CTET (Maths & Science) Official Paper-II Feb, 2014 (English-Hindi-Sanskrit) (Previous Year Paper)

"Jean Piaget", a swiss psychologist, belongs to the cognitive school of psychology, is famous for his work on child development. The figure in option number (1) which is showing discontinuous stages of development based on age is correctly representing the development in the context of the question because Piaget has made a systematic study of cognitive development in his theory that is categorised in different stages. He strongly believes that children are the little scientist and they actively develop and construct their understanding of the world in distinct and separate stages.

Principles of development define the basic process of human development. It will assess the role and importance of growth processes and levels and the principles of growth and behavior in the total life span. 

Important Points

In the above-mentioned situation, the teacher's assumption is associated with the principle that 'development tends to follow an orderly sequence' which is one of the important principles of "Development and Growth".

• This principle defines that development occurs in sequence and follows a pattern. Thus teacher's assumption is right. Since a child needs to learn how to stand before he can walk, similarly the student needs to learn to draw a square before he can draw a diamond.

Additional Information

 Principles of development include:

• Development is cumulative.
• Development is a continuous process.
• Development is predictable.
• Development is the process of interaction.
• Development follows uniformity of pattern.
• Development is sequential.
• Development proceeds from general to specific.
• Development rate varies from person to person.

Hence, we can conclude that the above scenario is related to the principle of development trends to follow an orderly sequence.

• Development refers to a qualitative change that results in an increase in structure for better and enhanced functioning of organs.
• Growth refers to a quantitative change that results in an increase in height, weight, and length of the child.

Human growth and development is influenced by both 'Hereditary and Environment' as they are the elements that play a vital role in determining the development of an individual.

The relative effects of heredity and environment vary in different areas of development​ as:

• All mental and social traits depend on the environment.
• All the inborn traits, instincts, and I. Q. depend on heredity.
• All the potential inputs for growth and development depend on heredity.
• Both are complementary to each other in molding the life of an individual.
• How a person will develop depends on the environment but how far a person can develop depends on heredity.
• Heredity places limit on IQ and the environment determines the numeric position of IQ within these limits.

Hence, it could be concluded that the relative effects of heredity and environment vary in different areas of development.

Important Points

• Heredity: It refers to the traits that pass down from the parents to their offspring. It is the most important personality and intelligence determinant.
• Environment: It refers to the circumstances in which an individual lives. Child's immediate environment strongly influenced their personality and intelligence.

Hidden curriculum refers to the unspoken or informal learning in educational settings such as the transmission of values, beliefs, norms and behaviours. In the context of socialization, school's hidden curriculum consists of the informal cues about social roles presented in schools through interaction and materials. It helps the children to grow better by determining the personality and directing the behaviour.

"Jean Piaget", a swiss psychologist, belongs to the cognitive school of psychology, is famous for his work on child development. He made a systematic study of cognitive development in his theory that is categorised into four stages.

Educational Implications of Piaget's theory:

• Discovery learning.
• Practical learning situation.
• Flexibility in the curriculum.
• Acceptance of individual differences.
• Simple to the complex method of teaching.
• Sensitivity to children's readiness to learn.
• Equal importance to co-curricular activities.
• The curriculum should be based on the child's developmental level.

Hence, we conclude that the need for verbal teaching​ cannot be derived from Piaget's theory of cognitive development.

Lawrence Kohlberg, an American psychologist, has propounded the 'theory of moral development'. The cross-cultural universality in moral development is one of the most important characteristics of his theory.

He has made a systematic study of moral development in his theory that is categorised in six culturally universal stages. It is based on Kohlberg's assumption that all people in all cultures face the basic universal moral issues, dilemmas and conflicts and use the universal concepts of morality.

Social constructivist approach is an approach of learning which gives primacy to collaborative learning & reciprocal teaching.

Key Points

• In these classrooms, students are actively involved in discussions and projects related to real-life situations and the teacher facilitates and directs the activities by providing a proper environment and material to make them learn at their own pace.
• It emphasizes collaboration with others for learning.
• It ensures the active involvement of learners and promotes peer tutoring.
• 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.

Hence it could be concluded that teachers and students draw on one another’s expertise while working on complex projects related to real-world problems in a social-constructivist classroom.

Additional Information

John Dewey, an American philosopher 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.

Key Points

• The above-mentioned term implies that all students should be provided with an education that is most appropriate to them and their future life at work.
• Progressive education promotes 'learning by doing to make children self-reliant and productive to use their knowledge, talents, and skills to sustain themselves and to promote economic growth.
• It emphasizes enhancing the skills and understanding of the learners by engaging with the contents and experiences.
• It ensures the active participation of students by working in a group and applying practical knowledge to complete an activity.

Hence, it could be concluded that in the context of progressive education, the term ‘equal educational opportunity’ implies that all students should be provided with an education that is most appropriate to them and their future life at work.

"Jean Piaget", a swiss psychologist, belongs to the cognitive school of psychology, is famous for his work on child development. He made a systematic study of cognitive development in his theory that is categorised in four stages.

In the context of language development 'social interaction' is the area which was underestimated by Piaget because he strongly believed that the child needs to first develop and mature mentally before language acquisition/development can occur.

The Stanford-Binet intelligence scale is the revised version of the Binet-Simon test. It is revised or created by Lewis Terman to diagnose developmental deficiencies in young children.

Here in this question Stanford-Binet Intelligence test score is distributed with a mu score(μ) of 100 and a standard deviation(σ) of 15 and we need to calculate z score corresponding to the Stanford-Binet Intelligence test score.

Z = x - μ/σ

= 130 - 100/15

= 2

According to the Stanford-Binet intelligence scale index 2 of Z refers to 97.7 % which is approx 98%.

The theory of Multiple Intelligence which consists of eight different kinds of intelligence is propounded by an American psychologist 'Howard Gardner'. 

The observation that damage to one part of the brain affects only a particular ability sparing others supports Gardener's theory because the theory proposed that intelligence can't be tied to a single domain, it is of several kinds rather than dominated by a general factor.

Ability grouping refers to a small group of students with similar abilities, talents or skills to perform a specific task. The statement that the teachers may use multilevel teaching to cater to different ability groups is true regarding ability grouping because multilevel teaching refers to teach a lesson to the entire group while meeting the children's diverse needs.

Assessment is a process of collecting, receiving, and using data for the purpose of improvement in the learning process. Assessment is a systematic way of collecting information to make a judgment about student learning.

Assessment can be of three types- assessment for learning (formative assessment), assessment of learning (summative assessment), and assessment as learning (authentic assessment).

Important Points

Formative assessment can sometimes be summative assessment and vice versa

• Both summative and formative assessment is an integral part of the teaching-learning process which helps in facilitating student learning and improving instruction.
• Purposeful planning and implementation of formative and summative assessment in the classroom does appear to contribute towards an improvement in student learning that can be beyond the surface level.
• This can lead to a richer experience that may be reflected in a higher level of achievement than previously predicted.

Summative assessment can be used as a formative assessment.

• Summative assessment can also be used for formative purposes. For example, if students are given tests periodically throughout a subject or topic, the tests will identify areas that require attention for improvement.
• It is important that the teacher feeds the information back to the student in a constructive manner identifying the areas where further development is required, and discussing how to raise the level of performance for the next assessment.

​Formative assessment can be used as a summative assessment.

• Formative assessment can be used effectively for summative purposes, and to a degree, can offer more in terms of the feedback and feed-forward that is given as part of the formative process.

Hence, we can conclude that the formative assessment can sometimes be a summative assessment and vice versa statement is true.

Additional Information

Some more types of assessments are as follows:

To create a balanced assessment approach in teaching-learning, different types of assessment strategies should be incorporated. Assessment can be of three types- assessment for learning (formative assessment), assessment of learning (summative assessment), and assessment as learning (authentic assessment).

Key Points 

From the above-mentioned situation, it could be interpreted that the teacher is assessing the students by conducting the formative assessment as it refers to monitor the child's progress throughout the teaching-learning process. In this case, it will help the teacher to know the children's learning needs regarding that topic and then meet the needs by remedial teaching.

