Mastering Algebra: A Comprehensive Guide for All

A Comprehensive Guide for Grade 10 and Beyond, Including Beginners, Middle School, and High School Students.

Created byLakshmi Narayana

Last updated 6/2023

English

What you'll learn

Polynomials
Pair of Linear Equations in Two Variables
Quadratic Equations
Arithmetic Progressions
At the end of the course, students will not only have learned about the topics in detail but also be able to solve various problems based on them.

Course content

4 sections • 325 lectures • 44h 3m total length

Introduction13:01
Introduction
Session 1 - Q 12:15
If one zero of the quadratic polynomial x2+ 3x + k is 2, then the value of k is
(A) 10 (B) –10 (C) 5 (D) –5
Session 1 - Q 23:25
If one of the zeroes of the quadratic polynomial (k–1) x2+ k x + 1 is –3, then the value of k is
(a) 4/3(b) (-4)/3(c) 2/3(d) (-2)/3
Test your understanding
Home Assignment
Session 2 - Introduction11:30
Geometrical Meaning of the Zeroes of a Polynomial
Session 2 - Q 14:44
Look at the graphs in Figure given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x).
Session 2 - Q 22:35
Which of the following is not the graph of a quadratic polynomial?
Session 2 - Q 30:57
In the adjoining figure, the graph of f(x) is drawn. Find the number of zeroes of f(x).
Session 4 - Q 41:07
The graph of y = f(x) is given in the adjoining figure. Write the number of zeroes of f(x).
Test your understanding
Home Assignment
Session 3 - Introduction8:44
Relationship between Zeroes and Coefficients of a Quadratic Polynomial & Formation of Quadratic Polynomial.
Session 3 - Q 111:00
Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients.
Session 3 - Q 27:54
Find the zeroes of the polynomial x2 – 3 and verify the relationship between the zeroes and the coefficients.
Session 3 - Q 36:58
If m and n are the zeroes of the polynomial 3x2 + 11x – 4, find the value of m/n + n/m.
Session 3 - Q 45:25
Find a quadratic polynomial, the sum and product of whose zeroes are –3 and 2, respectively.
Session 3 - Q 54:59
If one zero of 2x2 – 3x + k is reciprocal to the other, then find the value of k
Session 3 - Q 65:33
If zeroes α and β of a polynomial x2 – 7x + k are such that α – β = 1, then find the value of k.
Session 3 - Q 74:10
If α and β are the zeroes of the polynomial 2y2 + 7y + 5, then find the value of α + β + αβ.
Test your understanding
Home Assignment
Session 4 - Introduction5:10
Relationship between Zeroes and Coefficients of a Cubic Polynomial & Formation of Cubic Polynomial
Session 4 - Q 115:01
Verify that 3, –1, – 1/3 are the zeroes of the cubic polynomial p(x) = 3x3 – 5x2 – 11x – 3, and then verify the relationship between the zeroes and the coefficients.
Session 4 - Q 28:12
Find the cubic polynomial whose three zeroes are 3, -1 and – 1/3.
Session 4 - Q 37:15
If α, β and γ are zeroes of the polynomial 6x3 + 3x2 - 5x + 1, then find the value of α−1 + β−1 + γ−1.
Session 4 - Q 45:42
Test your understanding
Home Assignment
Session 5 - Introduction3:27
Division Algorithm for Polynomials
Session 5 - Q 16:59
Divide 2x2 + 3x + 1 by x + 2
Session 5 - Q 26:33
Divide 3x3 + x2 + 2x + 5 by 1 + 2x + x2.
Session 5 - Q 38:30
Divide 3x2 – x3 – 3x + 5 by x – 1 – x2, and verify the division algorithm.
Session 5 - Q 46:21
On dividing x3 - 5x2 + 6x + 4 by a polynomial g(x), the quotient and the remainder were x - 3 and 4 respectively. Find g(x).
Test your understanding
Home Assignment
Session 6 - Introduction2:19
Division Algorithm for Polynomials & Finding remaining zeroes
Session 6 - Q 19:30
Find all zeroes of the polynomial f(x) = x3+ 13x2 + 32x + 20. If one of its zeroes is - 2.
Session 6 - Q 214:24
Find all the zeroes of 2x4 – 3x3 – 3x2 + 6x – 2, if you know that two of its zeroes are √2 and −√2.
