibration:

• When Raman could no more fit his observation of the cat into the existing scheme ‘dog’, he must have felt some mental confusion or a situation of imbalance. This is known as cognitive disequilibrium.
• He would have wanted to remove this imbalance and regain balance. And in this process of trying to regain balance, a new mental scheme got developed – he constructed new knowledge(about cats and also about dogs). This process of searching for a balance to make sense of a new experience is called Equilibration.

Stages in Cognitive Development: Piaget’s theory proposes that Cognitive Development universally follows a pattern of four stages. As a person progresses to higher stages, her/his thinking becomes more refined and evolved. The fourth stage is the highest stage of cognitive development and is primarily located during pre-adolescence age till adulthood. 

• Sensorimotor Stage
• Preoperational Stage
• Concrete operational Stage
• Formal operational Stage

Key PointsConcrete operational stage: This stage spans from seven years to eleven years. That is middle school years. In this phase, children become capable of decentring and reversing actions mentally. Therefore, they can apply the conservation principle.

​This leads to the ability to think in the following ways:

• Children can understand that if we add and subtract the same amount from a given thing then there is no change, or there is compensation for the change.
• They are also able to classify objects based on one feature (say pickup all square objects from several shapes).
• They develop the capacity of applying a logic requiring seriation. That is, make sense of a series like A<B<C. Children can understand that B can be greater than A but smaller than C at the same time.
• Children develop the ability to engage in thinking based on reversibility. That is, s/he will be able to understand that if 4 + 2 = 6, then 6 – 2 = 4.
• Thus, children in the concrete operational stage can solve problems mentally but the problems themselves have to be related to materials and not symbols.

Additional InformationSensori-motor Stage: This stage spans from birth to two years. As the name of the stage suggests, children during the initial part of this stage, primarily make sense of the world through their senses – touching, tasting, listening, seeing, and sensing. The developments that take place in this stage include:

• Object permanence
• Co-ordinating reflexes
• Greater control over body movements
• Co-ordinating simple motor actions

Preoperational Stage: This stage spreads from two years to seven years. Elementary school teachers must understand this stage as the child starts attending school during the later part of this stage. The mental processes described in the previous stage are fairly developed by this stage:

• egocentrism
• not able to reverse
• unable to decentre

Formal operational stage: This stage starts from around eleven years and goes on till adulthood. That is, they gradually become capable of abstract thinking. That is, their thought is no longer tied only to concrete things; they can think and engage with symbols (like numbers).

• It is important to note that mathematics and grammar are subjects that demand higher abstract thinking as the student has to work with symbols and with ideas that may not be visible in concrete reality. It is only in this stage that children’s capacity to think mathematically emerges. Such thinking demands the ability for hypothetical (assumptions based), and deductive reasoning.

Constructivism: Constructivism is centered on the idea that human knowledge and learning are actively constructed by the learner, not passively received from the environment.

• Knowledge is always someone's knowledge. It is created or constructed by the experiencing individual. It is not impersonal or absolute.
• Learners actively build or 'construct' this new knowledge. They do this on the bedrock of their prior knowledge. Learners in a classroom have their individual experiences and a cognitive structure, which are built on those prior experiences.

Key PointsSocial Constructivism:

• Social constructivism is founded on the thesis that social processes are central to learning and cognitive development.
• It 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.
• Social Constructivism centers around the idea that the culture is a constituent of the mind and therefore provides for structures that determine the construction of reality.
• In this sense, no knowledge constructions are asocial or acultural. The learner appropriates and constructs meanings in response to his or her experiences in the social contexts.

Thus, socio-constructivist theorists consider the child as an active being involved in the creation of knowledge.

Lev Vygotsky is a Russian Psychologist who proposed the theory of Socio-cultural development. In this theory, Vygotsky emphasizes the role of society and culture in the development of the child. According to him, there are three main needs for the development of the child and these are- Social Interaction, Culture, and Language.

 Vygotsky also proposed three basic needs of students during learning, these are:

• Zone of proximal development (ZPD)
• Scaffolding
• Make knowledgeable others (MKO)

Key PointsScaffolding: Scaffolding  can be defined in simpler terms as “a technique to provide the right kind of support in the right amount at right time to increase a child’s competence.”

• Scaffolding is a technique to provide the right kind of support in the right amount at right time to increase a child’s competence.
• It helps a learner to move from a Zone of Actual Development to a Zone of Proximal Development and finally reach to Zone of Desired Development, with the help of a more experienced person like peers, elders in the family, or teachers.

Thus, encouraging dialogue among students and providing scaffolding are examples of creating a zone of proximal development.

Important Points Zone of Proximal Development (ZPD):

• Vygotsky’s idea of the Zone of Proximal Development (ZPD) has explained the role of interaction in learning.
• It is an area where a child cannot solve a problem alone but can do it successfully if an opportunity to interact with a more experienced peer is given.

Additional InformationTransfer of learning: It implies that training in one faculty of the mind may help in the functioning of older faculties as well as various faculties of mind - memory, reasoning, judgment, observation, etc. - are directed or trained through various academic subjects. 

• Languages and mathematics give training to the mind which helps in learning other subjects. A person who possesses a good knack for language can learn and retain any fact easily.

 Positive reinforcement:  Positive reinforcement is an increase in the probability of behavior due to an increase in the contingent event.

• Jane, a new manager in a company, began praising workers for submitting their reports on time. In a couple of weeks, this reinforcement by praise greatly increased on-time reports.
• Positive reinforcement, when appropriately used, is one of the most powerful of all behavior change tools.

Lev Vygotsky is known as the proposer of social constructivism. Social Constructivism approach talks of the importance of social interaction and context in learning.

• He believes that learning is social in nature. Through interactions, children shared their views and make their own meaning.
• It does not focus much on individual learning rather it emphasized social context; knowledge is mutually built and constructed.

Key PointsScaffolding: Scaffolding  can be defined in simpler terms as “a technique to provide the right kind of support in the right amount at right time to increase a child’s competence.”

• Scaffolding is a technique to provide the right kind of support in the right amount at right time to increase a child’s competence.
• It helps a learner to move from a Zone of Actual Development to a Zone of Proximal Development and finally reach to Zone of Desired Development, with the help of a more experienced person like peers, elders in the family, or teachers.
• Hence, Vygotsky proposed that new knowledge is constructed in a zone between what the child knows and what she is capable of knowing with support.

Important Points Zone of Proximal Development (ZPD):  Vygotsky’s idea of the Zone of Proximal Development (ZPD) has explained the role of interaction in learning.

• It is an area where a child cannot solve a problem alone but can do it successfully if an opportunity to interact with a more experienced peer is given.

MKO (more knowledgeable others)- Vygotsky defined the “More Knowledgeable Other” (MKO) as anyone who has a better understanding or a higher ability level than the learner, particularly in regards to a specific task, concept, or process. MKO could be teachers, parents, tutors, and even pe

To cater to children in a class with the varied ability and intelligence levels, varied interests and attitudes, varied age levels, and varied socioeconomic backgrounds, this approach emphasizes ‘learning by doing, ‘experiencing’ and ‘active participation on the part of the child. 

The child-centered approach is thus largely guided by the following two basic principles or

Assumptions:

• Children create their knowledge from their experiences and interactions with the world around them.
• Teachers foster children’s learning and development best by building on the existing knowledge, abilities, interests, needs, styles of learning, and strengths of the children in the class.

Key Points In a child-centered classroom:

• The child is not a passive but an active participant in the classroom process.
• Has a democratic climate so that the child gets maximum opportunities for interaction with other children in the class, with the teacher, and with a variety of teaching-learning material.
• The environment in the class is warm, joyful, and encouraging in which children feel secure and confident and participate freely and without fear.
• Varieties of activities/opportunities are available in the classroom, which enables each child to learn at her/his own pace and in tune with her/his learning style.
• The teacher is a friend and a facilitator for the children and allows the center of the action to shift in the classroom from herself/himself to the children.
• Activities planned by teachers and carried out by children become the medium of learning for the child rather than only the textbook.
• Teacher adopts a variety of teaching-learning strategies to address the needs of all children at the same time.

Thus, a class in which the students are sitting in groups and the teacher takes turns going to each group is illustrative of a child-centered classroom.

Lawrence Kohlberg's theory on moral development or moral reasoning can be applied to the classroom where rules, standards, and consequences are concerned. As an educator, consider where your students' personal development lies in terms of Kohlberg's six stages into three levels.

Key Points Level-2: Conventional morality:-   During this time, adolescents and adults internalize the moral standards they have learned from their role models and from society. At this level, people approach moral problems as members of society. There are two stages at this level of morality:-

• Stage 3 - The “good boy–good girl” orientation, or the morality of interpersonal cooperation. The desire to obey rules because they promote social harmony first appears in the context of close personal ties. Stage 3 individuals want to maintain the affection and approval of friends and relatives by being a “good person”—trustworthy, loyal, respectful, helpful, and nice. The capacity to view a two‐person relationship from the vantage point of an impartial, outside observer supports this new approach to morality. At this stage, the individual understands ideal reciprocity, as expressed in the Golden Rule.

Hence, The idea of ideal reciprocity as exhibited in the Golden Rule is the key characteristic of stage third  “good boy–good girl” orientation of moral development theory.

Important Points

 Refer to the table to be familiar with all the levels of Kohlberg's theory.

Howard Gardner (1983), an American Psychologist, proposed the theory of multiple intelligences.

• In his book ‘Frames of Mind’, he pointed out that he did not believe there was “one form of cognition which cut across all human thinking. There are multiple intelligences with autonomous intelligence capacities.” So, intelligence cannot be viewed as a single entity.

Key PointsMain Objectives of the theory of Howard Gardner:

• There are different types of intelligence that are independent of each other. Further, people may have varied combinations of this intelligence.
• Gardner initially proposed eight types of intelligence which later on he increased to nine. Thus Gardner views each individual as a unique combination of various intelligence, hence we cannot say that one is more intelligent and another is less intelligent.

Each one of us is talented in unique ways.

• The utility and value of each type of intelligence are culturally determined in the sense that an individual’s intelligent performance is determined according to the high desirability, usefulness, and demands of society for particular types of intelligence.
• For instance, one type of intelligence highly valued in a particular society may be of little significance in another.
• Hence, intelligence is a set of several distinct abilities according to Howard Gardner.

Additional InformationThe nine types of intelligence as given by Gardner:

• Linguistic Intelligence
• Logical-mathematical Intelligence
• Musical Intelligence
• Bodily-kinesthetic Intelligence
• Spatial Intelligence
• Interpersonal Intelligence
• Intrapersonal Intelligence
• Naturalistic Intelligence
• Existential Intelligence

Individual differences: It refers to variation among individuals concerning a single or several characteristics. According to Plato, “No two persons are born exactly alike, but each differs from the other in natural endowments, one being suited for one occupation and the other for another”.