Important Points 

Assessment for Learning (Formative Assessment):

• It is also referred to as internal evaluation.
• In this form of assessment, a teacher embeds various forms of assessment all through the teaching and learning process. Therefore, it is an ongoing assessment that allows teachers to monitor students on a day-to-day basis and modify their teaching based on what the students need to be successful.
• Formative assessment refers to a wide variety of methods that teachers use to conduct in-process evaluations of student comprehension, learning needs, and academic progress during a lesson, unit, or course.
• Effective formative assessment strategies involve asking students to answer well-thought-out, higher-order questions such as “why” and “how.”
• For students, it identifies learning errors that need to be corrected and for teachers, it provides information for modifying instructions.
• Questionnaires, quizzes, oral discussions, unit tests are some tools used for formative evaluation.

Hence, we can conclude that a teacher asks his/her students to draw a concept map to reflect their comprehension of a topic. He/She is conducting the formative assessment.

Benjamin Bloom's taxonomy is a set of three hierarchical models that refers to the classification of educational learning objectives. In the taxonomy, Bloom identified three domains of learning which include cognitive, affective, and psychomotor. 

• In 2001 the revised version of Bloom's taxonomy was published in which the 'evaluating' domain refers to judge the logical consistency of a solution.
• In this level, the students can critically examine information, make judgments, and justify decisions related to the value of the materials they've just learned, applied, and analyzed.

Diagram

Hence, in Bloom's revised taxonomy, Judging the logical consistency of a solution represents the domain 'evaluating'.

The term 'underprivileged' refers to the disadvantaged section of people who are economically, socially and vocationally in an unfavourable situation compared to the rest of the population of society. Thus, it is a relative term. They are underprivileged to the middle-class or upper-class people of their society.

Value Concerns at the School Stage: One of the major debates around value education is which values should be inculcated among students. Values are a complex mix of understanding, attitudes, beliefs, behaviours and skills. The following are the core values that need to be inculcated:

• Responsibility: 
• Towards Self Development: It is important to awaken the consciousness of students to take responsibility for their selves and develop a quest for personal improvement
• Towards One’s Work/Duty: If students assume responsibility for their actions/behaviour then they become willing to be accountable for their actions
• Social Responsibility: This involves gradual growth of consciousness from the self to the other and knowledge of the self as a member of a family, neighbourhood, village, town, city, community, nation and global society.
• Health and Hygiene: Cleanliness; healthy eating/food habits; posture; fitness, rest/relaxation, avoiding indulgence, etc. are related attitudes and skills.
• Love, Care and Compassion: Being a humane person is an essential attribute of an educated person. Love is an essential value for nurturing humaneness and human dignity of oneself and others.
• Critical and Creative Thinking: Critical thinking is highly valued which can help students to think logically, analyze situations critically, apply the judgement of what is good and bad, and examine their values vis-à-vis the values in the world, congruence or incongruence in them.
• Appreciation for Beauty and Aesthetics: Appreciation for beauty and aesthetics is valued as it equips students with an awareness of the ability to create, and express their ideas in ways that look and feel good, in addition to what is logical and right

Hence, we conclude that teachers must believe in Personal  Accountability for Students' success in the context of dealing with disadvantaged learners.

Stuttering is a speech disorder which affects the flow of the speech by repeating the same word again and again. It can be dealt by applying the method of 'prolonged speech'. In this technique, the person having the stuttering problem is taught to say words broken down into their syllables, and the utterance of the syllables is prolonged to replace the stuttering way of speaking with the smooth and controlled one.

Embedded learning opportunities (ELOs) are short teaching episodes that teachers set up for when there is a good match between classroom activities and a child’s individual learning objectives. This refers to teaching and learning that takes place during daily classroom activation and routines. Teachers plan opportunities to embed short, systematic institutional interaction into activities and routines to enhance a child's learning of specific skills. 

Key Points

Embedded learning- 

• The above-mentioned learning technologies/strategies are associated with 'embedded learning', which provides lots of opportunities for children to be skilled in literacy, language, and numeracy with vocational and lifelong skills.
• This learning program is aimed at making learning disabled children confident, competent, motivated to succeed in life by giving the quality experience of learning in natural ongoing routines.

Thus we can conclude that the above design is related to embedded learning. 

Additional Information

Interventionist learning-

• It refers to learning problems

Universal design for learning- 

• The UDL Guidelines are a tool used in the implementation of Universal Design for Learning.
• These guidelines offer a set of concrete suggestions that can be applied to any discipline or domain to ensure that all learners can access and participate in meaningful, challenging learning opportunities.

Inclusive classroom is a part of 'inclusive education' that refers to the inclusion of all children in the education system, regardless of their differences and disabilities. It is about making school a place where all children can participate and learn.

Key Points In inclusive classroom teachers create diverse and meaningful learning experiences for every learner as:

• It values the diversity, each child brings to the classroom and facilitates all with equal opportunities to learn and grow.
• Inclusive education improves the quality and making provisions of education for all.
• Inclusive education welcomes and celebrates diversity.
• It provides a provision to include disabled children along with normal children in a regular classroom environment.
• It refers to an education system that accommodates all children regardless of their physical, intellectual, social, emotional, linguistic, or other conditions.

Basic Principles of Inclusive Education:

• Equity and equal opportunities for all.
• Well constructed educational plan.
• Use of multilingualism as a resource.
• Use of specific pedagogical strategies.
• Sensitization towards individual differences.

Hence, it could be concluded that an inclusive classroom is where teachers create diverse and meaningful learning experiences for every learner.

Giftedness is a characteristic of children that refers to performing a task extraordinarily when compared with others of their peer group.

A gifted child always shows novelty in expression, curiosity, creativity and independency in thought.

Creating a prototype of a new Science book based on different themes would be an appropriate assignment for gifted students because they grab things fastly than of their age-peers that's why sometimes classroom seems monotonous to them. This assignment will involve them in creative work and will make learning interesting for them.

Dropout refers to the practice of leaving schools before completing a certain level of schooling. The institutional reason for children dropping out of government schools is that there is no alternative curriculum which refers to the curriculum designed for students who are not able to make progress in general education settings. The absence of the alternative curriculum makes the child obligated to follow the compulsory curriculum which later results in the dropout of children from the schools.

Other reasons for dropouts:

• Poverty, Accessibility and Availability: Often, schools are used for other purposes rather than what a school is meant for. For example, as an election booth, relief camp. Hence, there is no place for students to study.
• The School and Teachers: Sometimes school becomes a 'toxic' place for students where he does not like to come. For example, getting expelled for "talking back to teacher". He should be provided remedial teaching in such cases. Poor teaching and a hostile environment of school also lead to the dropout of students.
• Lack of Interest: Many a time students do not take interest in studies. Reason can be many behind this, as interest in sports, music, or sometimes teachers fail to create interest.
• Excessive Academic Pressure from School and Parents: The higher expectation is something students can not cope up with. Every parent needs to understand that a child has his own capability and interest, which makes him different from other children.
• Frequent Change of School: Transfer of parents many a time leads to change in school. As a result, the child loses his dearest friends, and for him, it is not less than a trauma, which leads him to drop out of school.
• Bullying: It is something every child faces in his school life. Some students consider themselves 'superior' to others and they like to misbehave with other children which leads to the demoralization of the child, and hence, he leaves school.
• Constant Failure: Failure in exam demoralizes students and that leads them to drop out.
• To Support Family: Students give up their studies because of their poor background, they have to work as a labourer to earn money so that they can support their family.
• Delinquency: It is usually seen in adult children where they are not aware of the facets of the world, and fascination is everything for them. They commit those crimes willingly-unwillingly which can cost them in the future.
• Education Not Considered Necessary: Often, children are way too practical that they believe that doing a job will get the money and success rather than studying. In this way, they don't consider education necessary.
• The Community they belong to: Some community do not consider education useful, especially for girls. Hence, they get girl children to drop out of school to get them to marry.

Learning disability is a disorder that affects people’s ability to either interpret what they see and hear or to link information from different parts of the brain.

• It refers to the neurological disorder that causes cognitive impairment.
• It can't be attributed to emotional disturbance or cultural differences because it also presents in children with average or above-average IQ.
• It make them struggle in a particular area (reading, writing, maths) where they need remedial educational help.

Hence, it becomes clear that learning disabilities are also present in children with average or above-average IQ.