Session 6 - Q 312:48
Obtain all other zeroes of the polynomial x4 + 5x3− 2x2− 40x − 48, if two of its zeroes are 2√2 and −2√2
Test your understanding
Home Assignment
Exercise 1 - Q 14:39
The graphs of y = p(x) are given in Figure below, for some polynomials p(x). Find the number of zeroes of p(x), in each case
Exercise 2 - Q 1 (i)10:06
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
(i) x2 - 2x - 8
Exercise 2 - Q 1 (ii)6:15
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
(ii) 4s2 - 4s + 1
Exercise 2 - Q 1 (iii)8:23
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
(iii) 6x2 – 3 - 7x
Exercise 2 - Q 1 (iv)7:24
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
(iv) 4u2 + 8u
Exercise 2 - Q 1 (v)8:00
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
(v) t2 - 15
Exercise 2 - Q 1 (vi)8:41
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
(vi) 3x2 – x - 4
Exercise 2 - Q 2 (i)4:31
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively
1/4 , -1
Exercise 2 - Q 2 (ii)3:03
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively
√2 , 1/3
Exercise 2 - Q 2 (iii)2:40
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively
0 , √5
Exercise 2 - Q 2 (iv)1:59
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively
1 , 1
Exercise 2 - Q 2 (v)3:30
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively
- 1/4 , 1/4
Exercise 2 - Q 2 (vi)2:03
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively
4 , 1
Exercise 3 - Q 1 (i)8:16
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following.
(i) P (x) = x3 – 3x2 + 5x – 3 , g(x) = x2 - 2
Exercise 3 - Q 1 (ii)7:26
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following.
(i) P (x) = x4 – 3x2 + 4x + 5 , g(x) = x2 + 1 - x
Exercise 3 - Q 1 (iii)4:56
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following.
P (x) = x4 – 5x + 6 , g(x) = 2 - x2
Exercise 3 - Q 2 (i)6:41
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.
t2 – 3, 2t4 + 3t3 – 2t2 – 9t - 12
Exercise 3 - Q 2 (ii)6:03
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.
x2 + 3x +1, 3x4 + 5x3 - 7x2 + 2x + 2
Exercise 3 - Q 2 (iii)4:32
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.
x3 - 3x +1, x5 - 4x3 + x2 + 3x + 1
Exercise 3 - Q 314:05
Obtain all other zeroes of 3x4 + 6x3 - 2x2 – 10x - 5 if two of its zeroes are √(5/3) and -√(5/3) .
Exercise 3 - Q 48:09
On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and -2x + 4 respectively. Find g(x).
Exercise 3 - Q 57:23
Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
Exercise 4 - Q 1 (i)14:07
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:
(i) 2x3 + x2 – 5x + 2; 1/2, 1, -2
Exercise 4 - Q 1 (ii)9:53
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:
x3 – 4x2 + 5x – 2; 2, 1, 1
Exercise 4 - Q 24:32
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.
Exercise 4 - Q 35:42
If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b.
Exercise 4 - Q 412:49
If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± √3, find other zeroes.
Exercise 4 - Q 510:22
If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a.

Session 1 - Introdcution11:44
Introduction to Pair of Linear Equations:
Session 1 - Q 12:30
Find the value of ‘a’ so that the point (a, 5) lies
on the line represented by 2x - 3y = 5 ?
Session 1 - Q 23:42
If x = α and y = β is the solution of the equations
x - 2y = 2 and x + 2y = 4, then find the values of α and β ?
Session 1 - Q 34:01
Given that 2x + 3y = 10, x - 3y = -4 and
y = mx + 3, then find the value of m ?
Test your understanding
Home Assignment
Session 2 - Introduction2:32
Method to Write a Given Statement as a Pair of Linear Equations in Two Variables (Algebraic representation):-
Session 2 - Q 18:01
Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a ring on the items kept in a stall, and if the ring covers any object completely, you get it). The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. If each ride costs ₹3, and a game of Hoopla costs ₹4, how would you find out the number of rides she had and how many times she played Hoopla, provided she spent ₹20. Represent this situation algebraically .
Session 2 - Q 26:50
Seven times a two digit number is equal to four times the number obtained by reversing the order of its digits. If the difference between the digits is 3.Represent this situation algebraically .
Session 2 - Q 35:18
The ratio of incomes of two persons is 11 : 7 and the ratio of their expenditures is 9 : 5. If each of them manages to save ₹400 per month. Represent this situation algebraically.
Session 2 - Q 47:04
Five years ago, sagar was twice as old as Tiru. After 10 years Sagar's age will be ten years more than Tiru's age. To find their present ages form system of Linear Equations.
Test your understanding
Home Assignment
Session 3 - Introduction8:04
Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla. The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. If each ride costs ₹3, and a game of Hoopla costs ₹4, how would you find out the number of rides she had and how many times she played Hoopla, provided she spent ₹20. Represent this situation algebraically and graphically (geometrically).
Session 3 - Q 115:58
Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla. The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. If each ride costs ₹3, and a game of Hoopla costs ₹4, how would you find out the number of rides she had and how many times she played Hoopla, provided she spent ₹20. Represent this situation algebraically and graphically (geometrically).