Key Points

• Every individual is unique and has his learning style and pace of learning. The general meaning of pace of learning reveals at what rate an individual learns.

Every learner does not learn at the same pace.

• In a class, learners learn differently, at a different pace, and as a teacher in a face-to-face class, it is almost impossible to cater to everyone’s learning needs but an understanding of these concepts will help us in accommodating diverse learning needs in the class.
• All the students have different environments and they also grow in different environments and cultures, thus their understanding is also different.
• Thus, Both (A) and (R) are false.

Important PointsChildren create their knowledge from their experiences and interactions with the world around them.

• Teachers foster children’s learning and development best by building on the existing knowledge, abilities, interests, needs, styles of learning, and strengths of the children in the class.
• The child is not a passive but an active participant in the classroom process.
• Activities planned by teachers and carried out by children become the medium of learning for the child rather than only the textbook
• Has a democratic climate so that the child gets maximum opportunities for interaction with other children in the class, with the teacher, and with a variety of teaching-learning material.
• Varieties of activities/opportunities are available in the classroom, which enables each child to learn at her/his own pace and in tune with her/his learning style.
• The teacher is a friend and a facilitator for the children and allows the center of the action to shift in the classroom from herself/himself to the children.

Additional Information Teachers can try to facilitate learning for learners at a different pace:

• Never present a lot of concepts at a time. Try to explain every concept and involve your learners to provide explanations of the concepts.
• Encourage learners to give examples based on their own experiences and observations; this will help the learners to link the concept with their own experiences and knowledge.
• If it is group work, you can assign a time-keeper role to one of the learners who will encourage all to complete the task in the given time.
• You should analyze the activity/task before assigning it to learners in terms of the time required to complete the task and plan accordingly.

Gender refers to the socially constructed differences between men and women. It refers to the masculine and feminine qualities, behavior, roles, and responsibilities that society upholds. Gender can be changed / re-oriented.

Gender discrimination: The term gender refers to the assignment of social roles to males and females on the basis of their sex.

Key Points Some of the examples of gender discrimination in a classroom are as follows:

• the segregated sitting arrangement of the boys and girls in the classroom on the bases of just they are of the opposite sex.
• Not equal opportunities are provided to all in discriminated cultures.
• Deciding the work on the respect of sex.
• Example: Maths and science streams are only for boys and arts and languages.
• Example: People say girls should nurse or teachers careers only or Boys should engage in sports and refrain from more creative pursuits.

Thus, encouraging girls to take up languages and arts and discouraging them to take up mathematics and science is an example of gender discrimination.

Important Points

• Gender equality is when people of all genders have equal rights, responsibilities, and opportunities. Everyone is affected by gender inequality - women, men, trans, and gender diverse people, children, and families.
• Gender equity is the process of being fair to women and men. To ensure fairness, strategies and measures must often be available to compensate for women's historical and social disadvantages that prevent women and men from otherwise operating on a level playing field. Equity leads to equality.

Socio-constructivism focuses on the collaborative nature of learning. Knowledge develops from how people interact with each other, their culture, and society at large.

• Vygotsky emphasized the role of language in learning. He has a firm belief that the children who use a lot of private speech are more socially competent than those who don’t.

Key Points

• For Vygotsky, children use a lot of private speech not only for social communication but also to plan, guide, and regulate their behavior in a self-regulatory fashion.
• He believed that children never have a “social” speech and at some point, their speech gets divided into two: speech directed at other people and at oneself (private speech).
• Younger children are often found talking aloud to themselves (for instance, “I will take blue crayon to color this picture”). Children, slightly older may whisper or mutter to themselves while engaged in a task.
• According to Vygotsky, this becomes internalized with age, eventually gets reduced to a silent speech, and finally remains as a thought. It has been found that private speech may not necessarily end with early or middle childhood.

Thus, the relationship between language and thought as per the socio-constructivist perspective is bi-directional.

Additional Information  In Socio-constructivist classroom students rely on others to help create their building blocks, and learning from others helps them construct their own knowledge and reality. 

Characteristics of Socio-constructivist classroom:

• It emphasizes collaboration with others for learning.
• It allows learners to foster their own strategy of learning to perform an activity.
• It views learners as makers of meaning and creators of knowledge through social interaction.

Assessment is considered as a part of the teaching-learning process and is often categorized as assessment of learning, assessment for learning, and assessment as learning.

Key PointsAssessment for learning: Assessment for learning is practiced by teachers during their teaching-learning process. Its main objective is to improve teaching and enhance learning by facilitating learners. It takes place along with the teaching-learning process in the classroom. It is more frequent and mostly unstructured, also referred to as ‘formative assessment’. Assessment for learning:

• Reflects a view of learning in which assessment helps students learn better, rather than just achieve a better mark;
• Includes clear goals for the learning activity;
• Provides effective feedback that motivates the learner and can lead to improvement;
• Reflects a belief that all students can improve.

Important Points Characteristics of Formative assessment:

• It gives regular feedback and a chance for students to reflect on their performance, take advice and improve upon it.
• It helps teachers to plan better and provide supportive, non - evaluative feedback to students.
• It is a type of evaluation that refers to monitoring the child's progress throughout the teaching-learning process.
• It identifies the learning difficulties of students and deficiencies of the teaching process during the instructional procedure.
• It continuously monitors students' progress in a non-threatening environment and enhances students' learning experiences.

Additional Information

• Assessment of learning: It basically focuses on learners’ achievement against some predefined outcomes and standards. Sometimes, it is referred to as summative assessment. Generally, teachers undertake this type of assessment at the end of a Unit or term, or semester in order to grade or rank the learners.
• Assessment as learning: When learners are asked to assess their performance on their own, they use various assessment techniques and strategies to assess themselves. This practice helps learners to identify their knowledge gaps, adopt appropriate learning strategy and use assessment as tool for new learning

Thus, options (i), (ii), (iii) are correct.

Inclusion is an unrelenting process of augmenting learning and participation for all students irrespective of their differences.

• It is a process where diversity in a group with respect to any aspect is appreciated and in which everyone is recognized and respected for his/her worth.

Key PointsInclusion in education: Inclusion starts when exclusionary Introduction to Diversity and Inclusion pressures are removed, the differences between students are respected and each one in the class group feels recognized, accepted, and valued for what he or she is.

• It is a process to bring all students together in one classroom and school, regardless of their strengths or weaknesses in any area, and it seeks to maximize the potential of all students
• It is an effort to make sure that diverse learners – those with disabilities, different languages and cultures, different homes and family lives, different interests and ways of learning – are taught using teaching-learning strategies adapted to individual learning needs
• It is a process that allows every individual to feel accepted, valued, and safe.
• It is a means of enhancing the well-being of every member of the community.

Hence, respect for diversity is the practice that promotes inclusion in education.

Important Points  In Inclusive education the main objectives are-

• All the students of different abilities, differences, and disabilities are treated equally.
• Inclusive education provides barrier-free access for all students.
• Creating an environment in which the child can learn with diversity, not creating a special environment for learning.
• Emphasis on their learning to read instead of emphasizing teaching.
• To use different teaching methods according to the needs of each student, so that every child can have access to the knowledge.
• Equitable education for all, including challenging, backward, disabled children.

Learning Disability: It is a neurological disorder that prevents a person from learning a skill and using it effectively. Generally, it occurs in childhood and is characterized by difficulty with certain skills such as reading, writing, speaking, etc.

Attention deficit hyperactivity disorder(ADHD) is a brain disorder that affects how you pay attention, sit, still, and control your behaviour. It happens in children and teens and can continue into adulthood. Children with ADHD may have trouble paying attention and controlling impulsive behaviours. ADHD is the most commonly diagnosed mental disorder in children.

Key PointsThe main symptoms of ADHD include the following:

• Physical movement: Lack of muscle coordination, so a person who is ADHD-disabled can not move easily.
• ​Inattention: Short attention span for age (difficulty sustaining attention) Difficulty listening to others.
• Impulsivity: Has difficulty waiting for his or her turn in school and/or social games, Takes frequent risks, and often without thinking before acting.
• Hyperactivity: Has difficulty remaining in his/her seat even when it is expected, Fidgets with hands or squirms when in his or her seat; fidgets excessively.

Thus, Attention Deficit Hyperactivity Disorder is a disability that causes challenges in paying attention and sustaining long-duration involvement in tasks.

Important Points

 ADHD children should be treated with certain strategies by a teacher: 

• Use a planner.
• avoid distractions.
• focus on one thing at a time.
• show long-duration movies.
• meditation and exercise.

Additional Information 

• Autism: is a serious mental disorder that affects the communication skill, learning skills, and social skills of the child. the child may feel difficulty in understanding what other people think and feel.
• Dyscalculia (learning difficulties in math): A specific learning difficulty that affects a child's ability to understand numbers and learn math facts. Children with this type of learning difficulty may also have poor comprehension of math symbols, may struggle with memorizing or organizing numbers, have difficulty telling time, or have trouble with counting.

The multilingual approach to education refers to the approach in which learners can interact in their own language and can be a mix of words from more than one language.

Key Points 

• A multilingual class is a class where different languages of culturally different learners are respected. It connects various communities together.
• It helps learners to know about the different cultures. It creates a democratic environment for the learners to learn freely without hesitation.
• Learners are allowed to communicate in a language that they are comfortable speaking.
• It is mainly helpful in countering the ill-effect of losing one's own language as the multilingual approach aims at making use of the languages of learners for teaching-learning.
• Communicating in own language increases the better innate understanding of how language works. It enhances creativity, divergent thinking, and appreciation of local languages.

Hence, it is clear that 'teachers should respect all languages and encourage students to communicate in a language which they are comfortable speaking' will be the most appropriate statement for a multicultural/multilingual classroom.

Hint

• Segregation occurs when students with disabilities are educated in separate environments designed for students with impairments or with a particular impairment.
• Labeling is a cognitive distortion in which we generalize by taking one characteristic of a person and applying it to the whole person.
• Example: Because I failed a test, I am a failure.
• A stereotype is a simplified and/or standardized conception or image with specific meaning, often held in common by people about another group. A stereotype can be a conventional and oversimplified conception, opinion, or image, based on the assumption that there are attributes that members of the other group hold in common.

Inclusive education: According to the concept of inclusive education, all the students of different cultures, languages, regions, intelligent students, weak students, students with disability in learning, etc are taught in the same classroom. So when these types of students learn under the same roof, they can also understand one another and the culture one another.

• In a truly inclusive setting, every child feels safe and has a sense of belonging. Students and their parents participate in setting learning goals and take part in decisions that affect them.
• Inclusive education means creating effective classrooms where the educational needs of all children are addressed irrespective of ability or disability.

