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:
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.
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.
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.
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/ Previous year Questions
SecA
1. Find the common difference of the A.P.
2. Find the 9th term from the end (towards the first term) of the A.P. 5,9,13, …, 185
3. How many two-digit numbers are divisible by 3?
4. How many terms of the A.P. 65, 60, 55, … be taken so that their sum is zero?
5. The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference
6. In an AP, if
7. Find the sum of all three digit natural numbers, which are multiples of 11.
SecB
1. The angles of a triangle are in A.P., the least being half the greatest. Find the angles.
2. Find whether -150 is a term of the A.P. 17, 12, 7, 2, … ?
3. Which term of the progression 20, 192, 183, 17 … is the first negative term?
4. Which term of the progression 4, 9, 14, 19, … is 109?
5. The
6. The 7th term of an A.P. is 20 and its 13th term is 32. Find the A.P.
7. Find 10th term from end of the A.P. 4,9, 14, …, 254.
8. How many natural numbers are there between 200 and 500, which are divisible by 7?
9. Find how many two-digit numbers are divisible by 6?
10. Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
11. Find the middle term of the A.P. 6, 13, 20, …, 216.
12. How many terms of the A.P. 27, 24, 21, … should be taken so that their sum is zero?
SecC
1. Which term of the A.P. 3, 14, 25, 36, … will be 99 more than its 25th term?
2. Determine the A.P. whose fourth term is 18 and the difference of the ninth term from the fifteenth term is 30.
3. The 19th term of an AP is equal to three times its 6th term. If its 9th term is 19, find the A.P.
4. If the seventh term of an AP is
5. Find the number of terms of the AP 18,
6. The 14th term of an AP is twice its gth term. If its 6th term is -8, then find the sum of its first 20 terms.
7. The 13th term of an AP is four times its 3rd term. If its fifth term is 16, then find the sum of its first ten terms.
8. If the sum of first 7 terms of an A.P is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P
9. The first term of an A.P. is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference of the A.P.
10. The nth term of an A.P. is given by (-4n + 15). Find the sum of first 20 terms of this A.P.
11. The sum of the first seven terms of an AP is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the AP.
12. If
SecD
1. If pth, qth and rth terms of an A.P. are a, b, c respectively, then show that (a – b)r + (b – c)p+ (c – a)q = 0
2. The 17th term of an AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, then find its nth term.
3. A sum of ₹1,600 is to be used to give ten cash prizes to students of a school for their overall academic performance. If each prize is ₹20 less than its preceding prize, find the value of each of the prizes.
4. Find the 60th term of the AP 8, 10, 12, …, if it has a total of 60 terms and hence find the sum of its last 10 terms.
5. An Arithmetic Progression 5, 12, 19, … has 50 terms. Find its last term. Hence find the sum of its last 15 terms.
6. The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
7. Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms
8. If the sum of the first 7 terms of an A.P. is 119 and that of the first 17 terms is 714, find the sum of its first n terms.
9. Find the number of terms of the A.P. -12, -9, – 6, …, 21. If 1 is added to each term of this A.P., then find the sum of all terms of the A.P. thus obtained.
10. If the ratio of the sum of the first n terms of two A.Ps is (7n + 1): (4n + 27), then find the ratio of their 9th terms.
11. In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two Sections, find how many trees were planted by the students.
12. Ramkali required ₹500 after 12 weeks to send her daughter to school. She saved ₹100 in the first week and increased her weekly saving by ₹20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
Value Based Questions
Problem1
Situation: A student decides to save money every month to donate to a charity. In the first month, they save $10. Each subsequent month, they increase their savings by $5 compared to the previous month.
1. What is the common difference in the amount saved each month?
2. How much money will the student save in the 6th month?
3. Calculate the total amount saved by the student in 12 months.
Problem2
Situation: An NGO is planting trees in an area, and they decide to plant trees in an arithmetic progression manner. They plant 5 trees on the first day, 8 trees on the second day, 11 trees on the third day, and so on.
1. Determine the common difference in the number of trees planted each day.
2. How many trees will they plant on the 10th day?
3. Calculate the total number of trees planted by the NGO in 15 days.
Problem3
Situation: A fitness trainer wants to encourage students to increase their daily exercise gradually. They start with 15 minutes of exercise on the first day and increase the duration by 3 minutes each day.