Session 3 - Q 29:38
Romila went to a stationery shop and purchased 2 pencils and3 erasers for ₹9. Her friend Sonali saw the new variety of pencils and erasers with Romila, and she also bought 4 pencils and 6 erasers of the same kind for₹18. Represent this situation algebraically and graphically.
Session 3 - Q 39:20
Two rails are represented by the equations x + 2y – 4 = 0 and 2x+ 4y – 12 = 0. Represent this situation geometrically.
Session 3 - Q 413:22
Champa went to a ‘Sale’ to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, “The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. Help her friends to find how many pants and skirts Champa bought.
Test your understanding
Home Assignment
Session 4 - Introduction2:27
Behaviour of lines representing a pair of linear equations (Checking consistency).
Session 4 - Q 17:23
On comparing the ratios a_1/a_2 ,b_1/b_2 and c_1/c_2 find out whether the lines representing the following pairs of linear equations intersect at a point or parallel or coincide:
3x - y = 7
2x + 5y + 1 = 0
Session 4 - Q 210:35
Check graphically whether the pair of equations x + 3y = 6 and 2x – 3y = 12 is consistent. If so, solve them graphically.
Session 4 - Q 310:11
Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions:
5x – 8y + 1 = 0
3x - 24/5y + 3/5= 0
Session 4 - Q 44:07
For which values of p does the pair of equations
given below has unique solution?
4x + py + 8 = 0
2x + 2y + 2 = 0
Session 4 - Q 57:04
For what values of k will the following pair of
linear equations have infinitely many solutions?
kx + 3y – (k – 3) = 0
12x + ky – k = 0
Test your understanding
Home Assignment
Session 5 - Introduction3:52
Algebraic Methods of Solving a Pair of Linear Equations:
Substitution Method:
Session 5 - Q 17:00
Solve the following pair of equations by substitution method:
7x – 15y = 2
x + 2y = 3
Session 5 - Q 25:24
Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Will the rails cross each other?
Session 5 - Q 310:51
Aftab tells his daughter, “Seven years ago,I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." then find their present ages?
Session 5 - Q 47:17
Romila went to a stationery shop and purchased 2 pencils and 3 erasers for ₹9. Her friend Sonali saw the new variety of pencils and erasers with Romila, and she also bought 4 pencils and 6 erasers of the same kind for ₹18. Find the cost of each pencil and each eraser.
Test your understanding
Home Assignment
Session 6 - Introduction6:21
Algebraic Methods of Solving a Pair of Linear Equations:
ü Elimination Method
Session 6 - Q 18:43
Solve the following pair of linear equations by the elimination method: 3x + 4y = 10 and 2x – 2y = 2.
Session 6 - Q 23:57
Use elimination method to find all possible solutions of the following pair of linear equations:
2x + 3y = 8
4x + 6y = 7
Session 6 - Q 311:48
The ratio of incomes of two persons is 9: 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save₹2000 per month, find their monthly incomes.
Session 6 - Q 411:26
The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2,find the number. How many such numbers are there?
Test your understanding
Home Assignment
Session 7 - Introduction5:47
Algebraic Methods of Solving a Pair of Linear Equations:
ü Cross-Multiplication Method
Session 7 - Q 113:25
Solve using cross multiplication method:
5x + 4y - 4 = 0
x - 12y - 20 = 0
Session 7 - Q 28:19
Solve the following pair of linear equations by
cross multiplication method:
x + 2y = 2
x - 3 y = 7
Session 7 - Q 312:37
From a bus stand in Bangalore, if we buy 2 tickets to Malleswaram and 3 tickets to Yeshwanthpur, the total cost is ₹46; but if we buy 3 tickets to Malleswaram and 5 tickets to Yeshwanthpur the total cost is ₹74. Find the fares from the bus stand to Malleswaram and to Yeshwanthpur.
Test your understanding
Home Assignment
Session 8 - Introduction3:46
Equations Reducible to a Pair of Linear Equations in Two Variables
Session 8 - Q 110:52
Solve the pair of equations:
2/x+ 3/y= 13;
5/x- 4/y= - 2
Session 8 - Q 211:16
Solve the following pair of equations by
reducing them to a pair oflinear equations:
5/(x - 1) + 1/(y - 2) = 2;
6/(x - 1) - 3/(y - 2) = 1
Session 8 - Q 316:45
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water.
Test your understanding
Home Assignment
Exercise 1 - Q 118:51
Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." (Isn't this interesting?) Represent this situation algebraically and graphically.
Exercise 1 - Q 215:40
The coach of a cricket team buys 3 bats and 6 balls for ₹3900. Later, she buys another bat and 3 more balls of the same kind for ₹1300. Represent this situation algebraically and graphically.
Exercise 1 - Q 314:54
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹300. Represent the situation algebraically and geometrically.