Key Points

• Dyslexia: A disorder in children who, despite conventional classroom experience, fail to attain the language skills of reading, writing, and spelling commensurate with their intellectual abilities.
• Autism: is a serious mental disorder that affects the communicative skill, learning skills, and social skills of the child. the child may feel difficulty in understanding what other people think and feel.
• Intellectual giftedness: Intellectual giftedness can be described as an unusual ability to deal with abstract and symbolic learning. Individuals with intellectual superiority can relate facts and ideas about numbers, time, and space in unusual ways. Students with intellectual superiority may or may not do well in school.
• Academic giftedness: Academic giftedness involves the skills and abilities necessary to perform well in school-related tasks. Among these skills and abilities are memory, logical reasoning, and the ability to make meaningful associations of facts and ideas. The facility in convergent thinking is the characteristic of this group of students.
• Thus these all are the disability and according to the concept of inclusive education, all type of children comes into the inclusive classroom such as physically disabled, mentally retarded, intelligent, belonging from different traditions and cultures, **Thus, (i), (ii), (iii), (iv) options are correct.**​

Important Points

Teaching Aids - Teaching Aids are devices by which the teacher helps the students to clarify, establish, and correlate accurate concepts, inspections, and appreciation through the utilization of more than one sensory channel.

• Teachers use teaching aids to make students understand the concepts and improve their learning, especially the students with various learning disabilities.

Learning Disorder: Difficulties in acquiring knowledge and skills to the normal level expected of those of the same age especially because of mental and cognitive disorders are known as learning disorders or learning difficulties.

Key Points

Visual Impaired Child - A visually impaired child is one whose visual impairment interferes with his optimal learning and achievement. 

Teaching Material for Visual impaired Learners: Using appropriate teaching-learning materials is vital for children with visual impairment.

Some of the common teaching-learning materials available in the market for educating children with visual impairment: ​

• Braille: Braille printed books, which have both braille and printed text on each page so that sighted students and adults can read along with students who have visual impairments.
• Tactile globe:  These globes have convex and concave features on the surface denoting coastlines and country borders which will useful for visually impaired students.
• Audio cassettes can also be used for teaching purposes. The audio materials should also have audio so that those without sight can understand their learning effectively.
• Screen reading software: Screen readers are software programs that allow blind or visually impaired users to read the text that is displayed on the computer screen with a speech synthesizer or braille display.

Thus, Visual impairment: Providing read-to-text software is a correctly matched pair of appropriate accommodation strategies for the inclusion of students with specific disabilities.

Additional Information

• Autism: is a serious mental disorder that affects the communicative skill, learning skills, and social skills of the child. the child may feel difficulty in understanding what other people think and feel.
• Dyscalculia (learning difficulties in math): A specific learning difficulty that affects a child's ability to understand numbers and learn math facts. Children with this type of learning difficulty may also have poor comprehension of math symbols, may struggle with memorizing or organizing numbers, have difficulty telling time, or have trouble with counting.

Thinking is the basis of all cognitive activities or processes and is unique to human beings. It involves the manipulation and analysis of information received from the environment. There are different kinds of thinking styles which include creative, logical, concrete thinking, etc.

• Effective listening is an active process and not a passive one to enhance thinking style.
• We will become more effective listeners as we practice at home, in our business dealings, and in other circles. One of the greatest gifts we can give another is that of truly listening.

Key Points Learning can be improved by listening as:

• Treat listening as a challenging mental task. Listening to a presentation of a Listening Skills learner is not a passive act-at least it shouldn't be. You need to concentrate on what is said so that you can process the information into your notes.
• It is, often remarked that listening is not like hearing and that a listener not only hears through the ears but also through the eyes.

Thus, passive listening does not facilitate students’ thinking. 

Additional Information For better learning, a teacher should-

• Helping the student to understand and define the problem.
• Creating a fear-free atmosphere in the class.
• Helping the student in analyzing or getting proper solutions to the problem.
• Encouraging the student to formulate and test the hypotheses.
• Motivate children to solve problems.
• Helping the student to develop critical thinking, open-mindedness, and a spirit of inquiry and discovery.
• The students in primary classes should be taught through various activities and hands-on experiences.
• Learning the concept in mathematics by doing meaningful, hands-on activities related to the concept.
• The teacher teaches their students according to their needs and interest. Teaching should be child-centered.
• The teaching should be connected with real life. The teachers should take examples from the daily life of students so that they feel connected and interested.

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

 Feature of Progressive Education:

• In progressive education, learning should be done by learning by doing.
• Learning is child-centered, in which students have all rights to ask questions and make discussions on various problems.
• Learning by doing promotes the engagement of the students in various activities, which make their thought process divergent, and make them able to explain problems.

Key Points

"Learning by doing" means Activities based learning.

• "Learning by doing" is the process of doing my own hands practically.it encourages the students to participate in their own learning experiences.

Activity-based Learning- 

• The students in primary classes should be taught through various activities and hands-on experiences.
• Learning the concept in mathematics by doing meaningful, hands-on activities related to the concept.
• The teacher teaches their students according to their needs and interest. Teaching should be child-centered.
• The teaching should be connected with real life. The teachers should take examples from the daily life of students so that they feel connected and interested.
• The teacher should use teaching aids from their real environment, nothing is better than this. For example, teachers should use pebbles to teach their students how to add and subtract

Therefore,  we inferred that Facilitating opportunity for hands-on activities is likely to improve learning among students

Context: Context implies the situation of learning, the value of the situation, and signals from environments. We should observe learning in the context including the social, physical, and psychological environment, where it takes place, and also the place and the situation. 

Learning is a relatively permanent influence on behavior, knowledge, and skill. It is a comprehensive process that refers to a change in understanding as a result of practice and experience.

 Key Points For better learning, a teacher should-

• Helping the student to understand and define the problem.
• Creating a fear-free atmosphere in the class.
• Helping the student in analyzing or getting proper solutions to the problem.
• Encouraging the student to formulate and test the hypotheses.
• Arrange activities, and hands-on experiences tasks, so that they can learn conceptually.
• Motivate children to solve problems.
• Give them tips and hints so that they can learn new knowledge.
• they should help to clarify their conceptual structure.
• Assisting the student in perceiving, defining, and stating the problem.
• Helping the student to develop critical thinking, open-mindedness, and a spirit of inquiry and discovery.

Thus, students learn best when they participate in activities that are related to their context and are correct in the context of learning.

Important Points  Characteristics of learning:

• Learning is transferable.
• Learning requires interaction.
• Learning is a lifelong process.
• Learning is a goal-directed process.
• Learning involves problems solving.
• Learning is the growth of organisms.

Knowledge: "Theory of Knowledge" has been construed as a branch of philosophy known as Epistemology. 'Epistemology' comes from the Greek words 'episteme' meaning Knowledge and logos meaning discourse or science. 

• Children come to the classroom with a lot of exposure to the environment.

Key Points

Prior knowledge is knowledge whose truth or falsity can be decided before or without recourse to experience.

• The knowledge that's a priori has universal validity and once recognized as true (through the use of pure reason) does not require any further evidence. Logical and mathematical truths are a priori in nature. They do not stand in need of empirical validations. Traditional philosophers have regarded a priori knowledge as superior to all other knowledge.
• Use the previous knowledge of whatever students know from their environment by connecting it with the topic of teaching.
• By connecting with learners’ prior experience and level, the teacher may and should try to build on the previous knowledge of the learner. There should be an effort on part of the teacher to assess what words pose more difficulty for the learner.

Thus, While introducing a new topic, a teacher should ask questions that relate to the topic to be studied with what students already know.

Lev Vygotsky is a Russian Psychologist who proposed the theory of Socio-cultural development. In this theory, Vygotsky emphasizes the role of society and culture in the development of the child. According to him, there are three main needs for the development of the child and these are-

• Social Interaction
• Culture
• Language

Key Points

Lev Vygotsky proposed a theory of cognitive development known as ‘Socio-Cultural Theory’. He believed that children gain knowledge through social and cultural experiences. 

• When the child is having interactions with peers and adults, they learn the values, beliefs, customs, and language of their culture. As per his socio-cultural theory, development takes place due to the intermingling of culture, social interaction, and language.
• It allows students to perform tasks and to reach levels of achievements (with others’ support) that they would be unable to reach independently.
• 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.
• Thus, the Socio-cultural context of students plays a significant role in the learning process.

Additional InformationCentral Concepts of Socio-Cultural Theory:

• 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.
• Zone of Proximal Development (ZPD) mainly refers to the difference between what a learner can do on his/her own and what he/she can do with someone's help.
• More Knowledgeable Other(MKO) refers to a person with a higher skill level and a better understanding of the concepts than the learners.

Reflection: Reflection is about students becoming aware of their thinking processes, and being able to make those transparent to others.

• It is a process of manipulation of knowledge and its reprocessing towards the set goal, and so, it is goal-directed.
• One ‘thinks’ when in uncertainty or difficulty so as to solve the ‘perplexity’, and the process leads to testing through some action.

Key Points

Dewey believed that effective education through reflection should aim at ‘making sense of the world’, and therefore, this is related to experience. 

• Learners are aware of and control their learning by active participation in reflective thinking.
• Teachers should have to encourage students to ask questions, take part in all tasks, and perform various activities to learn conceptually.
• In the reflective experience in which the environment is used as the object of reflection.
• Reflective learning, therefore, takes place in problem identification, hypothesis formulation, and its testing in action.

Thus, A teacher intends to facilitate reflective skills among her students. This can be done by encouraging students to ask themselves questions about their understanding.

Important Points Dewey’s concept of reflective thought and action, depicted comprises five phases: 

• Disturbance and uncertainty
• Intellectualization
• Formation of Hypothesis
• Reasoning
• Hypothesis Testing.

Lev Vygotsky, a Russian psychologist, proposed a theory of cognitive development known as ‘Socio-Cultural Theory’. He believed that children gain knowledge through social and cultural experiences.

• When the child is having interactions with peers and adults, they learn the values, beliefs, customs, and language of their culture. As per his socio-cultural theory, development takes place due to the intermingling of culture, social interaction, and language.

Key PointsScaffolding: Scaffolding  can be defined in simpler terms as “a technique to provide the right kind of support in the right amount at right time to increase a child’s competence.”

Characteristics of Scaffolding are:

• Scaffolding is a technique to provide the right kind of support in the right amount at right time to increase a child’s competence.
• Scaffolding is a form of facilitation that facilitates learning.
• required assistance is given to children according to their individual needs.
• temporary support is imparted to the children to enhance their learning skills and also correct their mistake points.
• individualized support is provided to children to increase their learning boundaries.
• interaction takes place between the students that give them ample opportunity to study.
• .Thus, A teacher should scaffold students to correct their errors themselves.

Additional Information

• Zone of Proximal Development: The concept of MKO is closely related to ZPD. According to Vygotsky, ZPD is the difference between the present level of development attained without anyone’s assistance and the potential level of development that can be attained under the guidance of MKO.
• MKO (make knowledgeable others): Vygotsky defined the “More Knowledgeable Other” (MKO) as anyone who has a better understanding or a higher ability level than the learner, particularly in regards to a specific task, concept, or process. MKO could be teachers, parents, tutors, and even peers.

