quadratic equation / chapter - 4 / class - 10 /Math / New St. Mery English School

Topics to be covered 

1- Need to quadratic equations in real life.

2-Recap (polynomial, equation, zeroes of a polynomial, relation between zeros of a polynomial, splitting of terms, completing the square method, quadratic formula, linear equation word problem

3- what is quadratic equation?

4- standard form of quadratic equation

5- Roots / zeroes/ solutions/poles of a quadratic equation

6- solving a quadratic equation

       a- factorization method

       b- completing the square method

       c- quadratic formula (sidharacharya law )

7- Nature of roots

8-word problems involving quadratic equation 

1- Need to quadratic equations in real life.

 1-It is used in tackling real life situation in the form of world problems.

2- It is used in solving puzzles

3- It is used in sports

4- It is used in study parabolic shape made by football 

2-Recap

term - The part of an algebraic expression which is the combination of variable and constant combined with multiply sign is called term 

Ex:- 6xy² , -4y² , 2x , 7x³y³z³       

Algebraic expression- The group of terms combined with plus ( + ) or minus ( - ) sign is called algebraic expression.

Ex:- 5y² + 2x – 3

             2x³ + 3x² – 4x + 8

Polynomial- An algebraic expresson whose powers are non-negative integer is called polynomial

Ex:- 5y² + 2x – 3

             2x³ + 3x² – 4x + 8

 Degree of a Polynomial - The highest power of a polynomial is called the degree of that given polynomial.

Ex:- 5y² + 2x – 3  |( Here the degree of polynomial is 2 )

             2x³ + 3x² – 4x + 8  ( Here the degree of polynomial is 3 )

There are four types of polynomial on the basis of degree

1- linear polynomial

2- quadratic polynomial

3- cubic polynomial

4- by-quadratic polynomial

What is equation?

Ans:- An equation is formed when two polynomials are combined by equal to sign ( = )

 What is quadratic equation?

Ans:- An equation that is in the form of  'quadratic polynomial = 0' than that equation is called quadratic equation.

Ex:- 5y² + 2x – 3 = 0

What is equation?

Ans:- An equation is formed when two polynomials are combined by equal to sign ( = )

 What is quadratic equation?

Ans:- An equation whose degree is 2 is called quadratic equation

                                                   or

An equation that is in the form of  'quadratic polynomial = 0' than that equation is called quadratic equation.

If p(x) is a quadratic polynomial than p(x) = 0 is a quadratic equation

 

 What is roots of the quadratic equation?

Ans:- Let p(x) = 0 is a quadratic equation, than the zeroes of the polynomials p(x) are called the roots of the equation p(x) = 0

or

variable का वह मान जिसे variable के स्थान पर रखने पर हमारा quadratic equation सटिस्फाय हो जाये तब वेरिएबल का वह मान ही roots of the quadratic polynomial कहलाता है 

therefore, x = ∝ is a root of p(x)=0, if and only if  p(∝) = 0

 

Speed-distance-time / class - 4-5-6 /Math / New St. Mery English School

Problem type - 1

1- Find the speed if distance = 45 km and time = 3 hours 

2- Find the speed if distance = 60 km and time = 4 hours

3- Find the speed if distance = 900 km and time = 18 hours

Problem type -2

1- if the distance covered by a bus is 250 km in 5 hours.Find the speed of the bus.

2- If the distance covered by a train is 424 km in 8 hours. Find the speed of a train.

3- find the speed of the bus which covers a distance of 600 km in12 hours.

4- If the distance covered by a car is 460 km in 10 hours. Find its speed.

5- If the distance covered by a train is 2500 km in 25 hours. Find its speed.

6- A boy can cover 25 km in 5 hours. find his speed.

Problem type -3

 1- If a train starting from New Delhi to Govindpur , covers a distance of 440 km in 5 hours and 30 minutes. What is the speed of train?

Problem type -4

1- A train starts from one city on thursday at 8:00 pm and reached in another city on saturday at 8:00 am. If the distance between the both cities is 1692 km, find the average speed of the train.

2- A motor car starts from a city A at 5:30 am and reaches city B 360 km away at 11:30 am. Find the average speed of the motor?

Problem type -5

1- Change 56 km/hr into m/s

2- Change 72 km/hr into m/s

3- Change 124 km/hr into m/s 

4- Change 90 km/hr into m/s 

Problem type -6

1- Express 35 metre / second into km / hr

2- Express 48 metre / second into km / hr

3- Express 800 metre / second into km / hr

Problem type -7

1- A bus travels at a speed of 45 km/hr. How much distance will it cover in 10 hours?

2- A  car travels at a speed of 60 km/hr. How much distance will it cover in 5 hours?

3-  A train runs at a speed of 125 km/hr. How much distance will it cover in 5 hours?

4- A bus travels at a speed of 65 km/hr. How much distance will it cover in 5 hours?

5- A train runs at a speed of 140 km/hr. How much distance will it cover in 7 hours?

Problem type -8

 1- A person travelling by a train crosses a tunnel in 4wholes 1/2 minutes. If the speed of train is 36 km/hr. Than find the length of tunnel.

2- A car traveling at the average speed of 50 km/hr. How much distance would it cover in 30 second.

Problem type -9

1- A train runs at a speed of 75 km/hr. How much time will it take to cover 225 km?

2- Mohit runs at a speed of 15 km/hr. How long time will he take to run 900 metre race?

3- Santosh runs at a speed of 10 km/hr. How long time will he take to run a 700 metre race?

4- A train runs at a speed of 14 km/ hr. How long will it take to cover a distance 280 km?

5- A car travels at a speed of 40 km/hr. How long time will it take to cover 160 km.

Problem type -10

 1- A 360 m long train is running at a speed of 45 km/hr. What time will it take to cross a 140m long bridge?

2- Mohan covers a distanceof 108 km at a speed of 15 m/sec by a car. How many hours will he take to cover this distance? 

Problem type -11

1- A train covers a distance of 140 km in 3 hours and 30 minutes. How much time would it take to cover a distance of 250 km running at the same speed.

Problem type -12

1- A train is running at 36 km/hr If it crosses a pole in 25 second. than find the length of train.

Problem type -13

1- A bus travels 38 km in first hour. 35 km in second hour. 52 km in third hour. and 35 km in last hour. Find the average speed of the bus in per hour