Exercise 2 - Q 1 (i)13:02
Form the pair of linear equations in the following problems, and find their solutions graphically.
(i). 10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz
Exercise 2 - Q 1 (ii)11:03
Form the pair of linear equations in the following problems, and find their solutions graphically.
(ii). 5 pencils and 7 pens together cost ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 46. Find the cost of one pencil and that of one pen
Exercise 2 - Q 211:57
On comparing the ratios a_1/a_2 = b_1/b_2 and c_1/c_2 find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide:
(i) 5x − 4y + 8 = 0;7x + 6y - 9 = 0
(ii) 9x + 3y + 12 = 0; 18x + 6y + 24 = 0
(iii) 6x − 3y + 10 = 0; 2x – y + 9 = 0
Exercise 2 - Q 315:58
On comparing the ratios a_1/a_2 = b_1/b_2 and c_1/c_2 , find out whether the following pair of linear equations are consistent, or inconsistent.
(i) 3x + 2y = 5, 2x − 3y = 7
(ii) 2x − 3y = 8, 4x − 6y = 9
(iii). 3/2x + 5/3y = 7, 9x − 10y = 14
(iv). 5x − 3y = 11, −10x + 6y = −22
(v). 4/3x + 2y = 8, 2x + 3y = 12
Exercise 2 - Q 4 (i)9:20
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(i). x + y = 5, 2x + 2y = 10
Exercise 2 - Q 4 (ii)2:24
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(ii). x – y = 8, 3x − 3y = 16
Exercise 2 - Q 4 (iii)11:03
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(iii). 2x + y - 6 = 0, 4x − 2y - 4 = 0
Exercise 2 - Q 4 (iv)3:12
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
iv). 2x − 2y – 2 = 0, 4x − 4y – 5 = 0
Exercise 2 - Q 56:12
Half the perimeter of a rectangle garden, whose length is 4 m more than its width, is 36 m. find the dimensions of the garden.
Exercise 2 - Q 612:08
Given the linear equation (2x + 3y – 8 = 0), write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i). Intersecting lines
(ii). Parallel lines
(iii). Coincident lines
Exercise 2 - Q 79:19
Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
Exercise 3 - Q 1 (i)4:16
Solve the following pair of linear equations by the substitution method.
(i). x + y = 14
x – y = 4
Exercise 3 - Q 1 (ii)4:26
Solve the following pair of linear equations by the substitution method.
(ii). s – t = 3
s/3 + t/2 = 6
Exercise 3 - Q 1 (iii)3:11
Solve the following pair of linear equations by the substitution method.
(iii). 3x – y = 3
9x − 3y = 9
Exercise 3 - Q 1 (iv)6:17
Solve the following pair of linear equations by the substitution method.
(iv) 0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3
Exercise 3 - Q 1 (v)3:41
Solve the following pair of linear equations by the substitution method.
(v). √2x + √3y = 0
√3x - √8y = 0
Exercise 3 - Q 1 (vi)6:46
Solve the following pair of linear equations by the substitution method.
vi). 3x/2 - 5y/3 = -2
x/3 + y/2 = 13/6
Exercise 3 - Q 26:25
Solve 2x + 3y = 11 and 2x − 4y = −24 and hence find the value of 'm' for which
y = mx + 3.
Exercise 3 - Q 3 (i)6:17
Form a pair of linear equations for the following problems and find their solution by substitution method.
(i) The difference between two numbers is 26 and one number is three times the other. Find them.
Exercise 3 - Q 3 (ii)6:46
Form a pair of linear equations for the following problems and find their solution by substitution method.
(i) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Exercise 3 - Q 3 (iii)9:37
Form a pair of linear equations for the following problems and find their solution by substitution method.
(iii). The coach of a cricket team buys 7 bats and 6 balls for ₹ 3800. Later, she buys 3 bats and 5 balls for ₹ 1750. Find the cost of each bat and each ball.
Exercise 3 - Q 3 (iv)9:33
Form a pair of linear equations for the following problems and find their solution by substitution method.
(iv). The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 105 and for a journey of 15 km, the charge paid is ₹ 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
Exercise 3 - Q 3 (v)9:02
Form a pair of linear equations for the following problems and find their solution by substitution method.
v). A fraction becomes 9/11 if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and denominator it becomes5/6. Find the fraction?
Exercise 3 - Q 3 (vi)8:58
Form a pair of linear equations for the following problems and find their solution by substitution method.
(vi). Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?
Exercise 4 - Q 1 (i)11:30
Solve the following pair of linear equations by the elimination method and the substitution method:
(i) x + y = 5, 2x – 3y = 4
Exercise 4 - Q 1 (ii)8:23
Solve the following pair of linear equations by the elimination method and the substitution method:
(ii) 3x + 4y = 10, 2x – 2y = 2
Exercise 4 - Q 1 (iii)10:33
Solve the following pair of linear equations by the elimination method and the substitution method:
(iii) 3x − 5y – 4 = 0, 9x = 2y + 7
Exercise 4 - Q 1 (iv)8:25
Solve the following pair of linear equations by the elimination method and the substitution method:
(iv). x/2 + 2y/3 = -1, x - y/3 = 3
Exercise 4 - Q 2 (i)9:37
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?