The term 'emotion' is derived from the Latin word ‘emovere’ which means to stir up, agitate, excite or move. Emotions are generally referred to as a stirred-up condition involving subjective experience and affective reactions. They may be pleasant or unpleasant. Pleasant emotions are the sources of joy whereas unpleasant emotions are related to disturbing mental states like aggression, fear, anxiety, etc. 

Key Points There are many emotions while dealing with different persons and objects in the environment. They can be negative emotions like fear and anxiety or positive emotions like pleasure and love.

• Anxiety: Anxiety is a state of painful discomfort in the mind. During anxiety, a vague fear or apprehension occurs. You may feel anxious if you don’t know the exact cause. The difference between fear and anxiety often refers to the involvement of the present situation. You can recognize the cause of fear in your present circumstances whereas anxiety may arise due to an anticipated or imaginary situation.
• So that we can say that anxiety will reduce performance in the examination if the learner is nervous and has high anxiety.​

Additional Information  It is also important to understand the functions of emotions, which are discussed as follows:

• Emotions prepare an individual for action: Emotions serve as a link between the situation and the individual’s reaction. For example, if an individual is crossing a road and suddenly sees a truck coming his/ her, the emotional reaction that s/he would display, that of fear which would be linked with physiological arousal.
• Emotions play a role in the shaping of the \future behavior of an individual: Learning takes place as a result of emotions experienced by us and thus, for example, the situations that evoke negative emotions are avoided by us.
• Emotions help in effective interaction with others: Emotions act as signals thus helping individuals understand what the other person is experiencing. The future behavior of individuals can also be predicted based on this.

Motivation: Motivation is a word derived from the Latin word movere which means to move or to move. It is a process that initiates, guides continue, and maintain a certain behavior.

• Motivation is a general term applied to the entire class of drives, desires, needs, wishes, and similar forces.

Key Points Various types of motivations can influence a person. These include achievement, affiliation, self-enhancement**, socialization, competence, power, change, curiosity, attitude, incentive, fear, and aggression motivation.** 

Motivation is of two types intrinsic or extrinsic.

Intrinsic motivation: Intrinsic motivation refers to motivation that comes from inside an individual rather than from any external or outside rewards, such as money or grades.

• The motivation comes from the pleasure one gets from the task itself or from the sense of satisfaction in completing or even working on a task.
• Curiosity is the motivation that comes from the soul of the learner, learners are eager to learn concepts as soon as possible.
• An intrinsically motivated person will work on a math equation,
• for example, because it is enjoyable. Or an intrinsically motivated person will work on a solution to a problem because the challenge of finding a solution provides a sense of pleasure.
• Thus, Curiosity – Intrinsic motivation is a correctly matched pair of a source of motivation and the type of motivation.

Additional InformationExtrinsic Motivation: Extrinsic motivation refers to motivation that comes from outside an individual. The motivating factors are external, or outside, rewards such as money or grades. These rewards provide satisfaction and pleasure that the task itself may not provide.

• An extrinsically motivated person will work on a task even when they have little interest in it because of the anticipated satisfaction they will get from some reward. The rewards can be something as minor as a smiley face to something major like fame or fortune.
• For example, an extrinsically motivated person who dislikes math may work hard on a math equation because he wants the reward for completing it. In the case of a student, the reward would be a good grade on an assignment or in the class.

Conceptual understanding is the understanding in which learners get the knowledge of the roots of the problem. Conceptual learning is easy to get if a learner has any prior experience in the related problem because experience (old ideas) helps them to get the concept (new ideas) in the best manner. 

Key Points A teachers should always try to build conceptual learning among the student, some of the ways to build concepts are:

• By asking students to present their views related to the problem.
• By establishing the inter-relation between the previous knowledge of the students and the concepts.
• In conceptual understanding, knowledge is constructed by the learners on the basis of their prior experiences.
• Conceptual understanding never promotes rote memorization-based learning or coping with the concept from other sources. So the concept is built by direct experiences or by performing various activities related to the problem.
• Organizing activities, seminars, and visits, so that students get socially active helps them to think conceptually.
• So we can say that "Asking students to copy the answers from the notes given by the teacher" never facilitates conceptual understanding.

Important Points Characteristics of Conceptual learning:

• Conceptual learning makes learners thought processes divergent, by which students can think about all the possible positive and negative aspects related to the problem.
• It opposes rote memorization.
• It improves the analysis and observational skills of the learners.
• The path of conceptual learning is from simple to complex, first students have to learn simple concepts, and then they have to learn complex concepts on the basis of simple concepts.
• Conceptual learners always think divergently, they cover all the possible ways to solve the problem,

Concept:

LCM: The LCM of any two is the value that is evenly divisible by the two given numbers.

HCF: The HCF is the greatest number that divides each of the two or more numbers. 

Calculation:

LCM of 198, 135, and 108 is 3 × 3 × 3 × 2 × 11 × 5 × 2 = 5940

HCF of 198, 135 and 108 is 3 × 3 = 9 

⇒ The sum of HCF and LCM is 5940 + 9 = 5949

∴ The sum of HCF and LCM is 5949.

The correct option is 3 i.e. 5949

Calculation:

\(\frac{\sqrt{450}}{\sqrt{338}} \div \frac{\sqrt{125}}{\sqrt{245}}\)

\(⇒ \frac{\sqrt{450}}{\sqrt{338}} \times \frac{\sqrt{245}}{\sqrt{125}}\)

After simplification:

\(⇒ \frac{21}{13}\)

\(∴ \frac{\sqrt{450}}{\sqrt{338}} \div \frac{\sqrt{125}}{\sqrt{245}} = \frac{21}{13}\)

The correct option is 3 i.e. 21/13

Calculation:

(a + b)-1 × (a-1 + b-1)

\(⇒ \frac{1}{(a + b)} \times (\frac{1}{a} + \frac{1}{b})\)

\(⇒ \frac{1}{(a + b)} \times (\frac{a + b}{ab})\)

\(⇒ \frac{1}{ab}\)

\(⇒ \frac{1}{\frac{5}{11} \times \frac{3}{7}}\)

\(⇒ \frac{1}{\frac{15}{77}}\)

∴ 77/15

The correct option is 4 i.e. 77/15

Concept:

Prime Number: Prime numbers are numbers greater than 1. They only have two factors 1 and the number itself. 

Composite number: Composite numbers can be defined as numbers that have more than two factors.

Odd number: Odd numbers have the digits 1, 3, 5, 7 or 9 in their ones place.

Even Number: Whole numbers that have the digits 0, 2, 4, 6 or 8 in their ones place are even numbers.

Calculation:

(a) Prime number can be even number or odd number.

(b) Except 2, all even numbers are composite numbers.

(c) The sum of two prime numbers can be even number or odd number.

(d) If an even number is divided by 2, the quotient is always zero.

The correct option is 3  i.e All (a), (b), (c) and (d)

Concept:

a × (-b) = -ab

Negative integers are always smaller than 0.

a - b = Difference will be a positive integer, where a > b

a - b = Difference will be a negative integer, where a < b

(-a) × (-b) = ab

Positive integers are always greater than negative integers.

Calculation:

Option 4:

a = -1

b = 1

ab = (-1) × 1 = -1

-1 < 0 

The correct option is 4 i.e. Product of a negative integer with a positive integer will be an integer less than 0.

Given:

The area of rhombus = 5880 m²

Length of diagonal₁ = 70 m

Formula Used:

The area of the rhombus = \(\frac{1}{2} × Product\space of\space diagonals\)

(Hypotenuse)² = (Base)² + (Perpendicular)²

Calculation:    

Let assume that diagonal₂ is x

⇒ 5880 = 1/2 × 70 × x

⇒ x = 168 m

Diagonal of rhombus bisect each other at 90° .

Hypotenuse = Side of rhombus

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

⇒ (Hypotenuse)2 = (84)2 + (35)2

⇒ (Hypotenuse)2 = 7056 + 1225

⇒ (Hypotenuse)2 = 8281

⇒ Hypotenuse = 91 m

∴ The side of the field is 91 m

The correct option is 2 i.e. 91 m

Given:

Side of the square = x units

Base of the triangle = x units

Formula Used:

The area of square = (Side)²

The area of triangle = 1/2 × Base × Height

Calculation:  

Let's assume that the altitude of the triangle is h

According to the question:

The area of the square ∶ The area of the triangle 

⇒ (x)² = 2 × 1/2 × x × h 

⇒ x = h

∴ The altitude of the triangle is x units     

The correct option is 2 i.e. x units

Given:

Total surface area of the cylinder = 3.52 m²

Radius of the cylinder = 0.35 m 

Formula Used:

TSA of cylinder = 2πr(r + h)

Calculation:       

3.52 = 2 × \(\frac{22}{7} \times 0.35 \times (0.35 + h)\)

⇒ 1.25 = h

∴ The height of the cylinder is 5/4 m 

The correct option is 1 i.e. 5/4 m

Formula Used:

Probability = \(\frac{Number\space of\space favorable\space event}{Total\space number \space of \space event }\)

Calculation:  

If a number is not prime then it will be a composite number.   

Composite number are 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40

Total number of events = 30

Favorable events = 22

⇒ Probability = 22/30 = 11/15

∴ The probability not to be a prime number is 11/15.

The correct option is 3 i.e. 11/15

Given: 

Mean of some observation = 54 

Each observation is increase by = 8 

Sum is divide by 2.

Concept used: 

Mean = Sum of all observations / Total number of observations

Calculation: 

Mean of some observation = 54 

Let number of observation whose mean is 54 = x

∴ Sum of all observations = 54x

Each observation is increase by 8.

Total increase in all observation = 8x 

Sum of all observation after increasing by 8 = 54x + 8x 

⇒ 62x

Sum is divided by 2 = 62x / 2

⇒ 31x

Mean of resulting observations = 31x / x 

⇒ 31

∴ The new mean is 31. 

∴ Option 2 is correct.