1. Identify the common difference in the exercise duration.
2. How many minutes will a student exercise on the 14th day?
3. Find the total exercise time over the first 20 days.
Problem4
Situation: A school is implementing a program to reduce plastic usage. They start by reducing plastic usage by 2 kg in the first week. Every week, they aim to reduce 0.5 kg more than the previous week.
1. Find the common difference in the reduction of plastic usage.
2. How much plastic will they reduce in the 8th week?
3. Calculate the total reduction in plastic usage over 10 weeks.
HOTS
Q1
1. In an arithmetic progression, the sum of the first 10 terms is 145, and the sum of the next 10 terms is 445.
(i) Find the common difference and the first term.
(ii) Calculate the sum of the first 30 terms of this sequence.
(iii) If every 3rd term of this arithmetic progression is doubled, what will be the sum of the first 15 terms of the new sequence?
Q2
2. An economist is analyzing the monthly savings of a person. The savings form an arithmetic progression. If the savings in the first month is $100, and the savings in the 5th month is $200:
(i) Find the monthly increase in savings.
(ii) What will be the savings in the 12th month?
(iii) Calculate the total savings in the first year.
(iv) If the person decides to save an additional fixed amount of $50 every month from the 6th month onwards, how will the new sequence look, and what will be the total savings in the first year?
Q3
3. In an arithmetic progression, the first term is 5, and the common difference is 3.
(i) Find the 20th term.
(ii) Calculate the sum of the first 20 terms.
(iii) If each term of the sequence is increased by 2, what will be the sum of the first 20 terms of this new sequence?
(iv) If every even term of the original sequence is doubled, what will be the sum of the first 20 terms of this modified sequence?
Q4
4. Find three numbers in A.P. whose sum is 21 and their product is 231.
Q5
5. If
NCERT Exemplar Solutions
Questions
1. Find p and q such that: 2p, 2p, q, p + 4q, 35 are in AP ?
2. If the numbers a, b, c, d and e form an A.P., then find the value of a – 4b + 6c – 4d + e. ?
3. What is the common difference of an A.P. in which
4. Two APs have the same common difference. The first term of one of these is -1 and that of the other is – 8. Then the difference between their 4th terms is ?
5. The famous mathematician associated with finding the sum of the first 100 natural numbers is ?
6. If the first term of an AP is -5 and the common difference is 2, then the sum of the first 6 terms is ?
7. The sum of first 16 terms of the AP: 10, 6 2, … is ?
8. Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?
9. Is 0 a term of the AP: 31, 28, 25, …? Justify your answer.
10. The taxi fare after each km, when the fare is Rs 15 for the first km and Rs 8 for each additional km, does not form an AP as the total fare (in Rs) after each km is 15, 8, 8, 8,… Is the statement true?
Case Based Questions
Question
A mathematics teacher of a school has taken his children to a science centre to visit the science and maths exhibition. When the students were visiting different stalls, one student, Rani, observed that some rectangular bars are arranged in ascending order as shown below. In the meantime, her teacher reached at the stall and asked some questions to Rani and the other students to verify whether the pattern is in AP or not? Just by observing the pattern shown below Rani and her friends answered.
Based on your understanding of the above case study, answer all the five questions below:
1. The difference between the heights of two consecutive bars is?
2. What is the height of
3. Which bar will have the height 34 cm from left?
4. If there are 30 bars, then height of
5. What will be the expression for the nth term of the above sequence?
Question 2
Rahul wanted to observe his 15th birthday in a restaurant. So, he requested his parents for the same and they agreed with his proposal. After the celebration they went to the hall to have dinner. In the hall Rahul observed that the hotel used square tables where only one person could sit on each side of the table.
Based on your understanding of the above case study, answer all the five questions below:
1. If two tables are joined together, how many people can sit together?
2. If three tables are joined together in a straight line and also four tables are joined together separately in a straight line, find the number of people that can sit in the respective arrangements
3. From the above context, how many tables can be put together in a straight line to accommodate 64 people at a time
4. How many rows are required with the above condition to accommodate 460 people at a times
5. If the first row contains one table, second row contains two tables, third row contains 3 tables jointly and so on, then which of the following shows the correct pattern of seating capacity?