Exercise 4 - Q 2 (ii)7:35
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
(i) Five years ago, Nuri was thrice as old as sonu. Ten years later, Nuri will be twice as old as sonu. How old are Nuri and Sonu?
Exercise 4 - Q 2 (iii)8:52
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
(i) The sum of the digits of a two–digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Exercise 4 - Q 2 (iv)7:25
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
(i) Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.
Exercise 4 - Q 2 (v)8:09
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Exercise 5 - Q 1 (i)6:57
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
(i). x – 3y – 3 = 0; 3x – 9y – 2 = 0
Exercise 5 - Q 1 (ii)7:29
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
(ii). 2x + y = 5; 3x + 2y = 8
Exercise 5 - Q 1 (iii)4:09
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
(iii). 3x − 5y = 20; 6x − 10y = 40
Exercise 5 - Q 1 (iv)8:06
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
(iv). x − 3y – 7 = 0; 3x − 3y – 15 = 0
Exercise 5 - Q 2 (i)11:00
(i) For which values of a and b does the following pair of linear equations have an infinite number of solutions?
2x + 3y = 7, (a − b) x + (a + b) y = 3a + b – 2
Exercise 5 - Q 2 (ii)5:30
(ii) For which value of k will the following pair of linear equations have no solution? 3x + y = 1, (2k − 1) x + (k − 1) y = 2k + 1
Exercise 5 - Q 311:42
Solve the following pair of linear equations by the substitution and cross- multiplication methods:
8x + 5y = 9
3x + 2y = 4
Exercise 5 - Q 4 (i)10:24
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
(i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay ₹1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹1180 as hostel charges. Find the fixed charges and the cost of food per day.
Exercise 5 - Q 4 (ii)8:24
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction
Exercise 5 - Q 4 (iii)9:18
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
Exercise 5 - Q 4 (iv)9:55
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
(i) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Exercise 5 - Q 4 (v)10:39
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle
Exercise 6 - Q 1 (i)12:45
Solve the following pairs of equations by reducing them to a pair of linear equations:
(i). 1/2x + 1/3y = 2; 1/3x + 1/2y = 13/6
Exercise 6 - Q 1 (ii)8:29
Solve the following pairs of equations by reducing them to a pair of linear equations:
(ii). 2/√x + 3/√y = 2; 4/√x - 9/√y = -1
Exercise 6 - Q 1 (iii)10:29
Solve the following pairs of equations by reducing them to a pair of linear equations:
(iii). 4/x + 3y = 14; 3/x - 4y = 23
Exercise 6 - Q 1 (iv)9:04
Solve the following pairs of equations by reducing them to a pair of linear equations:
(iv). 5/(x - 1) + 1/(y - 2) = 2; 6/(x - 1) - 3/(y - 2) = 1
Exercise 6 - Q 1 (v)10:29
Solve the following pairs of equations by reducing them to a pair of linear equations:
(v). (7x - 2y)/xy = 5; (8x + 7y)/xy = 15
Exercise 6 - Q 1 (vi)9:27
Solve the following pairs of equations by reducing them to a pair of linear equations:
(vi). 6x + 3y = 6xy; 2x + 4y = 5xy
Exercise 6 - Q 1 (vii)9:13
Solve the following pairs of equations by reducing them to a pair of linear equations:
(vii). 10/(x + y) + 1/(x - y) = 4; 15/(x + y) - 5/(x - y) = -2
Exercise 6 - Q 1 (viii)9:32
Solve the following pairs of equations by reducing them to a pair of linear equations:
(viii). 1/(3x + y) + 1/(3x - y) = 3/4; 1/(2(3x + y)) - 1/(2(3x – y)) = - 1/8
Exercise 6 - Q 2 (i)13:23
Formulate the following problems as a part of equations, and hence find their solutions.
(i). Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
Exercise 6 - Q 2 (ii)12:09
Formulate the following problems as a part of equations, and hence find their solutions.
(ii). 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
Exercise 6 - Q 2 (iii)12:13
Formulate the following problems as a part of equations, and hence find their solutions.
(iii). Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Exercise 7 - Q 113:43
The age of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.
Exercise 7 - Q 210:51
One says, “Give me a hundred, friend! I shall then become twice as rich as you.” The other replies, “If you give me ten, I shall be six times as rich as you.” Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II]
[Hint: x + 100 = 2(y – 100), y + 10 = 6(x – 10)].