Formula Used:

(a + b)(a - b) = a² - b² 

Calculation:

(3x + 2y)(3x - 2y)

⇒ 9x² - 4y²

Now,

⇒ (9x2 - 4y2)(9x2 + 4y2)

⇒ 81x4 - 16y4

∴ (3x + 2y)(3x - 2y)(9x2 + 4y2) = 81x4 - 16y4

The correct option is 4 i.e. 81x4 - 16y4

Concept:

a² - b² = (a - b)(a + b)

Calculation:

\(\frac{a^{2}-b^{2}+a(a+b)}{a(a-b)+b(a-b)} \)

\(⇒ \frac{(a + b)(a - b)+a(a+b)}{a(a-b)+b(a-b)}\)

\(⇒ \frac{(a + b)(a - b + a)}{(a-b)(a+b)}\)

\(⇒ \frac{(2a - b)}{(a-b)}\)

\(∴ \frac{a^{2}-b^{2}+a(a+b)}{a(a-b)+b(a-b)}\) = \(\frac{(2a - b)}{(a-b)}\)

The correct option is 3 i.e. \(\frac{(2a - b)}{(a-b)}\)

Calculation:

\(y-\frac{y-1}{2}=1-\frac{y-2}{3}\)

\(⇒ \frac{2y - y + 1}{2} = \frac{3 -y + 2}{3}\)

\(⇒ \frac{y + 1}{2} = \frac{5-y }{3}\)

By crossmultiplication:

⇒ 3(y + 1) = 2(5 - y)

⇒ 3y + 3 = 10 -2y

⇒ 5y = 7

⇒ y = 7/5

Now,

\(⇒ \frac{(5\times \frac{7}{5})+7}{2}\)

\(⇒ \frac{7+7}{2}\)

⇒ 7

\(∴ \frac{5 y+7}{2} = 7\)

The correct option is 4 i.e. 7

Calculation:

(3x2 - 8x + 11) + (- 6x2 + 12x + 17)

⇒ -3x2 + 4x + 28

Now,

⇒ (-3x2 + 4x + 28) - (x2 - x - 19)

⇒ -3x2 + 4x + 28 - x2 + x + 19

⇒ - 4x2 + 5x + 47

∴ Subtracting x2 - x - 19 from the sum of 3x2 - 8x + 11 and - 6x2 + 12x + 17, we get (- 4x2 + 5x + 47)

The correct option is 4 i.e. - 4x2 + 5x + 47

Given:

Selling Price = Rs. 1020

Profit% = 20%

Formula Used:

Cost Price = Selling price × \(\frac{100}{100 + profit%}\)

Calculation:      

Cost Price = 1020 × \(\frac{100}{100 + 20}\)

⇒ Cost Price = 1020 × \(\frac{100}{120}\)

⇒ Cost Price = Rs. 850

∴  The cost price of the toy is Rs. 850

The correct option is 4 i.e. Rs. 850

Concept:

Equilateral triangle has 3 lines of symmetry.

Isosceles triangle has 1 line of symmetry.

Scalene triangle has no line symmetry.

Calculation:

∴ The Scalene triangle has no line symmetry.

The correct option is 3 i.e. Scalene triangle only

Given: 

ABCD is a rhombus.

⇒ ∠BAC = 50°

Concept used:

Rhombus property, 

Diagonal bisects.

All sides are equal.

Angle sum in quadrilateral = 360º

Calculation: 

ABCD is rhombus.                   

AB = BC = CD = DA

Let ∠ ABC = ∠ ADC = y

Let ∠ BAD = ∠ BCD = 50º + x

AB II CD, AD II BC 

⇒ ∠DAC = ∠ BCA = 50º

⇒ ∠ ABC + ∠ BCD + ∠ CDA + ∠ DAB =

⇒ 360º

⇒ y + 50º +x +y + 50º + x = 360º 

⇒ 2x + 2y = 260º

x + y = 130º 

Diagonal bisects the angle in rhombus,

x = 50º , y = 130º- 50º = 80º 

⇒ 3  ∠ D - 2  ∠  DAC = 3 × 80º - 2 × 50º

⇒ 140º

∴ Option 2 is correct.

Calculation:

In ∆ABC and ∆DCB

BC = BC (Common)

AB = CD (Given)

AC = BD (Given)  

∆ABC \(\cong\) ∆DCB (By SSS congruency concept)

The correct option is 2 i.e. ∆ABC \(\cong\) ∆DCB

Given:

∠ A = 40°

 AC = BC

Concept:

Corresponding angles of an isosceles triangle are equal.

The sum of two opposite interior angles is equal to exterior angle.

The sum of all angles of a triangle is 180°.

Calculation: 

AC = BC

∠ A = ​∠ B = 40°

​∠ A + ​∠ B + ∠ C = 180° 

⇒ 40° + 40° + ​∠ C = 180° 

⇒ ​∠ C = 180° - 80° = 100° 

⇒ ∠ A + ​∠ B = ∠ ACD = 80° 

2∠ ACD + 3∠B

⇒ (2 × 80°) + (3 × 40°) 

⇒ 160° + 120° = 280° 

∴ 2∠ ACD + 3∠B = 280°

The correct option is 1 i.e. 280°

Given:

x + y = 80°

x and y are vertically opposite angles.

z is the complement angle of y.

Concept: 

Vertical Opposite angle: The angles opposite each other when two lines cross. Vertical Opposite angles are equal.

Complementary angle: Complementary angles are two angles that sum to 90°.

Calculation:

x = y (Vertical Opposite angle)

⇒ x + y = 80° 

⇒ x + x = 80°

⇒ x = y = 40°

⇒ y + z = 90° 

⇒ 40° + z = 90° 

⇒ z = 50°

Now,

3x - y + z 

⇒ 3 × 40° - 40° + 50° = 130° 

∴ 3x - y + z = 130° 

The correct option is 3 i.e. 130°

Mathematics is a subject where memorization is eliminated totally. Even the formulas in mathematics are not memorized but derived and obtained whenever they are needed by following a particular sequence or process. Mathematics includes processes like thinking problem solving and analysis which are better than memorization. 

Key Points

Memorizing an algorithm is not true  about the five steps of Mathematization because

• Memorization is not an indication of true learning.
• Memorization doesn't allow the child to think in different ways to solve a problem.
• If a child is habituated to memorization then there will be no chance for creativity and divergent thinking.
• A child can solve the same problem through memorization but he can't solve different problems on the same topic.
• Mathematics includes processes like thinking problem solving and analysis which are better than memorization.

​Hence Memorizing an algorithm is not true of the five steps of Mathematization.

Mathematics is a subject that has a number of concepts and those concepts are interconnected with each other. A child can't learn multiplication if he does not know addition that is why the concepts are arranged in a hierarchical order so that the children will depend on their previously learned concepts when they get promoted from one grade to another. 

Key Points

Number concepts and patterns are building blocks to algebraic thinking is an example of this because

• As algebra includes the basic operations on numbers number concepts play an important role in understanding algebra.
• Algebra also contains many identities which are to be understood to solve problems in algebra here patterns play an important role as a basic of algebra.
• If a child who doesn't know number concepts and patterns is directly introduced to algebra he/she may not understand anything as these two are an important and basic part of algebra.
• It is always suggested to teach children the basic concepts and continue the flow from basic to advanced.

Hence Number concepts and patterns are building blocks to algebraic thinking is an example of the statement new concepts and previously learned concepts are interconnected.

 Additional Information

On the other hand, all remaining options are not true regarding this statement because they indicate the reverse order of concepts where children can understand nothing.

Social constructivism focuses on the collaborative nature of learning. Knowledge develops from how people interact with each other, their culture, and society at large. Students rely on others to help create their building blocks, and learning from others helps them construct their own knowledge and reality. 

Key Points

Points involved in a social constructivist framework

• The role of the teacher in the social constructivist classroom is to help students to build their knowledge and to control the existence of students during the learning process in the classroom.
• Her teacher just acts as a facilitator and extends help only when required.
• Students work in collaboration on a project, activity, and problem and construct knowledge.
• Students are allowed in pairs to teach each other. Learners pose their own questions and seek answers to their questions via research and direct observation. They present their supporting evidence to answer the questions.

Hence the statement "Students working in collaboration on a project" is indicative of a mathematics classroom based on a Social Constructivist framework.

Additional Information

On the other hand, a teacher demonstrating the use of dienes block, students responding to a quiz by raising hands, and students working independently with Geoboards are examples of socio constructivism because here students remain individual and try to construct knowledge individually.

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

 Key Points

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

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

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

Additional Information

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

A portfolio assessment is a collection of student works that are associated with standards you are required to learn. This collection of work is often gathered over a long period of time to reflect what students have been taught as well as what students have learned. 

Key Points

• A portfolio can include classwork, artistic pieces, photographs, assignments, project reports, homework, models, unit tests, class tests, and a variety of other media all demonstrating the concepts that students have mastered.
• A portfolio assessment is often deemed an authentic form of assessment because it includes authentic samples of a student's work.
• A portfolio assessment demonstrates learning over the course of time rather than what a student knows on a particular day.
• A portfolio assessment provides an opportunity for a student to reflect on their learning and to self-assess.

 Hence the tool used by the teacher in the above example is a portfolio. 

Additional Information

Mathematics is not only a subject that involves only number concepts and problem-solving but it is also more about forming generalizations, seeing relationships, and developing logical thinking and reasoning. Mathematics should be visualized as a medium for a child to explore the concepts he or she has in their minds. 

Key Points

• The definition "Mathematics is a way to settle in the mind, a habit of reasoning" is given by Locke.
• According to Locke the main focus of teaching mathematics is to make the mind of a child a habit of reasoning which means a child's mind should automatically get activated to solve the problems which involve reasoning, problem-solving and divergent thinking which Locke considered as important processes of mathematics.

Hence it can be concluded that the definition "Mathematics is a way to settle in the mind, a habit of reasoning" is given by Locke. 

Additional Information

Data handling is considered to be one of the important topics in mathematics. This topic should be clearly taught to students from the primary stage itself because this has a lot of applications in daily life. 

Key Points

• Formulating the questions will be the first step in data handling a topic for the teacher to make a lesson plan because first, the questions have to be formulated in order to recognize the objective of the topic and motivate the students.
• Collecting the data will be the second step after formulating the questions because data is an important aspect of the whole topic of data handling.
• Once the data is collected it should be analyzed properly which means that the data should be broken into many parts and thoroughly understood if it is the correct one and suits the given context.
• Interpreting the results will be the last step as the whole process has been completed now the correct results can be compared with the current existing results so that improvement can be planned for the next sessions.

Hence (c), (a), (d), (b) will be the correct sequence.

Misconceptions are nothing but the wrong concepts and generalizations which are registered in the students' minds. This should be erased and replaced by the correct concept by the teacher as soon as possible because students will use the same concepts once they get promoted to a higher grade.

Key Points

• The congruence of figures is one of the important topics of mathematics.
• In the example, a student said that two regions having the same area are also congruent.
• This shows that the student has a misconception regarding the properties which leads to the congruence of the two figures.
• Hence this misconception should be addressed as soon as possible by the teacher and replaced by the correct concept.

Hence the statement "Student's misconception needs to be addressed by the teacher" is correct regarding the student's response in the above example.

The definition is the statement that defines and describes any word clearly. The whole meaning of a word can be clearly understood in a brief manner in its definition. 

Key Points

• The definition provides the first information which needs to be understood by the learner regarding a particular concept.
• For example, a number that is only divisible by 1 and itself is the definition of a prime number.
• Similarly in the above example, the definition of a common divisor is given as it is a number that divides both the given integers.

So it is an example of the definition. 

Additional Information

In Mathematics, symmetry means that one shape is identical to the other shape when it is moved, rotated, or flipped. The concept of symmetry is commonly found in geometry. 

In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. 