Problem-solving is a learner-centred approach that emphasizes the learner's active involvement in the learning process.

• It is more likely to succeed in schools where a flexible curriculum is in place to update itself according to the advancements and personalities of the learners.
• It helps the children to learn better by catering totality of their experiences that occur in the educational process.

Hence, Problem-solving is more likely to succeed in schools where ​a flexible curriculum is in place

Cognitive apprenticeship and instructional conversation both conceive learning as a social activity by providing children with lots of opportunities to learn in real-world settings.

Have a look for conceptual understanding:

• Cognitive apprenticeship: It is a pedagogical method that refers to involve students in authentic practices through activity and social interactions.
• Instructional conversation: It refers to the learning process where the teacher assists the learners through scaffolding to make them perform just beyond their current level.

Errors are the necessary condition in the learning process to give insight into children's thinking. It helps the teacher to be aware of their learning styles, to cater them according to their needs.

Correcting errors that interfere with the general meaning and understanding would be the right way for a teacher because it will help the teacher to develop a basic sense in children regarding the general idea of a topic.

Note: Every error of children shouldn't be corrected as it could make students hesitate to show their thought which will be a hindrance in the process of meaningful learning.

Emotion is a mental state associated with fear, anger, love, etc while emotional intelligence refers to the capability of an individual to recognise, control and manage one's own emotions and the emotions of others as well.

Key Points

Other skills involved in emotional intelligence:

• Social skills
• Self-confidence
• Conscientiousness
• Motivation and adaptability
• Self-regulation/Awareness

Note: Criticism of emotions is not a skill involved in emotional intelligence rather it indicates the lack of emotional intelligence because it is not related to the way an individual recognise and manage his/her emotions.

From the above-mentioned condition of Devika and Rajesh, it could be interpreted that their emotional experiences are most likely to differ concerning the 'level of adaption' which refers to the fact that response of an individual regarding a particular stimulus could be governed by his/her past experiences.

Here, in this case, it could be possible that Devika will have the past experience in appearing in an assessment while Rajesh won't have because adaption level theory also relates to the process which makes an individual insensitive to the effect of constant stimulant.

The Mid-day Meal Scheme, commonly known as MDMS, is a school meal programme of the Indian government designed for the better nutritional value of school children in the country.

Key Points

• This scheme is supported by the humanistic theory of motivation which refers to the fact that the basic needs of human beings affect their action.
• Abraham Maslow's "Hierarchy of Needs" is one of the famous humanistic theories of motivation in which he has proposed a series of needs to be fulfilled in life.
• The mid-day meal scheme is associated with the very first need of this theory which is physiological needs consisting of physical survival necessities such as food, water, and shelter.

Hence, it could be concluded that the Mid-Day Meal Scheme  is supported by the humanistic theory of motivation 

Additional Information

The above-mentioned phenomenon is related to the 'ecological system theory' of learning which was propounded by Urie Bronfenbrenner.

The theory emphasizes the fact that how the community, society, and different environments influence the development of a child throughout the lifespan.

The theory consists of five different types of systems including microsystem, mesosystem, exosystem, macrosystem, and chronosystem. The mesosystem is related to the context of the question because it relates the child's family experience with his/her school experience for better outcomes.

Children become inattentive in class when they are not able to understand certain topics or classroom environment seems monotonous to them. In such situations making the child sit in the most distraction-reduced area will be the best way to deal with them.

By following this idea the teacher could pay more attention to that particular child and could direct his/her activities according to the teaching-learning process which would be an appropriate strategy to regain his/her attention.

Given:

0.001 + 1.01 + 0.11

Calculations:

Solving the given terms,

⇒ 0.001 + 1.01 + 0.11

⇒ 1.12 + 0.001

⇒ 1.121

∴ The value of 0.001 + 1.01 + 0.11 is 1.121

Given:

Population of country = 30.3 million

Concept used:

1 million = 10 lakh

1 lakh = 100000

Calculations:

Solving the given value

⇒ 30.3 million = 30.3 × 10 lakh

⇒ 303 lakh = 303 × 100000

⇒ 303 lakh = 30300000

∴ The number which is the same as 30.3 million is 30300000

Given:

a3 = 1 + 7      ----(i)

33 = 1 + 7 + b      ----(ii)

43 = 1 + 7 + c      ----(iii)

Calculations:

Solving the equation (i)

⇒ a3 = 1 + 7

⇒ a3 = 8

⇒ a = 2

Solving the equation (ii)

⇒ 33 = 1 + 7 + b

⇒ 27 = 8 + b

⇒ b = 19

Solving the equation (iii)

⇒ 43 = 1 + 7 + c

⇒ 64 = 8 + c

⇒ c = 56

Using the values of a, b, and c,

⇒ a + b + c = 2 + 19 + 56

⇒ a + b + c = 77

∴ The value of a + b + c is 77

Given:

28 is a perfect number

Concept used:

A perfect number is a number that is the sum of all of its positive divisors excluding itself

Calculations:

The sum of all positive divisors of 28,

⇒ 1 + 2 + 4 + 7 + 14 

⇒ 28

Checking the condition of a perfect number in the given options

Option first,

⇒ 1 

Option second,

⇒ 1 + 2 + 5 

⇒ 8

Option third,

⇒ 1 + 2 + 3 

⇒ 6

Option fourth,

⇒ 1 + 2 + 3 

⇒ 6

In the given options, only the fourth option satisfies the condition of a perfect number

∴ The perfect number is 6

Concept used:

A perfect square is a number that can be expressed as the product of two equal integers

Calculations:

In the given options, only 548543241 can be expressed in terms of the product of pairs of prime factors

⇒ 548543241 = 3² × 372 × 2112 

∴ In the given options, a perfect square is 548543241

Given:

Product of two whole numbers = 24

Calculations:

All the possible product pairs of 24 are (1 × 24), (2 × 12), (3 × 8), (4 × 6)

Checking the sum for the given pairs

⇒ 1 + 24 = 25

⇒ 2 + 12 = 14

⇒ 3 + 8 = 11

⇒ 4 + 6 = 10

Amongst the given product pairs of 24, (4 × 6) gives the smallest sum 

∴ The smallest possible sum of these numbers is 10

Given:

$\frac{3^{502} - 3^{500} + 16}{3^{500} + 2}$

Calculations:

Dividing both the numerator and denominator by 3⁵⁰⁰

$⇒ \frac{3^{2} - 1 + \frac{16}{3^{500}}}{1 + \frac{2}{3^{500}}}$

∵ $\frac{16}{3^{500}}$ and $\frac{2}{3^{500}}$ are very very small and thus negligible. We can put 0 in their places 

$⇒ \frac{3^{2} - 1}{1}$

⇒ 9 - 1 

⇒ 8

∴ The value of the given expression is 8

Given:

800880 = 8 × 10x + 8 × 10y + 8 × 10z

Calculations:

Simplifying the given term

⇒ 800880 = 800000 + 800 + 80

Expressing in terms of the power of 10

⇒ 800000 + 800 + 80 = 8 × 105 + 8 × 102 + 8 × 101

By comparing, we get x = 5, y = 2, and z = 1

⇒ x + y + z = 5 + 2 + 1

⇒ x + y + z = 8

∴ The value of x + y + z is 8

Given:

x4 + x2 + 1

Concept used:

a^2_-- b² = (a + b)(a - b)

Calculations:

Factorizing the given expression,

⇒  (x2)² + 2(x2) × 1 + 1² - x2

⇒  (x2 + 1)2 - x²

⇒ (x2 + 1 - x)(x2 + 1 + x)

∴ One factor of x4 + x2 + 1 is x2 - x +  1

Given:

Scale of map = 1 ∶ 10000

Forest area on map = 10 cm × 100 cm 

Concept used:

1 km = 1000 m

1 m = 100 cm

1 km = 100000 cm

Calculations:

According to question, 1 unit on map = 10000 

Actual Length of forest = 10 × 10000 cm

⇒ 100000 cm

⇒ 1 km

Actual Breadth of forest = 100 × 10000 cm

⇒ 1000000 cm

⇒ 10 km

Area of forest = 1 × 10 = 10 km²

∴ The actual area of the forest is 10 km2

Given:

Fraction = $\dfrac{5}{8}$

Denominator + Numerator = 91

Concept used:

In a fraction, $\dfrac{p}{q}$

p = Numerator

q = Denominator

Calculations:

Let the numerator and denominator be 5x and 8x respectively

⇒ 5x + 8x = 91

⇒ 13x = 91

⇒ x = 7

Difference = 8x - 5x 

⇒ 3 × 7

⇒ 21

∴ The difference between numerator and denominator of this fraction is 21

Given:

Number = n

Calculations:

Applying the operations to the given number

Adding y to the double the number = 2n + y

Dividing the result by 2,

⇒ (2n + y)/2

⇒ n + (y/2)

Subtracting n from the result, 

⇒ n + (y/2) - n

$\Rightarrow \dfrac{y}{2}$

∴ The final result is $\dfrac{y}{2}$

Given:

Number of faces = 6

Number of vertices = 8

Formula used:

Euler's formula for polyhedron

F + V - E = 2

Where,

F = Number of Faces of Polyhedron

V = Number of Vertices of Polyhedron

E = Number of Edges of Polyhedron

Calculations:

Let the polyhedron has E edges,

⇒ 6 + 8 - E = 2

⇒ 14 - E = 2

⇒ E = 14 - 2

⇒ E = 12

∴ The Polyhedron has 12 edges

Concept used:

Basic mathematical operations of addition and subtraction

Calculations:

Solving the given expression,

⇒ 1957 - a9 = 18b8

⇒ 1957 - 18b8 = a9

At the unit digit, the number 7 is lesser than 8 thus 1 was borrowed from the number 5

The result shows that 1 was also borrowed to the number 5 from the number 9 in the hundredth position

⇒ 14 - b = a 

⇒ a + b = 14

∴ The sum of the digit a and b is 14

Given:

Number of cubes = 42

Side of cube = 1 cm

Perimeter of base of cuboid = 18 cm

Concept used:

The cubes that are at the 4 corners contribute 2 cm to the perimeter, and the rest cubes contribute 1 cm to the perimeter

Formula used:

Height of the cuboid = (Total number of cubes/Number of cubes in the base) × Side of the cube

Calculations:

Number of cubes in the base of the cuboid

⇒ 18 - 4 

⇒ 14 

Height of cuboid = (42/14) × 1

⇒ 3 cm

∴ The height of the cuboid is 3 cm

Given:

PQ = 4 cm

PR = 6 cm

QR = 3 cm

Concept used:

The angle opposite to the longest side of the triangle has the largest angle in the triangle

Calculations:

Using the sides of the triangle,

PR is the longest side of the given triangle, thus the largest angle of the triangle is ∠Q

QR is the smallest side of the given triangle, thus the smallest angle of the triangle is ∠P

The angles of the triangle are as follows: ∠Q > ∠R > ∠P

∴ Amongst the given options, ∠Q > ∠R satisfies the condition for the given triangle

Given:

AB = LM

AC = LN 

∠B = ∠M

Concept used:

SAS congruency: Two triangles are congruent if two sides and one included angle in a given triangle are equal to the corresponding two sides and one included angle in another triangle 

Calculations:

In the given two triangles, 

AB = LM

AC = LN 

∠B = ∠M

Two sides are equal but their corresponding angle is not equal so it is not a congruent triangle

∴ The two triangles are not congruent

Given:

Area of trapezium field = 720 m2, 

Distance between the two parallel sides = 20 m

Length of one of the parallel sides = 35 m

Formula used:

Area of Trapezium $= \frac{1}{2}\left( {a + b} \right) × d$

Where,

a, b = Two parallel sides

d = Distance between two parallel sides

Calculations:

Let the length of the other parallel side be 'x'

⇒ (1/2) × (35 + x) × 20 = 720

⇒ 35 + x = 72

⇒ x = 72 - 35

⇒ x = 37 m

∴ The length of the other parallel side is 37 m

Given:

Cost price of 10 candles = Selling price of 8 candles

Formula used:

Profit % = [(SP – CP)/CP] × 100

Calculations:

Let the cost price and the selling price be CP and SP respectively

⇒ 10 × CP = 8 × SP

⇒ SP/CP = 5/4

∵ SP > CP thus will result in gain

Gain = [(5 - 4)/4] × 100

⇒ (1/4) × 100

⇒ 25%

∴ The gain percent is 25%

Given:

Data = {7, 6, 7, 9, 8, 8, 10, 8}

Number of terms = 8

Concept used:

Mode is the most repeated value in a data

If the total number of observations (n) is an odd number,

Median = (n +1)/2^th term

If the total number of observations (n) is an even number,

Median = {(n/2)th term + [(n/2) + 1]th term}/2

Mean = (Median + Mode)/2

Calculations:

Arranging the terms in ascending order,

6, 7, 7, 8, 8, 8, 9, 10

Most repeated term in the data = 8 (3 times)

Mode = 8

Median = (4^th term + 5^th term)/2

⇒ (8 + 8)/2

⇒ 8

Mean = (8 + 8)/2

⇒ 8

∴ The mean of mode and median is 8

The teaching of mathematics in the class is not only concerned with the computational knowledge of the subject but is also concerned with the selection of the mathematical content and communication leading to its understanding and application. 

Key Points

Learning Mathematics depends heavily on the knowledge and experience that children bring with them to school. If a teacher conducted a debate in the class on the following topic: "Zero is the most significant number." this will help children learn in numerous ways.

• the task of a teacher is to help his/her students conceptualize abstractness through concrete experiences.
• by asking the students to speak their views on the topic the teacher is making her classroom more interactive and communicative.
• as a teacher, it is our duty to provide such type of activities that gives them first-hand experience to the learner to construct mathematical knowledge.

Important Points

After doing debate, students will learn these:- 

• It enhances student's mathematical ability.
• Students will be intrinsically motivated.
• Children will show interest in solving mathematical problems and reading literature.
• Children will actively participate in Mathematics club activities, exhibitions, quiz, etc.
• Children will show a positive attitude towards Mathematics.
• It will boost the children's confidence in learning Mathematics.

Thus, it is concluded that the teacher is making her classroom more communicative and reflective.

The exponent of a number shows how many times we are multiplying a number by itself. For example, 3⁴ means we are multiplying 3 four times. Its expanded form is 3×3×3×3. Exponent is also known as the power of a number. It can be a whole number, fraction, negative number, or decimals. 

• Inter-disciplinary implies the emergence of novel insights and understandings of a problem domain through integrating or deriving different concepts, methods, and epistemologies from different disciplines.
• Inter-disciplinary is a synthesis of two or more disciplines establishing a new level of discourse and integration of knowledge.
• An interdisciplinary approach to teaching requires planning that looks at the foundational objectives of a number of curriculum areas.
• Connecting curriculum in the interdisciplinary approach is an effective way to help teachers deal with the knowledge that grows at exponential proportions.
• A unit of study that uses the interdisciplinary approach enables teachers to teach the whole student and make links between disciplines.

Thus, it is concluded that the use of such examples reflects the inter-disciplinary approach.

Piaget‟s theory of cognitive development proposed four primary cognitive structures or developmental stages such as sensorimotor, preoperational, concrete operational and formal operational.

• In the sensorimotor stage, intelligence takes the form of motor actions.
• Intelligence in the preoperational stage is intuitive in nature.
• The cognitive structure during the concrete operational stage is logical and depends upon concrete concepts.
• In the final formal operational stage, thinking involves abstractions.

Key Points

• Cognitive structures change through the processes of assimilation and accommodation.
• Assimilation involves the interpretation of events in terms of the existing cognitive structure;
• as the introduction of a linear equation and learning techniques of solving it is assimilation because the child interprets the new knowledge in existing knowledge.
• Accommodation refers to changing the cognitive structure to make sense of the environment.
• a child connecting the linear equation and learning techniques to basics of the linear equation then it is accommodation because a child changed his cognitive structure.

Thus from the above-mentioned points, it is clear that according to Jean Piaget's theory introduction of a linear equation and learning techniques of solving it is assimilation, and extending the concept to a pair of linear equations may raise the problem of accommodation.