Exercise 7 - Q 312:30
A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h, it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Exercise 7 - Q 414:09
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Exercise 7 - Q 510:14
In a ∆ABC, ∠c = 3 ∠B = 2(∠A + ∠B). Find three angles.
Exercise 7 - Q 69:29
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co- ordinate of the vertices of the triangle formed by these lines and the y - axis.
Exercise 7 - Q 7 (i)6:34
Solve the following pair of linear equations:
(i). px + py = p – q; qx – py = p + q
Exercise 7 - Q 7 (ii)8:12
Solve the following pair of linear equations:
(ii). ax + by = c; bx + ay = 1 + c
Exercise 7 - Q 7 (iii)6:24
Solve the following pair of linear equations:
iii). x/a - y/b = 0; ax + by = a2 + b2
Exercise 7 - Q 7 (iv)7:17
Solve the following pair of linear equations:
(iv). (a - b)x + (a + b)y = a2 – 2ab – b2; (a + b)(x + y) = a2 + b2
Exercise 7 - Q 7 (v)8:29
Solve the following pair of linear equations:
(v). 152x – 378y = -74; -378x + 152y = -604
Exercise 7 - Q 811:30
ABCD is a cyclic quadrilateral (see figure). Find the angles of the cyclic quadrilateral.

Session 1 - Introduction10:42
Introduction:
Session 1 - Q 12:24
Determine the value of ‘k’ for which the
given value is a solution of the equation.
x2 + 2ax + k = 0, x = – a
Session 1 - Q 21:15
If one root of the equation x2 + ax + 3 = 0 is 1,
then its other root is
A. 2
B. -2
C. 3
D. -3
Session 1 - Q 33:00
Check whether –3 is a solution of the equation 3x2 + 5x + 2 = 0.
Test your understanding
Home Assignment
Session 2 - Introduction2:41
Representing word problems as Quadratic Equations
Session 2 - Q 15:06
Represent the following situations mathematically:
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
Session 2 - Q 23:46
Represent the following situations mathematically:
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. We would like to find out the number of toys produced on that day.
Session 2 - Q 34:04
The hypotenuse of a right angled triangle is 6 metres more than twice the shortest side. If the third side is 2 meters less than the hypotenuse, find the sides of the triangle.
Session 2 - Q 45:00
A man travels a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km an hour, the journey would have taken two hours less. Find the original speed of the train.
Test your understanding
Home Assignment
Session 3 - Introduction1:41
Method to check whether a given equation is quadratic or not & method to determine unknown constant involved in a Q.E.
Session 3 - Q 19:18
Check whether the following are quadratic equations:
(i) (x – 2)2 + 1 = 2x – 3
(ii) x(x + 1) + 8 = (x + 2) (x – 2)
(iii) x (2x + 3) = x2 + 1
(iv) (x + 2)3 = x3 – 4
Session 3 - Q 26:05
Which one of the following is not a quadratic equation?
(A) (x + 2)2= 2(x + 3)
(B) x2 + 3x = (–1)(1 – 3x)2
(C) (x + 2) (x – 1) = x2– 2x – 3
(D) x3– x2+ 2x + 1 = (x + 1)3
Session 3 - Q 34:26
Check whether 16/x – 1 = 15/(x+1) is a quadratic equation?
Session 3 - Q 46:01
Check whether 1/(x+1) + 2/(x+2) = 4/(x+4) is a quadratic equation?
Test your understanding
Home Assignment
Session 4 - Introduction15:05
Learning Objectives:
ü How to find Solutions or Roots of a Quadratic Equation.
ü Different methods to find Solution of a Quadratic Equation.
Session 4 - Q 17:35
Find the roots of the equation 2x2 – 5x + 3 = 0, by factorization.
Session 4 - Q 25:17
Find the roots of the quadratic equation 6x2 – x – 2 = 0.
Session 4 - Q 312:06
Find the roots of the quadratic equation 3x2− 2√6x + 2 = 0.
Session 4 - Q 49:54
A charity trust decides to build a prayer hall having a carpet area of 300 square metres with its length one metre more than twice its breadth. What should be the length and breadth of the hall?
Test your understanding
Home Assignment
Session 5 - Introduction11:59
Session 5 - Q 18:05
Find the roots of the equation 2x2 – 5x + 3 = 0, by the method of completing the square.
Session 5 - Q 26:28
Find the roots of the equation 5x2 – 6x – 2 = 0 by the method of completing the square.
Session 5 - Q 33:59
Find the roots of x2 – 4x – 8 = 0 by the method of completing square.
Session 5 - Q 46:08
Find the roots of 4x2 + 3x + 5 = 0 by the method of completing the square.