Key Points

• In the above example, the teacher folds a square sheet of paper into half and punches a hole in the folded sheet of paper, and then unfolds the paper.
• Here since the teacher has folded the paper into half the concept of a fraction can be clearly taught as half of the paper is folded so the paper can be divided into two parts and one part is taken from them as the numerator.
• In the same way, the concept of symmetry can also be taught because the teacher has punched holes in the folded sheet of paper when she opens the paper the hole will be there on both sides of the folded paper.

Hence the topics of Symmetry and fraction can be taught by using folded, punched paper.

Concept:

• Adaptation refers to the presence of specific features and habits which enable a plant or animal to live in a particular habitat and its geographical conditions.
• Adaptation is long term gradual and continuous process.
• Habitat refers to the surroundings where plants and animals live.
• The plants or trees species survive in their environment such as underwater, in deserts, on grassland, on the mountain range, etc
• For example, seaweed is a plant adapted for its underwater environment, cacti are adapted for a desert environment, conifers plants are adapted for a snowy environment, etc.

**Explanation:**​

• Characteristic features of trees in the mountain range:
• Plants or trees such as pines, firs, spruces, etc are adapted for a mountain environment.
• These trees are tall. straight and have cone-shaped.
• They have sloping branches so that snow slides off easily without damaging the branches and leaves.
• The leaves are needle-shaped with a wax-like coating.
• The trees have thick bark which helps the tree to withstand the cold.
• Whereas the desert plant has a waxy coating on the stem which helps to retain water as well as long penetrating roots for absorbing water.

Therefore, from the above discussion, we can say that the correct answer is A & B.

Concept:

Atmospheric pressure:

• Atmospheric pressure is defined as the weight of a column of air contained in a unit area from the mean sea level to the top of the atmosphere or we can say the pressure exerted by the weight of air on the earth's surface is atmospheric pressure.
• The SI unit is millibar.
• The atmospheric pressure at sea level is 1013.2 millibar.
• The pressure of the atmosphere is measured by a mercury barometer or aneroid barometer.
• As we go at a high altitude, the pressure falls rapidly.
• The atmospheric pressure is highest at sea level and decreases with height.

Explanation:

• The atmospheric pressure is comparatively low at high altitudes than at low altitudes because with the increase in altitude, the number of gas particles decreases, thus the collision between the gas particles also decreases. So, the pressure also decreases.
• Whereas the atmospheric pressure is high at low altitudes at the seashore. So, the Reason is incorrect.
• At high altitudes. with the decrease in air pressure, the vapor pressure exceeds and due to the increase in vapor pressure water boils easily. Thus, the boiling temperature of water decreases. So, Assertion is also incorrect.

Therefore, from the above discussion, we can say that Both Assertions and Reason are false.

Explanation:

Light :

• Light is electromagnetic radiation that can be perceived through the naked human eye.
• In simple words, light is an entity that makes things visible to us.
• There are mainly two phenomena associated with light:

Refraction of light:

• It is the change in the speed of light as it enters from one transparent medium to another.
• A light ray refracts whenever it travels at an angle into a medium of a different refractive index. Thus, the speed of light decreases as it continues to travel at a different angle.
• A light ray traveling obliquely from a denser medium to a rarer medium bend away from the normal whereas a ray bends toward the normal when it travels obliquely from a rarer to a denser medium.
• So, when the light ray travels from air into oil, then the light ray bends towards the normal line and the light slows down and changes its direction slightly.

​

Thus, from the above discussion, the correct answer is the speed of light decreases and the ray bends towards the normal.

Additional InformationReflection of light:

• Polished surfaces reflect back most of the light.
• Laws related to reflection:
• The angle of incidence is equal to the angle of reflection(∠i=∠ r)
• The incident ray, the normal to the mirror at the point of incidence, and the reflected ray, all lie in the same plane.

 Law of refraction of light:

• The incident ray, the refracted ray, and the normal to interface of two transparent media at the point of incidence, all lie in the same plane.
• The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This is also known as Snell's law of refraction.

           Sin i / Sin r = constant

Concept:

Force

• Force is any push or pull that changes or tends to change
• the state of rest or motion of the body
• speed of a body
• the direction of motion of the body
• the shape of the body
• Force always acts if two or more body interacts.
• Force is a vector quantity, which means both its magnitude (strength of force) and the direction of its application should be considered.
• For example, if two forces are acting in the same direction, their magnitude will be added up.
• Based on their application, force is of 2 types: Contact force and non-contact force.

Contact forces:

• They are defined as the forces that result when the two interacting objects are in contact with each other physically.
• Examples: frictional force, muscular force, drag force, etc.

Non-Contact forces:

• They are forces that are experienced by bodies even without being physically in contact with it.
• Examples: gravitational force, magnetic force, electrostatic force, etc.

Explanation:

• The electrostatic force is the force exerted by the charged body on another charged or uncharged body. It is a non-contact force because it attracts the bodies which does not require that bodies are in physical contact with each other.
• The force of friction is the contact force because it acts between two surfaces that are trying to move relative to each other (static friction) or is moving relative to each other (kinetic force).
• The magnetic force is the force exerted by the charged body when it moves in a magnetic field. It is a non-contact force because it attracts the objects which does not require that objects in physical contact with each other.
• The gravitational force is a non-contact force because this force does not influence the masses physically but will be experienced by both the masses.
• The muscular force is a contact force because it acts between two surfaces and these forces result due to the action of muscles of body parts like arms or legs and there is contact between the surface.
• The drag force is the force that is exerted on a solid body moving concerning a fluid due to the movement of the fluid. It is a contact force because it acts between two surfaces and these forces try to hinder the motion of the object moving concerning the particle of the medium.

Thus, from the above discussion, it is clear that the correct answer is a drag, muscular force, or the force of friction.

Concept:

Magnet:

• Magnets refer to an object which is capable of producing a magnetic field. and attracts iron pieces and settles itself along the north-south pole.
• Magnets have 2 poles: a North pole and a South pole.
• Magnetic poles always exist in pairs.
• Like poles of 2 magnets repel each other while unlike poles attract each other.
• The strength of the magnet is highest at the poles and weakest in the middle.

Explanation:

• When a magnet is broken into two halves, then each part will become an individual magnet.
• Each piece can contain a North pole at one end and a South pole at the other end.
• No matter how many times the magnet is broken into pieces, pole power remains the same and does not lose its magnetism.
• So, when these two pieces are brought closer to each other, they will either attract or repel because like poles repel each other whereas unlike poles attract each other.

Thus, from the above discussion, it is clear that the correct answer is may attract or repel.

Explanation:

According to Archimedes' Principle:

• When a body is immersed fully or partially in a fluid, it experiences a buoyant force that is equal to the weight of the fluid displaced by it.

For Object A:

• Weight of the liquid displaced  = 16N
• So, we know that buoyant force acting on an object =  weight of water displaced
• Therefore for the value of  Y = 16 N
• We know that Buoyant force acting on the body = weight of the stone in the air - the weight of the stone in water

           ⇒ 16 = 92 - X

           ⇒ X = 92 - 16 =  76 N

For Object B:

• The buoyant force acting on the body = 10 N
• So, we know that buoyant force acting on the body =  weight of water displaced
• Therefore for the value of Z = 10 N
• We know that Buoyant force acting on the body = weight of the stone in the air - the weight of the stone in water                 

⇒ 10 = Q - 70

⇒ Q = 70 + 10 = 80 N

Thus, from the above discussion, it is clear that the correct answer is X - 76, Y - 16, Z - 10, Q - 80.

Concept:

Summer solstice:

• The summer solstice occurs when the North pole is tilted closest to the sun.
• It occurs on 21^st June.
• It occurs in the Northern hemisphere.
• It is the longest day of the year marking the start of summer.
• The sun's rays directly fall over the tropic of cancer.
• A large portion of the Northern hemisphere receives sunlight and heat during the summer solstice.

Winter solstice:

• The winter solstice occurs when the North pole is tilted farthest to the sun.
• It occurs on 22^nd December.
• It brings the longest day in the southern hemisphere marking the start of winter.
• The sun's rays directly fall over the tropic of Capricorn.
• A large portion of the Southern hemisphere receives sunlight and heat during the winter solstice.

Explanation:

• The sun rises or sunset happens due to the spinning of the Earth around its axis in a counterclockwise direction i.e, from east to west.
• Since. there are 4 cardinal points called North, South, West, and East. The sun rises due east and sets due west only for 2 days in the year. On the other days, the sun rises either north or south of due east because each day rising point changes slightly. So, the Rising Sun is not considered an appropriate guide to locating the direction in all seasons.
• But the Pole star helps in locating direction accurately because the pole star always appears on the North pole indicating the North direction and it is also known as a fixed point.
• Since Earth's orbit around the sun is elliptical rather than circular and the Earth's axis of rotation is not perpendicular to the plane of the orbit. Thus, the Point of sunrise changes continuously.
• At the summer solstice, the sun travels the longest path through the sky. When the summer solstice happens in the Northern hemisphere, the sun's rays directly fall on the North pole.
• When the winter solstice happens in the Southern hemisphere, the sun's rays directly fall on the South pole.

Thus, from the above discussion, it is clear that the correct answer is S1, S2.

Additional Information

• During the equinox, the sun crosses the earth's equator and the day and night become equal lengths of time.
• At the equinox, Earth's two hemispheres i.e, the North and south hemispheres are receiving the sun's rays equally.
• There are 2 equinoxes:
• Vernal equinox (about 21^st March) - The day and night of equal length marking the start of spring. It takes place in the Northern hemisphere.
• Autumnal equinox (about 23^rd September) – The day and night of equal length marking the start of autumn. It takes place in the Southern hemisphere.

Concept:

• A strong acid is an acid that is completely ionized in water to produce hydronium ions. The conjugate base of the acid is very weak as it does not react with water at all.
• A strong base is an acid that is completely ionized in water to produce OH-. The conjugate acid is very weak as it does not react with water at all.
• A weak acid and base is an acid that partially reacts with water to produce hydronium and hydroxide ions respectively and the conjugate base and conjugate base and acid both are weak.

Explanation:

• Phenolphthalein is an acid-base indicator and it changes color in pH ranges between 8.3 to 10. In acidic solution, it appears colorless and in basic solution, it turns pink in color.
• In test tube A throughout the acid-base titration, the solution remains colorless after adding phenolphthalein. Thus, it is a strong acid.
• In test tube B, first, the solution remains colorless but after adding pink colorless, then the solution becomes pink. Thus, it is a weak acid.
• In test tube C, the solution become pink after adding the phenolphthalein indicator. Thus, it is a strong base.

Therefore, from the above discussion, it is clear that the correct answer is A = Strong Acid B = Weak Acid C = Strong Base.