Continuous assessment of learners' work not only facilitates their learning of Mathematics but also enhances their confidence in the application of learning in Mathematics. This view changes the focus of assessment from summative evaluation, where learners are evaluated at the end of the unit and provided grades, to the formative evaluation where learners are evaluated in the pursuit of learning. 

Key Points

Mathematics laboratory:

• is a unique room or place, with relevant and up-to-date equipment, known as instructional materials, designed for the teaching and learning of mathematics and other scientific or research work, whereby a trained and professionally qualified person (mathematics teacher) readily interacts with learners on a specified set of instructions.
• it helps learners to comprehend mathematical concepts effectively by utilizing concrete objects and experiencing real situations.
• learners can test and experience theoretical knowledge and discover different mathematical properties.
• the teacher can assess the students through the lab activities. These activities can be used for both formative and summative assessments of the learner.
• it enhances the interest and motivation of learners to learn mathematics.
• math labs provide objects and materials, which help learners to relate concepts with their daily life activities and nature.

Thus from above-mentioned points, it is clear that 'Maths lab-activities' can be used for both formative as well as a summative assessment.

Mathematics education has its own aims. According to David Wheeler, it is “more useful to know how to Mathematize than to know a lot of mathematics”. It is echoed in the National Curriculum Framework 2005, “Developing children’s abilities for mathematization is the main goal of mathematics education.” According to George Polya, there are two kinds of aims in mathematics for school education such as broader and narrower aims. 

Key Points

• The narrower aim of teaching Mathematics at school is to develop useful capabilities, particularly those relating to numeracy- numbers, number operations, measurements, decimal, algebra and percentage.
• The broader aim is to develop the child to think and reason mathematically, to pursue assumptions to their logical conclusions and to handle abstractions. School Mathematics curriculum should help the children learn to enjoy Mathematics.

Thus from above-mentioned points, it is clear that as per the NCF, 2005 narrow aim of teaching Mathematics at school is to develop numeracy - related skill and the higher aim is to develop problem - solving skill.

Important Points

Considering the broader and narrower aims of mathematics education, the followings are some of the major aims of mathematics education: 

• To develop the powers of thinking and reasoning.
• To solve mathematical problems of daily life.
• To understand and acquainted with the environment and culture
• To prepare the child for various technical and general future professions.
• To prepare the child for higher study.
• To develop in the child the power for invention.

Bloom attempted to answer the question by developing a method of classification for thinking behaviours that were believed to be important in the processes of learning. Eventually, this framework became taxonomy and was found in three domains. 

• The cognitive – knowledge-based domain, consisting of six levels
• The affective – attitudinal based domain, consisting of five levels,
• The psychomotor – skill-based domain, consisting of six levels.

Key Points 

Bloom's Revised Taxonomy- 

• Bloom's taxonomy has been revised by considering the present demand of teaching-learning activities. The changes are found in three broad categories: terminology, structure, and emphasis.
• In this case, the lowest level is ‘remembering’ whereas the apex level is ‘creating’. It follows from lowest to highest in this stairway—remembering, understanding, applying, analyzing, evaluating, and creating. This structure is known as Bloom’s revised taxonomy. The new terms are defined as:
• Remembering:
• Retrieving, recognizing, and recalling relevant knowledge from long term memory
• Understanding:
• Constructing meaning from oral, written, and graphic messages through interpreting, exemplifying, classifying, summarizing, inferring, comparing, and explaining.
• Applying:
• Carrying out or using a procedure through executing, or implementing.
• Analyzing:
• Breaking material into constituent parts, determining how these parts relate to one another and to an overall structure or purpose through differentiating, organizing, and attributing.
• Evaluating:
• Making judgments based on criteria and standards through checking and critiquing.
• Creating:
• Putting elements together to form a coherent or functional whole; recognizing elements into a new pattern or structure through generating, planning, or producing.

Thus from above-mentioned points, it is clear that prepare a PowerPoint presentation on the contribution of Indian mathematicians creating.

There are two primary approaches to teaching Maths- instrumental and relational understanding.

Key Points

• Relational understanding is students' understanding of which procedures to use and the reasons for each step.
• Instrumental understanding is the understanding of students in knowing the formulae and how to learn them.

• Teacher A focuses on instrumental understanding as she was just introducing the way to solve linear equations so it builds rote learning.
• Teacher B focuses on relational understanding as she was explaining the concept by establishing connections.
• The foundations of instrumental mathematics are rote learning, memory, rules, and accurate responses.
• Relational mathematics emphasises the establishment of links, the development of understanding over time, the application of concepts to different issues, and the progressive increase in complexity of problems.
• In truth, effective mathematical instruction necessitates a combination of approaches. In the long run, however, a focus on the Relational approach leads to a deeper knowledge of math and more confidence in students.
• The Instrumental (or, procedural) method can sometimes be easier to pick up. It provides rules to get the right answers and can be a rewarding option for arriving at the correct answer quickly. The risk? It doesn’t promote a deeper understanding of maths as found in the Relational (or, connected) approach — where what is learnt can be adapted to new tasks, becomes easier to remember and exists on an intuitive, organic level

Thus, it is concluded that teacher A emphasizes instrumental understanding while teacher B emphasizes relational understanding.

Mathematics teaching is often criticized for its emphasis on memorizing basic facts, rules, and formulae.

• If some students in your class are not able to do well in the mathematics tests consistently, then as a teacher you will first diagnose the reasons and take remedial steps.
• Giving more and more tests to practice without knowing and diagnosing the reasons is the act of putting mental pressure on the children.
• Children who do not perform well in the classroom, make them sit with high achievers, can develop an inferiority complex in children and a negative attitude can arise, so such children need to diagnose the causes and take steps for remediation.

Key Points

The above activity can be used by the teacher as a formative assessment task because the student's responses will help the teacher to diagnose their understanding regarding finding dimensions, calculations, knowledge of formulae for perimeter and area, etc. 

• ​After explaining the concept the teacher can take tests and ask about all the concepts or formulae related to the topic.
• The purpose of conducting the formative assessment is to monitor the learning progress of the learner; it is also conducted to know whether the learning objectives have been achieved or not and to provide feedback on the teaching-learning process.
• It includes diagnostic testing by formal and informal assessment procedures conducted by teachers during the learning process in order to improve learning activities and student's performance.

Thus, it is concluded that the above activity can be used by the teacher as a formative assessment task because the student's responses will help the teacher to diagnose their understanding regarding finding dimensions, calculations, knowledge of formulae for perimeter and area, etc.

Mathematics is the study of patterns, numbers, geometrical objects, data, and information. It deals with data analysis, integration of various fields of knowledge, involves proofs, deductive and inductive reasoning, and generalizations.

• It involves the mathematization of thoughts that develops through mathematical reasoning which consists of abstract statements and their proofs.
• In mathematics teaching, teachers should focus more on providing practical exercises and abstract knowledge to students to foster their individualized discovery-oriented learning.

Important Points

Square roots:- 

• A square root of a number n is a number m which, when multiplied by itself, equals n.
• The square roots of 16 are 4 and – 4 because 42 = 16 and (– 4)2 = 16.
• If m² = n, then m is a square root of n.

​

Key Points

• Students need math skills in real life. They probably recognize the need for simple math like addition, subtraction, etc.
• Students need to assess every maths concept that can be used in a real-life situation.
• Students need to understand the concept of a square root in order to understand other math concepts. Studying math is like building a block wall or a building: you need the blocks on the lower part so you can build on them, and if you leave holes, you can't build on the hole.
• Students ability to apply the concept of square roots in real-life situations can be assessed through the following problem- 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and number of plants in each row as they have to find the equal number of rows and plants by using the concept of square roots. If they are aware of it, they can easily do it.​

Thus, it is concluded that 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and number of plants in each row can be used to assess the concept of square roots in a real-life situations.

• In the given question $\frac{10 cm}{12 cm} = \frac{5}{6} cm$

$\frac{15 cm}{15 m} = 1000 \ m$

This student has the concept of units, conversion of units, fractions but missed the concept that ratio does not have units. 

Concept of units:-  A unit of measurement is some specific quantity like m, cm, mm, km, etc.

Conversion of units:- How to convert one unit to another like m into cm etc.

Fraction:- A fraction is a part of a whole.