Test your understanding
Home Assignment
Session 6 - Introduction10:26
Solution of a Quadratic Equation by Quadratic Formula:
Session 6 - Q 113:04
Find the roots of the following quadratic equations,
if they exist, using the quadratic formula:
(i) 3x2 – 5x + 2 = 0
(ii) x2 + 4x + 5 = 0
(iii) 2x2 – 2√2x + 1 = 0
Session 6 - Q 212:00
Find the roots of the following equations:
(i) x + 1/x = 3, x ≠ 0
(ii) 1/x-1/(x-2) = 3, x ≠ 0, 2
Session 6 - Q 310:27
The area of rectangular plot is 528m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot. Solve the situation by using the quadratic formula.
Test your understanding
Home Assignment
Session 7 - Introduction3:39
Solution of a Quadratic Equation - word problems
Session 7 - Q 110:07
Find two consecutive odd positive integers,
sum of whose squares is 290.
Session 7 - Q 210:30
A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square meters more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m (see figure). Find its length and breadth.
Session 7 - Q 38:25
A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Session 7 - Q 49:53
P & Q are centres of circles of radii 9 cm and 2 cm respectively. PQ = 17 cm. R is the centre of the circle of radius x cm which touches given circles externally. Given that angle PRQ is 90°. Write an equation in x and solve it.
Session 7 - Q 59:29
A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?
Test your understanding
Home Assignment
Session 8 - Introduction5:09
Nature of Roots
Session 8 - Q 13:18
Find the discriminant of the quadratic equation
2x2 – 4x + 3 = 0, and hence find the nature of its roots.
Session 8 - Q 24:02
Find the discriminant of the equation 3x2 – 2x + 1/3 = 0 and
hence find the nature of its roots. Find them, if they are real.
Session 8 - Q 35:56
If – 3 is a root of quadratic equation 2x2 + px – 15 = 0, while the quadratic equation x2 − 4px + k = 0 has equal roots , find the value of ‘k ’ .
Session 8 - Q 47:29
If the equation (1 + m2) x2 + 2 mcx + (c2 − a2) = 0
has equal roots, prove that c2 = a2 (1 + m2).
Session 8 - Q 55:55
Find the value of ‘k ’ for the quadratic equation
kx (x − 2) + 6 = 0, so that they have two equal roots.
Session 8 - Q 64:54
Find the non-zero values of ‘ k ’ for which the roots of the quadratic equation 9x2 - 3kx + k = 0 are real and equal.
Test your understanding
Home Assignment
Exercise 1 - Q 120:19
Check whether the following are Quadratic Equations.
(i) (x + 1)2= 2 (x − 3)
(ii) x2 - 2x = (−2) (3 − x)
(iii) (x − 2) (x + 1) = (x − 1) (x + 3)
(iv) (x − 3) (2x + 1) = x (x + 5)
(v) (2x − 1) (x − 3) = (x + 5) (x − 1)
(vi) x2 + 3x +1 = (x - 2)2
(vii) (x + 2)3 = 2x(x2 - 1)
(viii) x3 - 4x2 - x + 1 = (x - 2)3
Exercise 1 - Q 2 (i)4:22
Represent the following situations in the form of Quadratic Equations:
(i) The area of rectangular plot is 528m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Exercise 1 - Q 2 (ii)2:40
Represent the following situations in the form of Quadratic Equations:
(ii) The product of two consecutive positive integers is 306. We need to find the integers.
Exercise 1 - Q 2 (iii)3:52
Represent the following situations in the form of Quadratic Equations:
(iii) Rohan's mother is 26 years older than him. The product of their ages (in years) after 3 years will be 360. We would like to find Rohan's present age.
Exercise 1 - Q 2 (iv)9:14
Represent the following situations in the form of Quadratic Equations:
(iv) A train travels a distance of 480 km at uniform speed. If, the speed had been 8km/h less, then it would have taken 3 hours more to cover the same distance. We need to find speed of the train.
Exercise 2 - Q 120:54
Find the roots of the following quadratic equations by factorization:
(i) x2 – 3x – 10 = 0 (ii) 2x2 + x – 6 = 0
(iii) √2x2 + 7x + 5√2 = 0
(iv) 2x2 - x + 1/8 = 0 (v) 100x2 - 20x + 1 = 0
Exercise 2 - Q 2 (i)12:11
Represent the following situations mathematically:

(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
Exercise 2 - Q 2 (ii)9:13
(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. We would like to find out the number of toys produced on that day.
Exercise 2 - Q 36:14
Find two numbers whose sum is 27 and product is 182.
Exercise 2 - Q 48:00
Find two consecutive positive integers, sum of whose squares is 365.
Exercise 2 - Q 58:37
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Exercise 2 - Q 610:55
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If, the total cost of production on that day was ₹90, find the number of articles produced and the cost of each article.
Exercise 3 - Q 1 (i)13:41
Find the roots of the following quadratic equations if they exist by the method of completing square.