Concept:

Acids and bases: 

Acid-base Indicator:

• Acid-base indicators are dyes or mixtures of dyes that are used to indicate the presence of acids and bases.
• Examples of Natural Indicators of acid and base are:
• Litmus paper
• Red cabbage leaves
• Turmeric
• China rose

• Examples of synthetic Indicators of acid and base are:
• Methyl orange
• Phenolphthalein.​

Explanation:

• Red cabbage leaves are a natural acid-base indicator and it is red in color. the red cabbage leaves remain red in acidic solutions but turn green on adding to basic solutions.
• Similarly, turmeric is also a natural acid-base indicator. It contains a yellow dye and remains yellow in an acidic medium but it turns red in a basic solution.
• Salt is neither acid nor base. It is formed by the reaction between acid and salt. Hence, indicators do not affect salt.
• Banana leaves contain a little bit of acid but it does not change color when the solution turns acidic or basic. Hence, it is not an acid-base indicator.
• Lemon juice contains citric acid and it is an olfactory indicator Hence, it is not an acid-base indicator.

Thus, we can say that the correct answer is Red cabbage leaves and turmeric.

Explanation:

• Pickles contain acetic acid in the form of vinegar.
• If the pickles are stored in metal containers made up of aluminum, brass, and copper then the metal reacts chemically with the acid present in the pickles which leads to the formation of toxic or hazardous compounds that affects our health.
• When metal comes in contact with acid, then salt and hydrogen gas form which would also spoil the pickles.
• Metals + Acid  →  Salt + Hydrogen gas

Therefore, we can say that pickles should be stored in a glass container to avoid any chemical reaction

Explanation : 

• When sulphur is burnt, it reacts to form sulphur dioxide (SO₂).
• When sulphur dioxide reacts with water it forms sulfurous acid.

         SO₂ + H₂O→ H₂SO₃

• Sulfurous acid is a reducing agent.
• When sulfur is heated in a spoon and immediately put in a gas jar and covered, a small amount of water was added to the jar and the solution was tested for acidity or basicity, it turns blue litmus paper red
• Because Acid turns blue litmus paper to red.
• It means the solution is Acidic in nature.

So, the correct answer is, material 'M' is Sulphur.

Additional Information

• Sulfurous acid is an important component of acid rain which is harmful to all living organisms.
• Acid rain causes many skin diseases like skin cancer.

Concept :

Roughage:

• Our body needs dietary fibres and water. Dietary fibres are also known as roughage.
• Roughage is mainly provided by plant products in our food.
• Whole grains and pulses, potatoes, fresh fruits and vegetables are the main sources of roughage.
• Roughage does not provide any nutrient to our body, but is an essential component of our food and adds to its bulk.
• This helps our body get rid of undigested food.

Explanation:

Cellulose:

• Cellulose occurs exclusively in plants and it is the most abundant organic substance in the plant kingdom. It is a major component of the cell wall of plant cells. It is a type of fibre which forms a major part of the diet and is not digestible by the human digestive system. It helps in the smooth functioning of the intestine.
• Fruits and vegetables contain cellulose in small amounts which can be easily digestible.
• Fibres contain cellulose which acts as roughage,  which adds bulk to the diet and helps in the smooth passage of the food in the digestive tract. It is insoluble in water.
• Humans cannot digest cellulose because they lack the enzyme cellulase. Cellulose helps in the growth of bacteria in the digestive tract. The cellulose digesting bacteria converts cellulose into digestible fibres.

So, the correct answer is A is true and R2 is the correct explanation for A.

Additional Information 

• A high fibre diet reduces the risk of colon cancer as it reduces the time, the faeces stay in the colon wall.
• Consuming food that does not contain cellulose over a long period of time results in constipation.

Concept :

• The process of digestion includes both mechanical and chemical processes.
• Mechanical digestion includes churning or mastication of food.
• The chemical process includes the action of certain enzymes which break down the food and convert it into simpler forms.

Explanation :

Bile juice:

• The bile secreted by the hepatic cells passes through the hepatic ducts and is stored and concentrated in a thin muscular sac called the gall bladder.
• It does not contain any enzyme.
• Bile helps in the emulsification of fats, i.e., breaking down the fats into very small micelles. Bile also activates lipases.

Pancreatic juice:

• The exocrine portion of the pancreas secretes an alkaline pancreatic juice containing enzymes and the endocrine portion secretes hormones, insulin, and glucagon.
• The pancreatic juice contains inactive enzymes – trypsinogen, chymotrypsinogen, procarboxypeptidases, amylases, lipases, and nucleases.

Salivary juice:

• The saliva secreted into the oral cavity contains electrolytes and enzymes, salivary amylase, and lysozyme.
• The chemical process of digestion is initiated in the oral cavity by the hydrolytic action of the carbohydrate-splitting enzyme, the salivary amylase.

Gastric juice:

• Rennin is a proteolytic enzyme found in the gastric juice of infants which helps in the digestion of milk proteins.

 

 Additional Information

• Trypsinogen is activated by an enzyme, enterokinase, secreted by the intestinal mucosa into active trypsin, which in turn activates the other enzymes in the pancreatic juice.
• The bile released into the duodenum contains bile pigments (bilirubin and biliverdin), bile salts, cholesterol, and phospholipids.

Concept :

Latent heat:

• It is the heat energy that is given to change the state of a substance.
• 'Latent' means' hidden' i.e. heat in the substance undergoing the change of state, and does not change its presence by raising the temperature.
• Latent heat does not raise the temperature of the substance​
• But the latent heat has always to be supplied to change the state of a substance.

Explanation

• The latent heat supplied is used up in overcoming the forces of attraction between the particles of a substance during the change of state.
• The latent heat does not increase the kinetic energy of the particles of the substance.
• Since, there is no increase in the kinetic energy of the particles, the temperature of a substance does not rise during the change of state.
• Ice will lose more heat as it is the heat energy that prevents the temperature from further cooling.
• Heat energy does not warm the temperature but rather stops further cooling and this happens at thermal equilibrium.
• So, the correct answer is A will lose more heat than B.

Additional Information

• About 334 J of energy is required to melt 1g of ice at 0°C, which is the latent heat of melting.

Concept :

Joints :

• Joints are the contact points between bones, or between bones and cartilages.
• The muscles generated force through joints which are used to carry the movement, where joints act as a fulcrum.
• Joints are important for all types of movements that involve the bony parts of the body.

Explanation :

• The joints are functionally classified on the basis of the type of movement they allow.
• There are six types of joints :

 1) Ball and socket joint 2) Pivotal joint 3) Hinge joint 4) Gliding joint  5) Saddle joint 6) Fixed joint

 

              

                    Fig: Joints in humans

Ball and socket joint :

• This type of joint is present between the shoulder and arm.
• It allows movement in all directions.

Pivotal joint :

• This type of joint is present between the neck and head.
• It allows forward and backward movement.

Hinge joint :

• This joint is present in the elbow.
• It allows back and forth movement.

Fixed joint :

• This joint is present between the upper jaw and the lower part of the head.
• It does not allow any movement i.e. fixed.

So, the correct answer is the Hinge joint.

Additional Information

• Saddle joints are those which allow movement in two planes. E.g. Joint of the thumb.
• Ellipsoid joints are those which allow movement in two planes i.e. back and front and side to side. E.g. joint in wrists.
• The bones of birds are hollow and the forelimbs are modified to form wings.

Concept : 

Deficiency diseases : 

• If a  person is having enough food, sometimes that food may not contain a particular nutrient.
• If this condition continues for a long time, the person may suffer from its deficiency.
• The diseases that occur due to a lack of nutrients over a long period of time are called deficiency diseases.

Explanation :

Vitamins :

• Vitamins are organic substances that are required for the proper functioning of the body.
• Vitamins are divided into two groups:
• Fat-soluble (Vit. A, D, E, and K)
• Water-soluble ( Vitamins of B group and Vit. C).

So, the correct answer is Vitamin K.

 Additional Information 

Concept:

Refraction of Light:

• When a ray of light propagating in a medium enters the other medium, it deviates from its path.
• This phenomenon of change in the direction of propagation of light at the boundary, when it passes from one medium to another medium, is called the refraction of light.
• When a ray of light enters from a rarer medium to a denser medium from (air to water) it deviates towards the normal drawn on the boundary of two media at the incident point.
• The entity that doesn't change is the frequency.
• The entity that changes are wavelength and velocity.
• The refractive index is also equal to the velocity of light c of a given and the wavelength in empty space divided by its velocity v in a substance.
• Thus, Velocity, Wavelength & Refractive index change when light travels from one medium to another but Frequency remains unchanged.
• Similarly, in passing from denser to rarer medium, a ray deviates away from the normal.
• If the light is incident normally on the boundary, i.e. parallel to normal, it enters the second medium undeviated.

Explanation:

• The refractive index is also equal to the velocity of light c of a given wavelength in empty space divided by its velocity v in a substance,n = (c/v)
• Hence, light travels faster in water.
• The speed of light is faster in water. The refractive index of water is 1.3 and the refractive index of glass is 1.5.

 

• Looking in the option it is clear that the option with "decrease, increase, decrease, increase, decrease, increase", is the correct choice.

Additional information

• The refractive index of a medium for a wave of a given wavelength is defined as the ratio of the speed of a wave in a vacuum to its speed in the medium.
• The refractive index of water is 1.33.
• The refractive index of air is 1.
• The refractive index of glass is 1.5.

Concept :

Breathing:

• We take in air through our nostrils. When we inhale air, it passes through our nostrils into the nasal cavity.
• From the nasal cavity, the air reaches our lungs through the windpipe.
• Lungs are present in the chest cavity  This cavity is surrounded by ribs on the sides.
• A large, muscular sheet called a diaphragm forms the floor of the chest cavity.
• Breathing involves the movement of the diaphragm and the rib cage.

Explanation: 

• During inhalation, ribs move up and outwards and the diaphragm moves down.
• This movement increases space in our chest cavity and air rushes into the lungs.
• The lungs get filled with air.

 

 Additional Information

• Cockroaches have small openings on their sides which are called spiracles and act as respiratory organs.
• Earthworms breathe through their skin.
• Frogs have a pair of lungs for respiration and they can also breathe through their skin.

Concept :

• ABO blood groups are controlled by gene I.
• The gene (I) has three alleles I A, I B, and i. Because humans are diploid organisms, each person possesses any two of the three I gene alleles.
• I A and I B are completely dominant over i, in other words when I A and i are present only I A expresses, and when I B and i are present I B expresses.
• But when I A and I B are present together they both express their own types this is because of co-dominance.
• Since there are three different alleles, there are six different combinations of these three alleles that are possible, and therefore, a total of six different genotypes of the human ABO blood types

Explanation :

• Therefore, if a man having a blood group A marries a woman with a blood group B. The blood group of their son/daughter will be A, B, AB, or O.

​So, the correct answer is Either A, B, O, or AB.​

Additional Information

• Karl Landsteiner is known as the father of blood groups.
• Decastello and Sturle discovered AB blood groups.