In this question, the student knows all the concepts of units, fractions, conversion of units but he is unaware that ratio does not have units. The ratio is written like this:-Numerator/denominator 5/6   

Thus, it is concluded that Option 4 is correct.

Explanation:

Human Excretory System

• The waste present in the blood is required to be removed.
• For this, a mechanism has been developed commonly known as the Human Excretory System.

The Process

• Blood capillaries in the kidney do the process of filtration of blood.
• Both useful and harmful substance is present in the blood which reaches both kidneys. (E)
• The useful substances are absorbed waste is removed with water in form of urine. (D then A)
• The urine from the kidney goes to the urinary bladder.
• This is done through a tube-like passage called ureters. (C)
• It is stored in the bladder.
• After that, it is passed out through the urinary opening at the end of a muscular tube called the urethra. (B).

Conclusion:

From the above-explained process, we can say that the correct sequences according to the given statements are as below.

(E) → (D) → (A) → (C) → (B)

The correct option is (E), (D), (A), (C), (B).

Additional Information

• When the Kidney do not function properly, artificial kidney is used This process is called dialysis
• Excretion in Different Organisms'
• Aquatic animals like fishes, excrete cell waste as ammonia which directly dissolves in water.
• Some and animals like birds, lizards, snakes excrete a semi-solid, white-colored compound (uric acid).
• Plants remove excess of water through transpiration.

Concept:

Micro-organisms:

• The living organisms which cannot be seen through our naked eyes are called micro-organisms.
• Microorganisms are classified into four major groups. These groups are bacteria, fungi, protozoa and some algae.

Explanation:

• Amoeba is a single-celled organism belonging to the group protozoa.
• Amoeba has no definite shape, unlike other organisms.
• It keeps on changing its shape. various projections of varying lengths keep protruding out of its body. These are called pseudopodia (pseudo: false; podia: feet).
• These pseudopodia perform various functions like movement and locomotion, capturing of prey (food), etc.
• Thereby, the correct option is ''movement and capture of food''.

Diagram showing how amoeba captures its food using pseudopodia.

Explanation:

Parasitic mode of Nutrition

• Organisms following a parasitic mode of nutrition do not prepare or look out for their own food.
• They are dependent upon other organisms for their nutrition.
• In plants, Cuscuta is an example of a parasite as it depends upon other plants.
• It does not have chlorophyll and it takes food from another plant which is known as the host.
• In animals, bedbugs, Leeches, and Lice are examples of parasitics.
• Bedbugs, leeches, and lice feed themselves on the blood of other animals.

So, the correct option here is (B), (C), (D), and (F).

Additional Information

Some Other Types of Nutrition

• Symbiotic and Parasitic are heterotrophic mode of nutrition where plant directly or indirectly depends upon autotrophs for their food.

Concept:

Fermentation

• This process of conversion of sugar into alcohol is known as fermentation.
• Yeast and bacteria are helpful in process of fermentation.
• Fermentation is also used for making alcoholic beverages.
• The process is used to make food items like dosa and idli.
• Louis Pasteur discovered fermentation in 1857.

Penicillin

• Penicillin is a type of antibiotic.
• It was discovered by a Scottish bacteriologist, Alexander Fleming in 1928.
• It was widely used to treat the different types of bacterial infections that plagued man.
• Penicillin was an accidental discovery, but it was a landmark discovery in the field of medicine.
• Penicillin is acquired from a mold called Penicillium notatum (also known as Penicillium chrysogenum).

Vaccine

• Our body produces antibodies if the microbes causing diseases enter.
• The body also remembers how to fight the microbe if it enters again.
• This is the formula used for preparing vaccines.
• If dead or weakened microbes are introduced into a healthy body, the body can fight by developing suitable antibodies.
• Government promotes vaccination and vaccination drives like pulse polio Abhiyan were quite successful.
• Edward Jenner discovered the vaccine for smallpox in 1798.
• A worldwide campaign against smallpox has finally led to its eradication from most parts of the world.

Disease-causing Microbes

• Microbes cause certain communicable diseases in animals, human beings,s, and Plants also.
• These are spread through touch, air, water, or other mediums.
• Examples of such diseases include cholera, common cold, chickenpox, and tuberculosis.
• Anthrax bacterium causes anthrax which is a dangerous human and cattle disease.
• Robert Köch (1876) discovered the bacterium Anthrax also known as Bacillus anthracis.

Lactobacillus bacterium

• This bacterium is important for curd formation.
• Lactobacillus promotes the formation of curd.
• It multiplies in milk and converts it into curd.

Explanation:

• So, the question is regarding microorganisms, their uses, diseases caused by them, and discoveries related to them.
• Alexander Fleming discovered Penicillin.
• Edward Jenner discovered the smallpox vaccine.
• Louis Pasteur discovered fermentation.
• Robert Koch discovered Anthrax bacterium.

Therefore, the correct match is (a) - (iv), (b) - (v), (c) - (ii), (d) - (i).

Key Points

• The biosphere reserves are the areas meant for the conservation of biodiversity.
• These are large areas of protected land for the conservation of wildlife, plant and animal resources and traditional life of the tribals living in the area.
• The biosphere reserves help to maintain the biodiversity and culture of that area.
• A biosphere reserve may also contain other protected areas.
• The Pachmarhi Biosphere Reserve consists of one national park named Satpura and two wildlife sanctuaries named Bori and Pachmarhi

Additional Information

• There are a total of 18 biosphere reserves in India Eg. Nilgiri biosphere reserve, Nanda biosphere reserve, Pachmarhi biosphere reserve

The correct statements are (A), (B) and (C)

Key Points

• The cell is the structural & functional unit of life.
• Based on the presence or absence of nuclear membrane cells can categorize as prokaryotic & eukaryotic cells.

Prokaryotic Cell -

• The cells having nuclear material without a nuclear membrane are termed prokaryotic cells.
• The organisms with these kinds of cells are called prokaryotes (pro: primitive; karyon: nucleus).
• Examples of prokaryotes are bacteria and blue-green algae.
• Hence, statements A & C are correct.

Eukaryotic cell - 

• The cells having a well-organised nucleus with a nuclear membrane are designated as eukaryotic cells.
• All organisms other than bacteria and blue-green algae are called eukaryotes. (eu : true; karyon: nucleus).
• Hence, statement D is incorrect.​

The single cell of unicellular organisms can perform all the basic functions performed by a variety of cells in multicellular organisms.

Hence, statement B is correct.

Explanation:

• Hormones are chemical substances that perform certain important actions in the body.
• Hormones are secreted from endocrine glands or endocrine systems.
• The pituitary gland is the master gland of the body as it controls the functioning of many other endocrine glands.
• Apart from puberty, there are certain other hormones that are secreted by different endocrine glands present over the body.

The location of the various endocrine gland is present in the below diagram.

• From the above diagram, it is clear that A is the Pituitary gland, B is the thyroid gland, C is the adrenal gland, and D - Pancreas.
• So, the correct option is A - pituitary gland, B - thyroid gland, C - adrenal gland, D - pancreas.

• The functions of these endocrine glands are represented in the table.

Additional Information

• The changes which occur in adolescence are carried out by these hormones. 
• The male hormone or testosterone begins to be released by the testes at the start of puberty.
• The female hormone which onsets puberty is estrogen which causes changes in female at adolescence.

Concept:

Pressure: 

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

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

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

Pressure by Liquid

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

• As we go toward depth the more liquid is above to exert the pressure. So, pressure increases as we go in depth.
• Consider the following diagram.
• The pressure at A will be less than B, as less amount of liquid is present above it to exert the pressure.

Explanation:

• Now, coming to the question.
• At point C, the pressure will be highest as it is at the lowest point.
• The amount of liquid present at C is more than B and at B it is more than A.
• So, most pressure will be exerted at C.

 Hence, the sequence of applied pressure will be ​pressure at C > ​pressure at B > ​pressure at A.

Concept:

Reflection of Light

• The phenomenon of bouncing back of light when it strikes any surface is called the reflection of light.
• When the reflected light from any object strikes our eyes, we can see the object.
• The reflection taking place across the universe is governed by the laws of reflection.

Laws of Reflection

1. it states that, if a light ray is reflected from a plane flat polished surface its angle of the incident will always be equal the angle of reflection  i.e., The angle of incidence (θ i ) = Angle of reflection (θ r )
2. The incident ray reflected ray, normal all lies on the same plane.

