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.
Sample Question Paper
Sec A
1. Explain whether the number 0 is a rational number or an irrational number. Justify your answer.
2. Determine whether the following statements are true or false:
(i) Every integer is a rational number.
(ii) The sum of a rational number and an irrational number is always irrational.
3. Simplify and express in decimal form:
Sec B
1. The simplest rationalisation factor of
(a)
(b)
(c)
(d)
2. Simplify and express in simplest form:
Sec C
1. Verify whether
Value-Based Questions
Problem 1
A school committee is planning a field trip for 72 students. If each bus can accommodate 36 students, how many buses are required for the trip? Discuss the significance of division and rounding in logistical planning for group activities.
Problem 2
Maya wants to distribute 300 notebooks and 450 pens among students in her neighborhood. If each student receives the same number of notebooks and pens, what is the maximum number of students that can receive the stationery items without any left over? Illustrate how division helps in fair distribution of resources.
Problem 3
Akash and Neha are organizing a charity drive in their school to raise funds for underprivileged children. They collected a total of ₹15,000. They decide to distribute the funds among three charities: Charity A, Charity B, and Charity C, in the ratio of
HOTS
Q1
Raju observed that the sum of the digits of any multiple of 9 is always divisible by 9. Prove this statement using mathematical reasoning and provide examples.
Q2
Ananya claims that the square root of any positive integer is either an integer or an irrational number. Discuss with examples and counterexamples to validate her claim.
NCERT Exemplar Solutions
Questions
1. If a =
2. Decimal representation of a rational number cannot be:
(a) terminating
(b) non-terminating
(c) non-terminating repeating
(d) non-terminating non-repeating
3. Which of the following is irrational?
(a)
(b)
(c)
(d)
4. Which of the following is irrational?
(a) 0.14
(b) 0.1416
(c) 0.1416
(d) 0.4014001400014........
5. A rational number between
(a)
(b)
(c) 1.5
(d) 1.8
6.
(a)
(b) 6
(c)
(d)
7. If
(a) 2.4142
(b) 5.8282
(c) 0.4142
(d) 0.1718
8. The product of
(a)
(b) 2
(c)
(d)
9. Find which of the variables x, y, z and u represent rational numbers and which irrational numbers :
(a)
(b)
(c)
(d)
10. Show that 0.142857142857... =
11. Express 0.6 + 0.7 + 0.47 in the form
12. Simplify :
13. Express 0.123 in the form
14. Find the value of a in the following :
15. Simplify:
16. Are there two irrational numbers whose sum and product both are rationals? Justify.
Case-Based Questions
Q 1
Rohan is participating in a math competition. The first round of the competition focuses on the number systems, and he is given the following scenario to solve:
Rohan’s school organizes a fundraiser event, and the total amount collected is ₹10,000. The collected amount is to be distributed equally among three different charity organizations: Organization A, Organization B, and Organization C. However, Rohan realizes that the distribution can also be represented using fractions and decimals, and he decides to explore the number system properties in the process.
Based on this scenario, answer the following questions:
1. How much money will each organization receive if the total amount collected is distributed equally among the three organizations? Represent your answer in both fraction and decimal form.
2. Verify your answer by summing the distributed amounts to ensure it equals the total amount collected. Show your calculations.
3. If the distributed amount to each organization is represented as a fraction, simplify the fraction to its lowest terms. Explain the steps taken to simplify the fraction.
4. Convert the fraction obtained in Question 3 to a decimal. Compare the decimal representation with your answer from Question 1 to check for consistency.
5. Discuss the properties of rational numbers illustrated in this scenario, focusing on their representation as fractions and decimals. How does understanding these properties help in real-life applications like fundraising and distribution?