Enhanced Curriculum Support

SecA

1. If the roots of quadratic equation px2 + 6x + 1 = 0 are real, then find p.

2. For what value of the quadratic equation 9x2 – 3ax + 1 = 0 has equal roots?

3. For what values of k, the roots of the equation x2 + 4x + k = 0 are real?

4.The condition on ‘a’ for ax2 + bx + c = 0 to represent a quadratic equation is:

5. The roots of the equation ax2 + bx + c = 0 are non- real, if

6. The roots of equation ax2 + bx + c = 0, a ≠ 0 are real, if b2 – 4ac is

7. If n denotes the number of roots of a quadratic equation, then

8. The positive value of c for which the equation x2 + kx + 9 = 0 and x2 – 12x + k = 0 will both have real roots

9.The equation (a2 + b2)x2 – 2 (ac + bd) x + c2 + d2 = 0 has equal roots, then

10.The sum of a number and its reciprocal is 103, then the number is:

11.The value of k for which – 5 is a root of 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots is

SecB

1. Find the value of k for which the equation x2 + k(2x + k – 1) + 2 = 0 has real and equal roots.

2. If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k

3.The product of two consecutive positive integers is 306. Find the integers.

4.The difference of two natural numbers is 5. If the difference of their reciprocals is 110, find the two numbers.

5. What constant should be added or subtracted to solve the quadratic equation x2 – 52x – 4 = 0 by the method of completing the square?

SecC

1. A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.

2.Find the value of p for which the quadratic equation (2p + 1)x2 – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.

3.A journey of 192 km from a town A to town B takes 2 hours more by a ordinary passenger train than a super fast train. If the speed of the faster train is 16 km/h more, find the speeds of the faster and the passenger train.

4.Speed of a boat in still water is 15 kmh. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

SecD

1. A person on tour has ₹ 360 for his expenses. If he extends his tour for 4 days, he has to cut down his daily expenses by ₹ 3. Find the original duration of the tour.

2.The hypotenuse of a right triangle is 1 m less than twice the shortest side. If the third side is 1 m more than the shortest side, find the sides of the triangle.

3.A thief runs with a uniform speed of 100 m/ minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief?

4. A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed ?

Problem1

A charitable organization is creating a scholarship fund for underprivileged students. The organization decides to distribute the funds equally among students, ensuring each student gets a certain amount. If the total amount of funds is $5000 and the number of students is represented by x, the quadratic equation for the amount each student receives is x2 -50x + 5000 = 0. How many students will receive the scholarship, and how much will each student get? Discuss the role of education in empowering underprivileged communities.

Problem2

A village cooperative society is planning to build a water reservoir to support agriculture. The depth of the reservoir is to be 5 meters more than its width. If the reservoir's base area is 500 square meters, find the width and the depth of the reservoir. Discuss the importance of water conservation for agricultural sustainability.

Problem3

A community decides to create a rectangular green space to plant trees. The length of the green space is 10 meters more than its width. The area of the green space is 600 square meters. The community wants to plant one tree for every 10 square meters. How many trees can they plant in the green space?

Problem4

A person plans to invest in a fixed deposit scheme that yields a quadratic growth in returns. The quadratic equation representing the returns after x years is 2x2 +3x - 5 = 0. Determine the number of years after which the returns are zero and discuss the importance of financial planning and investment.

Q1

1. A rectangular park is to be designed with a length 10 meters more than its width. The area of the park is 600 square meters. Find the dimensions of the park.

Q2

2. A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h more, it would have taken 3 hours less. Find the original speed of the train.

Q3

3. A farmer wants to build a rectangular pen with one side against a barn. If he has 120 meters of fencing and wants to maximize the area of the pen, what dimensions should he use?

Q4

4. Determine the nature of the roots of the quadratic equation 4x2 + 12x + 9 = 0.

Q5

The sum of the squares of two consecutive natural numbers is 145. Find the numbers.

Questions

1. State whether the following quadratic equations have two distinct real roots. Justify your answer.

2.Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?

3. Is 0.2 a root of the equation x2 – 0.4 = 0? Justify.

4. If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify?

5.Find a natural number whose square diminished by 84 is equal, to thrice of 8 more than the given number.

5. Given equation is x2 + 55x – 70 = 0 On comparing with ax2 + bx + c = 0, we get a = 1 ,b = 55 and c = -70

6. A natural number, when increased by 12, equals 160 times its reciprocal. Find the number?

7. If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?

8. At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than t24 minutes. Find t?

Question

When a tennis player hits a ball the ball moves up to a certain height , then it comes down. The path of tennis ball is shown in figure-1 and figure-2.This path is parabolic in shape.If the time taken in x-axis and height of the ball is taken in y-axis, we get a parabolic graph. A parabola is the graph that results from p(x)=ax2+bx+c. Parabolas are symmetric about a vertical line known as the Axis of Symmetry. The Axis of Symmetry runs through the maximum or minimum point of the parabola which is called the vertex and x-coordinate of the vertex is given by −b2a. In this case , h = 3 + 14t - 15t2 (where, ‘h’ is the height of the ball in feet and ‘t’is the time in second ).

Based on your understanding of the above case study, answer all the five questions below:

1. What is the quadratic equation when the ball hits the ground?

2. When does the ball hits the ground?

3. At what time the ball reachs the maximum height?

4.The ball reaches a maximum height of?

5. If height ‘h’ is given by , h = 5t2 - 5t -2 After how many seconds of hitting the ball, the ball will teach a height of 8 feet?

Question 2

Small scale industries (SSI) are those industries in which manufacturing, providing services, productions are done on a small scale or micro scale. For example, Agarbatti making, Chalk making, Biodiesel production, Sugar candy manufacturing, Wood making, Rice mill, Potato chips making, Toy making, Microbrewery, Liquid soap making, Honey processing etc. Small scale industries play an important role in social and economic development of India.

A small-scale industry produces a certain packet of Agarbatti in a day. Number of Agarbatti packets prepared by each worker on a particular day was 3 more than twice the number of workers working in the industry. The number of Agarbatti packets produced in a particular day was 90.

Based on your understanding of the above case study, answer all the five questions below:

1.If the number of workers working in the industry is x, what was the number of Agarbatti packets produced by each worker on that particular day?

2. The quadratic equation representing the above situation is:

3. The nature of roots of the above Quadratic equation are

4.Number of workers working in the industry is

5. Some workers were absent on a particular day resulting decrease in production of Agarbatti packets to 65 on that day. How many workers were present on that day?