• These laws of reflection are valid for all kinds of surfaces.
• In all these cases, the angles are measured by considering the point of incidence.

Conclusion:

• Since the angle of incidence is equal to the angle of reflection is valid for all kinds of surfaces, All three surfaces will follow this.
• The correct option is 'All the three surfaces'

Additional Information

• When light reflects at many angles after the incidence on the surface, such a reflection is called as diffuse reflection.
• Light rays are not parallel to each other after irregular reflection, but they obey laws of reflection at each point of reflection.

Concept:

Human Eye 

• The human eye is one of the most valuable and sensitive sense organs.
• It uses light and enables us to see the colorful world around us.
• The human eye is more or less like a photographic camera.
• The lens system of the eye forms an image of an object on a light-sensitive screen.

Conclusion:

• If we compare, the parts A,B,C and D with the actual human eye diagram with labeling, we will get
• A - ciliary muscle, B - iris, C - lens, D - cornea.

Additional Information

Functions of Parts

• Cornea: The cornea is the outer transparent part of the eye that protects the eyes from external agents.
• Iris controls the pupil which controls the amount of light. Iris gives distinct color to the eyes. The brown eye or blue eye actually is the color of iris.
• The eye lens is a spherical lens that forms an image of the object on the retina.
• The retina is a screen that sends the information to brain through the optic nerves
• The focal length of the eye lens is maintained by the ciliary muscles. It reduces the focal length by stretching itself to see nearby objects and relaxes to increase the focal length to see far objects.

Concept:

Human Eye

• The human eye consists of a convex lens.
• The convex lens forms an inverted real image on a screen behind it which is called the retina.
• The optic nerves carry this information to the brain.

Explanation:

• The impression of an image does not vanish immediately from the retina.
• It persists there for about 1/16^th of a second.
• This means if the next image of the same object comes before that, the object will appear to be moving.
• In other words, if still images of a moving object are flashed on the eye at a rate faster than 16 per second, it will appear to our eye as a moving object.
• Here, the closet option of 1/16^th of a second is 1 / 15 the second.

The correct option is $\frac{1}{15}$ second. 

Additional Information

Blind Spot

• The optic nerves are made up of two cells, cones, and rods.
• Cones are sensitive to bright light and rods are sensitive to dim light.
• Cones sense color. At the junction of the optic nerve and the retina, there are no sensory cells.
• Thus, no vision is possible at that spot. This is called the blind spot.

Human Eye

Functions of Parts

• Cornea: The cornea is the outer transparent part of the eye that protects the eyes from external agents.
• Iris controls the pupil which controls the amount of light. Iris gives distinct color to the eyes. The brown eye or blue eye actually is the color of iris.
• The eye lens is a spherical lens that forms an image of the object on the retina.
• The retina is a screen that sends the information to brain through the optic nerves
• The focal length of the eye lens is maintained by the ciliary muscles. It reduces the focal length by stretching itself to see nearby objects and relaxes to increase the focal length to see far objects.

Explanation:

The process of Irrigation

• The supply of water to crops at regular intervals is called irrigation.
• Water is important for the proper growth and development of all Organisms and hence also for the crops.
• Plants contain nearly 90% water.
• Due to these reasons, the Germination of seeds does not take place under dry conditions.
• This is also a fact that the nutrients and minerals get transported to each part of the plant in the dissolved form. Thus, water is required for the purpose.
• Apart from this Water protects the crops from both frost and hot air currents.
• It helps plants to maintain their metabolism during these unfavourable conditions.

So, the correct option is (A), (B) and (E).

• The time and frequency of irrigation are different for different types of crop and soil.
• The various sources of irrigation are wells, tube-wells, ponds, lakes, rivers, dams and canals.
• The supply of water to crops at different intervals do not improve the soil texture instead, the soil texture can be improved by manuring.

Concept:

Cell

• The cell is the basic structure or building block of all living beings.
• On basis of a number of cells, organisms are divided into unicellular and multicellular organisms.
• Unicellular organisms can perform all kinds of life processes like respiration, digestion of food, reproduction, and excretion of waste.
• Examples of unicellular organisms include amoeba, bacteria, etc.

Inside the cell

• The cell consists of various cell organelles or components which help it to survive by performing certain life processes.
• The basic components of a cell are the cell membrane, cytoplasm, and nucleus.
• The cytoplasm and nucleus are enclosed within the cell membrane.
• The cell membrane is also known as the plasma membrane. 
• It is a porous structure that allows the exit and entry of certain materials according to its requirement.
• This is the major function of the cell membrane.
• The cytoplasm is between the cell and the nucleus. 
• Cell organelles like mitochondria, Golgi bodies, ribosomes, etc. are present in the cytoplasm.
• The nucleus is the special structure located generally at the center of the cell. 
• The nuclear membrane separates the cytoplasm from the nucleus.
• The nucleus contains a central part called nucleolus and chromosomes.
• Chromosomes and nucleolus coexist in the nucleus. Chromosomes are not present in the nucleolus.
• Chromosomes carry genes and help in the inheritance or transfer of characters from the parents to their children.

Explanation:

• (A) Chromosomes are located in the nucleolus. This statement is wrong as chromosomes are located in the nucleus, not in the nucleolus.
• (B) Genes are located in the chromosomes. This is true.
• (C) Unicellular organisms respire and reproduce. This is true, amoeba can respire by the process of cellular respiration as well as reproduce asexually by binary fission.
• (D) The most important function of the cell membrane is to control the entry and exit of materials from cells. This is also true.

So, from the given concepts and explanation we can say that the correct option is '(B), (C) and (D).'

Additional Information

• The cell was first discovered by Robert Hooke in 1665
• He observed slices of cork under a simple magnifying device.
• The size of the smallest cell is 0.1 to 0.5 micrometer.

Concept:

Sound Wave

• Sound is a longitudinal mechanical wave that travels by creating alternate compression and rarefaction in the medium.
• Sound is produced by vibrations.
• Sound needs a medium to travel.

Frequency: 

• The number of the complete cycle of compression and rarefaction produced in one second is called the frequency of sound
• The frequency can also be defined as the number of vibrations produced by the source of sound in one second.
• The unit of frequency is Hertz (Hz).
• Infrasonic sounds have a frequency of less than 20 Hz and these are generally produced by sources of a bigger size such as earthquakes, volcanic eruptions, etc.
• Sound waves with frequencies below the audible range are called infrasonic.
• Audible sounds have the frequency of 20-20000 Hz since these are sensitive to the human ears
• And if the frequency is greater or less than audible frequency, the human ear won't be able to sense it
• Ultrasonic sounds have a frequency greater than 20000 Hz and certain creatures such as dogs, cats, bats can hear this kind of sound.

Explanation:

Ultrasound

• The sound whose frequency is more than 20,000 Hz is known as ultrasound.
• This has many applications in science and technology.
• This due to its ability to travel along well-defined paths even in the presence of obstacles.
• Ultrasound has many applications in medical science.

So, the correct option is above 20000 Hz.

Additional Information

• Applications in medical science
• It is used in medical technologies like ‘echocardiography’.
• It is used in the internal mapping of organs.
• It is used to clean parts located in hard-to-reach places, for example, spiral tubes, odd-shaped parts, electronic components, etc
• SONAR (Sound Navigation And Ranging) uses ultrasonic waves to measure the distances and other related parameters of any object.

Concept:

Pressure:

• The force per unit area is called pressure. It is denoted by P.
• The SI unit of pressure is the pascal (Pa).
• It is a scalar quantity because the pressure acts in all directions at a point inside a gas.
• The basic formula for pressure is given by:

${\rm{Pressure (P)}} = \frac{{{\rm{Force (F)}}}}{{{\rm{Area (A)}}}}$

Explanation:

• We have a solid rectangular box of iron which is kept over the table with different faces touching the table.
• The block will exert a force on the table which is equal to the weight of the block.
• Since the weight of the block will remain the same, the force applied by the box on the table will remain the same.
• But, since, the surface area in contact with the table will be different in different cases, the pressure will differ.

So, the correct option is the same force but different pressures.

Mathematical Explanation:

Suppose the dimension of the iron block is as shown in the figure.