Concept :

• Sound is a mechanical wave.
• It needs a material medium like air, water, steel, etc. for its propagation.
• It cannot travel through a vacuum.
• When sound is propagated through a medium, the density of the medium oscillates between a maximum value and a minimum value.
• The change in density from the maximum value to the minimum value, again to the maximum value, makes one complete oscillation.
• The number of such oscillations per unit time is the frequency of the sound wave.

Explanation :

• The loudness or softness of a sound is determined basically by its amplitude.
• The amplitude of the sound wave depends upon the force with which an object is made to vibrate.
• If we strike a table lightly, we hear a soft sound because we produce a sound wave of less energy (amplitude).
• If we hit the table hard we hear a loud sound. Loud sound can travel a larger distance as it is associated with higher energy
• As sound moves away from the source its amplitude as well as its loudness decreases.
• Frequency only tells about the vibrations in an object.
• The number of times the table is beaten per unit time is the frequency.

So, the correct answer is only R1 is the true and the correct explanation for A.​

Additional Information

• ​The speed of sound is defined as the distance which a point on a wave, such as a compression or a rarefaction, travels per unit of time.
• So, speed, v = distance / time
• Speed of sound in dry air at 20 °C = 343 m / s.

National Curriculum Framework, 2005, is a complete document to rejuvenate Indian schools as well as Teacher Education.

• “Science education should enable the learner to know the facts and principles of science and its applications, consistent with the stage of cognitive development”, guides that objectives, curriculum, methods, assessments, etc. should be different for different levels.

Key Points

Objectives of Teaching Science at the upper-primary stage are:-  

• Learners have the opportunity to explore various elements of science and start making sense of science in daily experiences and thus science education transit from environmental studies to elements of science and technology at the upper primary stage.
• The integrated approach to teaching is followed by emphasizing teaching science as a single subject.
• Learners recognize science concepts through hands-on activities and experiments, even then not necessary to strictly follow the inductive approach of inquiry**.**
• The problems that learners sense as meaningful and significant (arrived through discussions in the classrooms in the presence of a teacher, communication with elders, from newspapers, etc.) must be tested and experimented with apart from simple experiments and hands-on activities.
• The practice of pass and fail and no-detention policy is to be avoided but steps may be implemented to organize periodic assessments of learners through unit tests, term tests, etc.
• Role play, skits, and cooperative learning strategies should be adopted to ensure larger participation and sharing of learning outcomes.
• Scientific concepts are learned better if learners explore them through activities and experiments.
• Engaging learners in learning principles of Science through familiar experiences, working hands-on to design simple technological units and modules, and continuing to learn more about the environment and health through various activities
• The in-service teachers should prepare question papers that assess learners' problem-solving skills, data analysis skills, application of learned knowledge in various situations, solving numerical problems, etc.

Hence, it is concluded that Using systematic experimentation as a tool to discover/verify theoretical principles is not the objective of science teaching at the upper-primary stage. 

Additional Information

Objectives of Teaching Science at Secondary Level -

• It is suggested that at the secondary stage, learners should be engaged in learning science as a composite discipline.
• Provide the opportunity to engage in activities and analysis on issues surrounding the environment and health.
• Systematic experimentation is suggested as a tool to discover/ verify theoretical principles and work on locally significant projects involving science and technology.

India may be the only nation with a constitutional provision a fundamental duty ‘to develop scientific temper among its citizens.

Article 51A (h) is: “To develop the scientific temper, humanism and the spirit of inquiry and reform”. This reflects how we thought about Science.

 Key Points

• Science is neither a pedagogical discipline nor a group of certain subjects. We have perceived Science as a way of life with rational thinking.
• Scientific feeling and understanding should be inculcated among learners since childhood to perceive Science as a part of their life.
• A scientific law is a general statement that describes some general facts or regularity of the universe.
• A scientific law is the description of descriptions of the relationships between observable phenomena. It doesn't explain why the phenomenon exists or what causes it.
• A scientific law is not a law in the sense that it must be obeyed. It is a law by virtue of the fact that no one has yet found an instance where the law does not hold.
• Laws are description often mathematical descriptions of natural phenomena, for example, Newton's Law of Gravity or Mendel's Law of Independent Assortment. These laws simply describe the observation. Not how or why they work.

Thus, it is concluded that Scientific laws are descriptions of the relationships between observable phenomena is the most accurate description of scientific laws.

When children play and push things like tables, they realize that some effort is required. For certain things, more effort is required to move them from one place to the other compared to certain other things.

• Asking questions is critical for ensuring that students comprehend the material and keeping them involved in the activities. It is essential to the way students receive and process information and it encourages independent and critical thinking.

Key Points Here, the teacher asks the question, Which is heavier - 1 kg of cotton or 1 kg of iron"? and observes that a large number of students think that 1 kg of iron is heavier than 1 kg of cotton. The following strategies would be useful in addressing this idea:-

• Demonstration of the equivalence of the two by scales.
• Providing an opportunity to handle & weigh cotton balls and iron blocks of different sizes.
• Explanation of the difference between heaviness and density.

These all strategies help them to understand the concept of iron and cotton which helps them in finding the answer to the question.

Thus, it is concluded that Defining the concept of density would be the least useful in addressing this idea.

Hint Defining the concept makes them rote memorize, they would not be able to understand it.​

Scientific thinking is a way of looking at the processes of assumptions, scientific explanation, use, and merits of science.

• Scientific thinking refers to the mental process of manipulating scientific information to generate scientific ideas.

Important Points Research tells us that children come to formal science learning with many prior ideas that do not match the scientific explanations.

 The following is true in respect of these ideas:-

• They are based on everyday experiences.
• They influence children's school learning.
• Even adults can hold these ideas.

Key Points Younger children due to their limited experiences, come up with many impossible explanations. Facilitators should assist them to understand this.

• make an effort to use some idea or concept for explaining the observation or relationship
• use concepts or ideas acquired in one situation to explain another situation
• understand the relative and changing nature of scientific explanations
• put forward many explanations that are possible concerning one situation
• put forward a verifiable explanation
• suggest testable explanations under the guidance of the adults.

Thus, it is concluded that They can be easily changed is NOT true in respect of these ideas.

Vygotsky is known as the proposer of social constructivism**.** The Social Constructivism approach talks about the importance of social interaction and context in learning. He believes that learning is social in nature. Through interactions, children shared their views and make their own meaning.

Key Points

• Constructivism is basically a theory, based on observations and scientific studies about how people learn.
• In the classroom, the constructivist view of learning can point toward a number of different copy teaching practices in the most general sense, it usually means encouraging students to use active techniques.
• Helping students in talking, thinking, arguing, and writing about science is the most crucial teaching strategy for helping students construct a meaningful understanding of science.
• A learning environment facilitating learning through the construction of meaning and development of understanding among children on their own may be viewed as a constructive learning environment.

Thus, it is concluded that Option 4 is the correct answer.

Additional Information Different types of teaching strategies used in social constructivism are - 

• Personal constructions of reality i.e. whatever children construct within their own minds is their own reality. They construct their own meaning based on their experiences.
• Simulated authentic learning environments i.e. the learning environment designed and developed on the basis of real-life experiences. A teacher has to simulate real-life situations, problems, and complexities for learners to give them an opportunity to find their solutions.
• Multiple Perspectives i.e. providing the opportunity to experience various dimensions. There should be an opportunity to see the same concept in various ways and develop an understanding with varying objectives and expectations.
• Active learning is a situation where children construct their knowledge by their active engagement in the learning process. It is in contrast to objectivism, where knowledge was supplied by a teacher or a more learned person to a young learner or less knowledgeable person.
• Collaboration is another key practice of a constructive learning environment. Collaboration is not a means to acquire knowledge from someone else, rather it is a means to create individual meaning with the help of others.

Assessment is a process of describing certain traits, processes, and programs in qualitative terms. It has to be done in the context of the objectives of the system of education”

Key Points Following are helpful for assessing the thought processes or ideas of science learners:-

• Posing questions to students in a one-on-one conversation:- It is a probing question and discussion session where the child is expected to come up with his thoughts and ideas.
• Interviewing students intensively:- The students will use their critical and reflective thinking skills to answer the questions asked by the teacher.
• Asking students to depict their thought processes through concept maps/diagrams/sketches:-Concept maps are a constructivist tool that helps the child use his previous knowledge and experiences and connect with the present.

Thus, it is concluded that Asking students to prepare a chart/poster for exhibition/display would be least helpful for assessing the thought processes or ideas of science learners.

Hint **Asking students to prepare a chart/poster for exhibition/display:-**The child is directed to prepare the chart and therefore, he/she will make no use of their thought process. So, it will be not helpful in assessing the ideas of the science learners.

Learners may develop some predictions or tentative answers based on their observations.

Some of their answers may be testable or not, the teacher has to help them in identifying the testable tentative answers. These tentative or testable answers to the testable questions are often termed as hypothesis.“Hypothesis is an educated guess based on the observation”.

Key Points

• 'Hypothesis' is defined as a tentative solution or working proposition suggested as a solution to the problem, and the 'theory as the final hypothesis. which is defensibly supported by all evidence.
• Experiments and further observations are often used to test the hypothesis.
• A scientific experiment is a carefully organized procedure in which the scientist intervenes in a system to change something, then observes the result of the change in scientific inquiry often involves doing experiments, though not always.

Thus, it is concluded that Experimentation is best suited for testing a hypothesis in science.

A liquid is a sample of stuff that conforms to the shape of the container in which it is contained and obtains a defined surface in the presence of gravity. The term liquid is also used to describe the state or condition of materials that have this attribute.

Hint 

• As per the situation giving in the question, the student claims that substances such as flour and salt are "liquid' because they take the shape of the container in which they are put. The teacher responds that they are solids because even though a whole mass of tiny grains of flour or salt does not have a definite shape, but the individual grain does have a definite shape.

Key Points

• A solid has a fixed volume and shape, while a liquid has a fixed volume but no fixed shape.
• As a result, the student will learn that while the entire mass of microscopic grains of wheat or salt does not have a particular shape, each grain does have a fixed shape, and hence they are solid.
• The instructor will explain to the children how liquids and solids vary because solids are relatively hard, with definite volume and structure.
• The atoms and molecules of a solid are so tightly bound that they vibrate in position but do not move and the liquids have a fixed volume but can change form as they flow.
• Atoms and molecules are loosely linked in a liquid.

Consequently, we might conclude that a student believed that substances like wheat and salt are "liquid" because they adopt the form of the container in which they are stored.

Additional Information

• A 'liquid' substance has no set shape; it adopts the shape of the container into which it is put. Salt and flour are both liquids. This is incorrect since they are solids because, whereas a large mass of microscopic grains of wheat or salt does not have a particular shape, each grain has a particular shape.
• Flour and salt are not liquids since they lack the wetting feature this is the right statement but, they are fluids because they 'flow,' which is incorrect because flour and salt do not flow.
• The definition of a "solid" is incomplete because it excludes wheat and salt. This is an incorrect statement since wheat and salt are solids with specific mass, volume, and form.