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.
SecA
1. Find the value of x in the equation: 7x+3 = 5x+15.
2. Solve for x : 2x + 5 = 11.
3. Find the value of y in the equation 3y − 7 = 8.
4. Solve for x : 3x + 5 = 2x + 8.
5. Solve for x in the equation
SecB
1. A father is three times as old as his son. Five years ago, he was four times as old as his son. Find their present ages.
2. Ramesh bought 3 pens and 4 notebooks for ₹100. If a notebook costs ₹5 more than a pen, find the cost of each pen and notebook.
3. The sum of three consecutive integers is 51. Find the integers.
4. Solve the equation 4x − 7 = 3(x+5).
5. Solve the equation:
6. Solve the equation 3x + 4 = 2x − 7.
7. Find the value of x if 5x + 3 = 2x + 18.
SecC
1. Solve the following equations:
(a)
(b)
(c)
2. The denominator of a fraction is 4 more than its numerator. If 1 is subtracted from both the numerator and the denominator, the fraction becomes
3. The sum of three consecutive integers is 45.Form a linear equation to represent the situation and find the integers.
4. A number is 7 more than 3 times another number. If their sum is 25, find the numbers.
5. Solve for x : 3(x+5) = 4(x−2) + 9.
6. Solve the equation : 5(2x+4) = 7(x−1)+3x.
Sec D
1.A car rental company charges a fixed amount of 20 dollars plus 5 dollars per hour for renting a car. If the total bill for renting a car is 50 dollars, write a linear equation and solve for the number of hours the car was rented.
2. The sum of a number and 5 is equal to 3 times the number minus 7. Form a linear equation and find the number.
3. A bag contains 15 more red balls than blue balls. If the total number of balls is 75, write a linear equation and solve for the number of red and blue balls.
4. The sum of the digits of a two-digit number is 12. The tens digit is 3 less than the units digit. Find the number.
5. A person is 4 years older than 3 times the age of his brother. The sum of their ages is 34 years. Form a linear equation and find their ages.
6. A rectangle’s length is 3 more than twice its width. If the area of the rectangle is 40 square units, find the length and the width of the rectangle.
Problem 1
An energy-saving campaign suggests reducing electricity usage by 10% per month. If a household currently uses 500 kWh per month, how much will they use after 3 months of consistent reduction? Why is energy conservation crucial for the environment?
Problem 2
A student aims to read 5 books every month to improve their knowledge. If they have read 30 books so far, how many months will it take to read a total of 75 books? Why is continuous learning important in personal and professional growth?
Problem 3
A dietitian recommends consuming 30 grams of fiber per day. If a person gets 𝑥 grams of fiber from fruits and needs an additional 18 grams from vegetables, how much fiber do they get from fruits if the total intake is 30 grams? Discuss the importance of a balanced diet.
Q1
The formula for the perimeter of a rectangle is P = 2l + 2w, where 𝑙 is the length and w is the width. If the perimeter of a rectangle is 30 units and the length is 4 units longer than the width, find the dimensions of the rectangle. Explain your solution process.
Q2
A car rental company charges Rs.30 per day plus Rs.0.25 per km driven. If a customer spends Rs.75 for renting a car for one day, how many kilometres did they drive? Explain how you arrived at your answer.
Q3
An amusement park charges an entrance fee of Rs.20 per person plus Rs.5 per ride. If a group of friends spends Rs.150 in total for entrance and rides, how many rides did they take? Justify your solution process.
Questions
1. A home-owner is installing a fence around the square garden. The garden has a perimeter of 6480 cm. Write and solve the equation to find the garden’s dimensions.
2. Distance between two stations A and B is 690 km. Two cars start simultaneously from A and B towards each other, and the distance between them after 6 hours is 30 km. If the speed of one car is less than the other by 10 km/hr, find the speed of each car.
3. A steamer goes downstream from one point to another in 7 hours. It covers the same distance upstream in 8 hours. If the speed of stream be 2 km/hr, find the speed of the steamer in still water and the distance between the ports.
4. The present age of father is four times the age of his son. After 10 years, age of father will become three times the age of his son. Find their present ages.
5. Solve:
State whether statements are True or False:
6. (a)Three consecutive even numbers whose sum is 156 are 51, 52 and 53.
(b) x = –12 is the solution of the linear equation 5x –3(2x + 1) = 21 + x
Choose the correct option for the below given questions
7. If 3x – 4 (64 – x) = 10, then the value of x is:
(a) –266
(b) 133
(c) 66.5
(d) 38
8. If x = a, then which of the following is not always true for an integer k:
(a) kx = ak
(b)
(c) x – k = a – k
(d) x + k = a + k
Fill in the blanks:
9. (a) Fifteen added to thrice a whole number gives 93. The number is ?.
(b) If
Q1
Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Rs. 1,00,000. Based on the above situation, answer the following questions:
(i) Write the linear equation formed in the above situation.
(ii) How much money did Anima have?
(OR)
How much money educational institute have?
(iii) How much money did Anima‘s son and daughter have?
Sol 1
Solution:
Anima left:
One-half of her property to her daughter
One-third of her property to her son
The remaining amount was donated to an educational institute, valued at Rs. 100,000.
(i) Write the linear equation formed in the above situation:
Let 𝑃 denote the total amount of money (in Rs.) that Anima had.
The equation based on the distribution is:
This equation represents the total amount of money Anima had, considering she divided her property between her daughter, son, and the donation.
(ii) How much money did Anima have?
To find out how much money Anima had, solve the equation:
Subtract
100,000 = P −
100,000 =
P = Rs. 600,000
(iii) Now that we know the total amount Anima had, let's calculate how much her son and daughter received:
Amount left for distribution after donation:
Amount left = P − 100,000 = 600,000 − 100,000 = Rs. 500,000
Amount for daughter =
Amount for son =
Q2
A home-owner is installing a fence around the square garden. The garden has a perimeter of 7840 cm. Write and solve the equation to find the garden‘s dimensions.
(a) Find out the side of garden.
(b) Why garden is important for us?
Sol 2
(a) The perimeter P of a square with side length s is given by:
P = 4s
We are given the perimeter of the garden as 7840 cm. So we can write the equation:
4s = 7840
Divide both sides of the equation by 4 to find the side length s:
s =
So, the side length of the garden is 1960 cm.
(b) Overall, gardens contribute to the environment, support biodiversity, enhance physical and mental health, provide fresh produce, and offer aesthetic and recreational benefits.