The different surface areas of this cuboid will be l × b,  b × h, l × h. 

if l > b > h, the maximum area will be obviously l × b, and the minimum area will be b × h. 

So, if the box is placed along its length and breadth, then the surface area facing the table is A₁ = l × b. 

Pressure will be be 

${\rm{ (P_1)}} = \frac{{{\rm{ (F)}}}}{{{\rm{ (A_1)}}}}$ -- (1)

f the box is placed along with Its height and breadth, then the surface area facing the table is A₂ = h × b. 

${\rm{ (P_2)}} = \frac{{{\rm{ (F)}}}}{{{\rm{ (A_2)}}}}$ -- (2)

Since applied force (F) is the weight of the block and the same in all cases.

Since A₁ > A₂

P₁ < P₂ 

As a fraction with the same numerator and the higher denominator is smaller. 

So, pressure is different in different cases and force is the same.

In the following case, Case (a) will have more pressure as the area is less. 

Concept:

Cell

• The cell is the basic structure or building block of all living beings.
• On basis of a number of cells, organisms are divided into unicellular and multicellular organisms.
• Unicellular organisms can perform all kinds of life processes like respiration, digestion of food, reproduction, and excretion of waste.
• Examples of unicellular organisms include amoeba, bacteria, etc.
• Cell have certain components called cell organelles which makes cell to survive.
• Some of the cell organelles are vacuole, mitochondria, plastids, etc.
• Plant cells and animal cells have certain differences according to their need.
• The difference can be observed in the below diagram.

Explanation:

From the above diagram, if we compare to the question diagram (animal cell) we will get

A- cell membrane, B - vacuole, C - nucleus, D - cytoplasm is the correct option. 

Functions of organelles

• Cell Membrane: It is a porous structure that allows the entry or exit of materials from the cell according to the requirement.
• Vacuole: It is a blank-looking structure present in the cell which is used for storing food.
• Nucleus: It contains a central part called nucleolus and chromosomes. Chromosomes carry genes from parents to offspring.
• Cytoplasm: It is a jelly-like structure between the nucleus and cell membrane which contains other organelles.
• Plastids: It is present in the plant cells. The green-colored plastids contain chlorophyll and help in photosynthesis.
• Mitochondria: It is the powerhouse of the cell. it performs cellular respiration.

Concept:

• Speed: Total distance traveled by the total time taken is called speed.
• Speed measures how fast the body is moving.

$\rm speed = \dfrac{total \ distance}{total \ time}$

⇒ distance = speed × time

• Odometer: It is the device that is used to measure the distance traveled by a vehicle.
• Conversion of speed from km / hr to m /s

1 km = 1000 m

1 hr = 3600 second

1 km / 1 hr = 1000 m / 3600 second = $\frac{5}{18} \ m / s$

Calculation:

Odometer reading at 8:00 a.m. = 36540 km 

Odometer reading at 10:00 a.m. = 36666 km.

The difference in reading of meter = 36666 km - 36540 km = 126 km

Time taken (between 10:00 a.m. and 8:00 a.m.) = 2 hrs

$\rm speed = \dfrac{ 126 \ km}{2 \ hr} = 63 \ km /hr$

Now, this is needed to be converted into m /s.

For this the speed has to be multiplied by 5 / 18

So, speed 

$v = 63 \times \frac{5}{18} = \frac{35}{2} = 17.5 \ m/s$

So, the correct option is 17.5.

Concept:

Acid and Base

Indicators

• The indicators are chemicals or natural substances which change their colour in presence of acid or base.
• Litmus paper is an indicator that is obtained from lichens.
• Some indicators and their colour change are given in the table below:

Explanation:

• Turmeric is a natural indicator.
• It remains yellow in acidic solution and turns red in basic solution.
• This property of turmeric is also used in painting.
• Hydrochloric acid is an acid hence turmeric will remain yellow in that solution.
• Sodium hydroxide is the base, so turmeric will turn red in the sodium hydroxide solution.

So, the correct option is 'Yellow in hydrochloric acid and red in sodium hydroxide.'

Concept:

Absorption in Small Intestine

• The food stored in the stomach, after going through the required processes goes to the small intestine.
• The absorption of food takes place here first.
• This is the process of absorbing food by the blood vessels.
• For the process to happen, finger-like projection is present in the small intestine which is called villi.
• They have thin walls and mostly covered with a thin channel of blood capillaries.
• This increases the surface area and ensures maximum absorption.
• Each villus has a network of thin and small blood vessels close to its surface.

Conclusion:

• So, the correct Statements are
• (A) They are finger-like outgrowths and thousands in number:
• (B). They have very thin walls.
• (C) They have a network of thin and small blood vessels close to the surface.

Correct option is (A), (B) and (C).

Concept:

Test For Starch:

1. Take a small quantity of a food item or a raw ingredient. Put 2-3 drops of dilute iodine solution on it
2. Observe if there is any change in the colour of the food item.
3. A blue-black colour indicates that it contains starch.

Explanation:

• The food items containing starch will give a blue-black colour.
• Starch is a carbohydrate.
• The carbohydrate-containing food items in the above list are boiled and mashed potato and a slice of bread.
• The boiled and chewed rice is added to the iodine solution then the colour of iodine will not change because of the digestion of starch into sugars.
• The sugar solution and Coconut oil does not contain starch and hence will not give a blue-black colour.
• Thereby the correct option is (A) and (C).

Key Points

A spring balance is primarily meant for measuring the weight (force) of an object. However, in laboratories, a spring balance is often used to measure the mass of an object. The correct method of using a spring balance is-

• Record the least count of the spring balance.
• Note the zero error.
• Note the position of the pointer on the graduated scale
• Calculate the actual reading.

Thus from above-mentioned points, it is clear that the correct sequence of the steps to be followed is (D), (A), (C), (B).

Science refers to the study of structure and behaviour of the physical and natural things through observation and experimentation. In other words, science is a classified knowledge gained from a systematic study of the behaviour of nature. Science education should enable the learner to know the facts and principles of science and its applications, consistent with the stage of cognitive development. 

Key Points

At the upper primary level-

• The emphasis is on engaging the learner in learning principles of science through familiar experiences, working with hands to design simple technological units and modules and continuing to learn more about environment and health through activities and surveys.
• To acquire scientific literacy as the learners should be given the opportunity to explore science in their everyday experiences.
• To develop rational thinking, A teacher should engage learners (preferably in groups) in meaningful investigations -particularly of the problems they perceive to be significant and important.
• A teacher should encourage discussions with the teacher and peers.
• You can ask your learners to gather information from newspapers, knowledgeable persons in the neighborhood, and from easily available sources and discuss them in class with peers and teachers.
• Role play, skits, cooperative learning strategies should be adopted to ensure larger participation and sharing of learning outcomes.
• It is advised that biographical narratives of scientists and inventors can be used.

Thus, from the above-mentioned points, it is clear that performing better in the competitive examinations is not the desired objective of learning Science at the upper primary stage.

Teaching-Strategy: It is a process, which is explicitly and systematically designed to, ensure that the learners accomplish the instructional objectives. The purpose of instruction is to improve performance.

There are a variety of teaching methods that can be used by the teacher for teaching theory and skills in the classroom setting. These are broadly classified as:

• teacher-centred teaching methods
• Student-centred teaching methods

Key Points

Role Play Method-

• Role-play is another student-centred method of teaching, it ensures the active participation of students in the process of learning.
• Roleplay is defined as the spontaneous acting of roles in the context of clearly defined social situation by two or more persons for subsequent discussions by the whole class.
• Role-play is the medium to express one's opinion and feelings about a certain social situation, what people can think, and feel and why they behave and what can be done to handle the situations through presentation and discussion in the group.
• This method thus can generate data about human behaviour and human relations which are not available by traditional methods.

Advantages: 

• Develops skills in leadership, interviewing, and social interaction, e.g., how to lead a discussion, and how to be a member of the team responsible for patient care.
• Provides an opportunity for the student to put herself in another's place and to become more sensitive to another's feelings.
• Develops skills in group problem-solving. It helps the student in identifying critical issues and to come to a neutral agreement.
• Allows the student to practice selected behaviour in a real-life situation without the stress of making a mistake.