Extra Curriculum Support
Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
1.Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
2.Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.
3.Exam Preparedness: Sample Question Papers and NCERT Exemplar Solutions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
4.Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.
Sec A
1.
A.
B.
C.
D.
2. a × a × a × a × y × y × y × y × z × z can be written as
A.
B.
C.
D.
Sec B
1. Mass of earth is approximately 5,970,000,000,000,000,000,000,000 kg. Express this mass in standard form.
2. Express the following numbers in exponent form.
(i) 343000
(ii) 2048
3. If
Sec C
1. 8. In a factory, 9.2 kilograms of pumpkin pie filling is made per minute. How many kilograms of pie filling will be made in 6 minutes?
2. In triangles ABC and PQR, AB = 3.5 cm, BC = 7.1 cm, AC = 5 cm, PQ = 7.1 cm, QR = 5 cm and PR = 3.5 cm. Examine whether the two triangles are congruent or not. If yes, write the congruence relation in symbolic form.
Sec D
1. If
2. The population of a town increases by 5% every year. If the current population is 20,000, what will be the population after 3 years? Express your answer in scientific notation.
Value-Based Questions
Problem 1
How does the presence of symmetry in nature (such as in leaves, flowers, and animals) inspire a sense of harmony and balance in our surroundings? Discuss the value of symmetry in promoting environmental awareness.
Problem 2
Why is symmetry important in architecture and design, and how does it reflect values like stability, order, and balance in society?
HOTS
Q1
A polygon has rotational symmetry of order 6. If one of its interior angles is 120°, can you determine how many sides the polygon has, and explain how rotational symmetry affects the overall structure of the polygon?
Q2
In architecture, some famous buildings are designed with reflective symmetry across multiple planes. How would you analyze the structural stability and aesthetic impact of such designs, and what role does symmetry play in the architectural success of these structures?
Q3
Consider a scenario where a butterfly's wings display bilateral symmetry. If one side of the wings experiences damage, how would the lack of symmetry potentially affect the butterfly's ability to fly? Relate this to the importance of symmetry in biological functions?
Q4
In mathematics, certain fractals exhibit both self-similarity and symmetry. How would you apply the concept of symmetry to analyze the infinite patterns in fractals, and what conclusions can you draw about the role of symmetry in complex geometric shapes?
NCERT Exemplar Solutions
Questions
1.In the word “MATHS” which of the following pairs of letters shows rotational symmetry.
(a) M and T (b) H and S (c) A and S (d) T and S
2. A net of a 3-D shape is a sort of skeleton - outline in 2-D, which, when folded results in the 3-D shape.
3. Construct a triangle PQR such that PQ = 6 cm, QR = 7 cm and PR = 4.5 cm.
4. A triangle can be constructed by taking its sides as:
(a) 1.8 cm, 2.6 cm, 4.4 cm (b) 2 cm, 3 cm, 4 cm
(c) 2.4 cm, 2.4 cm, 6.4 cm (d) 3.2 cm, 2.3 cm, 5.5 cm
5. All faces of a pyramid are always:
(a) Triangular (b) Rectangular
(c) Congruent (d) None of these
6. If we rotate a right-angled triangle of height 5 cm and base 3 cm about its base, we get:
(a) cone of height 3 cm and base 3 cm
(b) cone of height 5 cm and base 5 cm
(c) cone of height 5 cm and base 3 cm
(d) cone of height 3 cm and base 5 cm
7. ? and ? are the capital letters of English alphabets that have one line of symmetry but they interchange to each other when rotated through 180°.
8. In oblique sketch of the solid, the measurements are kept proportional.
9. An isometric sketch does not have proportional length.
10. Rotation turns an object about a fixed point which is known as centre of rotation.
11. By what minimum angle does a regular hexagon rotate so as to coincide with its origional position for the first time?
12. Draw the net of triangular pyramid with base as equilateral triangle of side 3 cm and slant edges 5 cm.
13. Draw the net of a square pyramid with base as square of side 4 cm and slant edges 6 cm.
14. Draw the net of rectangular pyramid with slant edge 6 cm and base as rectangle with length 4 cm and breadth 3 cm.
Case-Based Questions
Q1
Case: A stained glass window in a cathedral features intricate geometric patterns, many of which exhibit line and rotational symmetry. The architect wants to ensure that the new design maintains these symmetrical properties.
Question: If the window design has three lines of symmetry and rotational symmetry of order 4, how would the architect ensure that these features are preserved during construction? Discuss how symmetry enhances both aesthetic appeal and structural balance in this case.
Q2
A garden is being designed with a central fountain and symmetrical flower beds surrounding it. The designer must ensure that the pathways between the flower beds also follow a symmetrical pattern.
Question: How can the designer use reflective and rotational symmetry to create a visually pleasing and functional garden layout? What are the challenges involved in maintaining symmetry in large outdoor spaces?
Q3
Case: In a robotics competition, teams are required to build a robot with symmetrical features to ensure balance during movement. The design should include symmetry in both the robot’s structure and its movement patterns.
Question: What factors should be considered when designing the robot to maintain both structural and dynamic symmetry, and how does symmetry contribute to the robot's efficiency in performance?