Extra 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 Questions
Sec A
1.Given that,
(a) 60.4 (b) 70.4 (c) 74 (d) 64.4
2.The value of
(a) 13 (b) 16 (c) 14 (d) 12
3.The square of 39 is:
(a) 1521 (b) 1500 (c) 378 (d) none of these
4.The smallest number by which 396 must be multiplied so that the product becomes a perfect square is:
(a) 11 (b) 5 (c) 2 (d) 3
5.A side of square is
(a)
6.How many natural numbers lie between
(a) 37 (b) 30 (c) 36 (d) 35
Sec B
1.Find the square root of 1764 by the Prime Factorisation Method.
2.Find the square root of 529 by Division method.
Sec C
1.Is 2352 a perfect square? If not, find the smallest multiple of 2352 which is a perfect square. Find the square root of the new number.
2.Find the least number which must be subtracted from 4000 so as to get a perfect square. Also find the square root of the perfect square so obtained.
3.Find the least number which must be added to 525 so as to get a perfect square. Also find the square root of the perfect square so obtained.
Value Based Questions
Problem 1
1.A group of students is raising funds to support an underprivileged school. They decide to sell square-shaped handmade greeting cards. Each card has an area of 121 square centimeters. The students plan to make 100 cards.
(a) What is the side length of each card?
(b) Why is it important to help those who are less fortunate?
(c) How can small efforts, like making and selling greeting cards, make a big difference in someone's life?
Problem 2
2.A neighborhood association decides to clean up a square park that has an area of 1,024 square meters. They want to involve children in the cleanup drive to teach them the value of maintaining cleanliness in public spaces.
(a) What is the side length of the park?
(b) Why is it important to keep public spaces clean?
(c) How can involving young people in such activities help in promoting a culture of cleanliness?
HOTS
Q1
1.Consider the sequence of perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ...
(a) Observe the difference between consecutive perfect squares (e.g., 4−1, 9−4, etc.). What pattern do you notice?
(b) Based on the pattern you observed, what will be the difference between the square of the next number and the square of the current number?
(c) Can you generalize the relationship between the squares of consecutive integers? How can this be expressed algebraically?
Q2
2.You know that
Without using a calculator, estimate the value of
Use a more precise method to refine your estimate (e.g., averaging, successive approximations). What is your refined estimate for
How might this method of estimation be useful in real-life situations where quick mental calculations are needed?
Q3
3.You are given that
Solve these two equations simultaneously to find the values of a and b.
Verify your solution by substituting the values of a and b back into the original equations.
What does this problem illustrate about the relationship between addition and subtraction of square roots? How might this be applied in more complex algebraic situations?
NCERT Exemplar Solutions
Choose the correct option
Questions
1.Which of the following will have 1 at its units place?
(a)
2.How many natural numbers lie between
(a) 30 (b) 37 (c) 35 (d) 36
3.Which of the following is not a perfect square?
(a) 361 (b) 1156 (c) 1128 (d) 1681
4.If one member of a pythagorean triplet is 2m, then the other two members are:
(a)
(b)
(c)
(d)
5.Which letter best represents the location of
(a) A (b) B (c) C (d) D
Fill in the blanks
Questions
1.The value of
2.The square of 6.1 is ?
State whether the given statements are True or False
Questions
1.The square of 0.4 is 0.16.
2.There are 21 natural numbers between
3.The square root of a perfect square of n digits will have
Answer the below given questions
Questions
1.Discuss whether 9.5 is a good first guess for
2.Check whether 90 is a perfect square or not by using prime factorisation.
3.Using distributive law, find the square of 43.
4.Write a pythagorean triplet whose smallest number is 6.
5.A couple wants to install a square glass window that has an area of 500 square cm. Calculate the length of each side and the length of trim needed to the nearest tenth of cm.
6.A ladder 10m long rests against a vertical wall. If the foot of the ladder is 6m away from the wall and the ladder just reaches the top of the wall, how high is the wall?
7.Find the smallest perfect square divisible by 3, 4, 5 and 6.
8.A student said that since the square roots of a certain number are 1.5 and –1.5, the number must be their product, –2.25. What error did the student make?
9.During a mass drill exercise, 6250 students of different schools are arranged in rows such that the number of students in each row is equal to the number of rows. In doing so, the instructor finds out that 9 children are left out. Find the number of children in each row of the square.
10.A General wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out?
11.A king wanted to reward his advisor, a wise man of the kingdom. So he asked the wiseman to name his own reward. The wiseman thanked the king but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days. Without making calculations, find how many coins will the advisor get in that month?
Case Based Questions
Q1
1.Ravi has a rectangular garden in his backyard. He wants to create a square flower bed inside the garden. The area of the rectangular garden is 576 square meters, and the flower bed will occupy exactly one-fourth of the garden's area.
(a) What is the area of the square flower bed?
(b) Find the side length of the square flower bed.
(c) If the rectangular garden was actually a square, what would be the side length of the garden?
(d) How does the side length of the flower bed compare to the side length of the square garden (if it was a square)?
Q2
2.A community park is square-shaped and has an area of 625 square meters. The park management decides to build a square-shaped pond inside the park, such that the side of the pond is half the side of the park.
(a) Calculate the side length of the square park.
(b) Determine the side length of the pond.
(c) bCalculate the area of the pond.
(d) What is the difference in area between the park and the pond?
Q3
3.Tsunamis, sometimes called tidal waves, move across deep oceans at high speeds with barely a ripple on the water surface. It is only when tsunamis hit shallow water that their energy moves them upward into a huge destructive force.
(i) The speed of a tsunami, in metre per second, can be found by the formula r =
(a) Suppose the water depth is 6400m. How fast is the tsunami moving?
(ii) The speed of a tsunami in km per hour can be found using r =
(a) How fast is the tsunami moving in km per hour?
(b) How long would it take a tsunami to travel 3000 km if the water depth was a consistent 3000 m?