(i) 2x2 – 7x + 3 = 0
Exercise 3 - Q 1 (ii)7:11
Find the roots of the following quadratic equations if they exist by the method of completing square.
(ii) 2x2 + x – 4 = 0
Exercise 3 - Q 1 (iii)5:40
Find the roots of the following quadratic equations if they exist by the method of completing square.
(iii) 4x2 + 4√3x + 3 = 0
Exercise 3 - Q 1 (iv)4:44
Find the roots of the following quadratic equations if they exist by the method of completing square.
(vi) 2x2 + x + 4 = 0
Exercise 3 - Q 214:52
Find the roots of the following quadratic equations if they exist by the method of completing square.
(i) 2x2 – 7x + 3 = 0
(ii) 2x2 + x – 4 = 0
(iii) 4x2 + 4√3x + 3 = 0
(vi) 2x2 + x + 4 = 0
Exercise 3 - Q 312:01
Find the roots of the following equations:
(i) x - 1/x = 3, x ≠ 0
(ii) 1/(x+4) - 1/(x-7) = 11/30, x ≠ -4,7
Exercise 3 - Q 49:05
The sum of reciprocals of Rehman's ages (in years) 3 years ago and 5 years from now is1/3. Find his present age.
Exercise 3 - Q 510:20
In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Exercise 3 - Q 611:03
The diagonal of a rectangular field is 60 meters more than the shorter side. If, the longer side is 30 meters more than the shorter side, find the sides of the field.
Exercise 3 - Q 710:26
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Exercise 3 - Q 811:08
A train travels 360 km at a uniform speed. If, the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Exercise 3 - Q 916:10
Two water taps together can fill a tank in 93/8hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Exercise 3 - Q 1013:16
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If, the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of two trains.
Exercise 3 - Q 1112:13
Sum of areas of two squares is 468 m2. If, the difference of their perimeters is 24 meters, find the sides of the two squares.
Exercise 4 - Q 113:46
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them.
(i) 2x2 - 3x + 5 = 0
(ii) 3x2 - 4√3x + 4 = 0
(iii) 2x2 - 6x + 3 = 0
Exercise 4 - Q 27:17
Find the value of k for each of the following quadratic equations, so that they have two equal roots.
(i) 2x2 + kx + 3 = 0
(ii) kx (x − 2) + 6 = 0
Exercise 4 - Q 35:56
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
Exercise 4 - Q 410:00
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Exercise 4 - Q 59:36
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.

Session 1 - Introduction13:22
Introduction
Session 1 - Q 12:22
For the AP: 3/2, 1/2,-1/2,-3/2, . . ., write the first term ‘a’
and the common difference ‘d’.
Session 1 - Q 21:46
Find the common difference of the AP: 1/p, (1-p)/p, (1-2p)/p,....
Session 1 - Q 34:25
Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
(i) 4, 10, 16, 22, . . .
(ii) 1, – 1, – 3, – 5, . . .
(iii) – 2, 2, – 2, 2, – 2, . . .
(iv) 1, 1, 1, 2, 2, 2, 3, 3, 3, . . .
Session 1 - Q 48:34
In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.
1) The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs 400.
2) The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs 250, and it increases by Rs 50 for the next higher class.
3) The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10% per annum.
4) The number of bacteria in a certain food item after each second, when they double in every second.
Test your understanding
Home Assignment
Session 2 - Introduction3:20
Method to write an AP, when first term and common difference are given:
Session 2 - Q 12:20
The nth term of an AP is 7 – 4n, then its common difference is
A . – 3
B . 3
C . 4
D . – 4
Session 2 - Q 22:28
An A.P is defined by an = 4n + 5 , then write the sequence.
Session 2 - Q 35:36
Write the first three terms of the AP, when ‘a’ and ‘d’ are as given below:
a = 1/2, d = −1/6
a = −5, d = −3
a = √2, d = 1/√2
Session 2 - Q 45:03
Find the first 5 terms of the sequence defined by
an = (−1)n – 1 × 2n
and check whether the sequence is in AP?
Session 2 - Q 52:28
Which is the next term of the AP: √2, √8, √18, √32,....?
Session 2 - Q 63:04
For what value of k will k + 9, 2k − 1, and 2k + 7
are consecutive terms of an AP.
Test your understanding
Home Assignment
Session 3 - Introduction3:17
Session 3 - Q 12:05
Find the 10th term of the AP: 2, 7, 12, . . .
Session 3 - Q 25:36
Which term of the AP: 21, 18, 15, . . . is – 81?
Also, is any term 0? Give reason for your answer.
Session 3 - Q 33:21
Check whether 301 is a term of the list of numbers
5, 11, 17, 23, . . .
Session 3 - Q 44:25
Which term of the AP: 121, 117, 113, .....
is its first negative term?
[Hint: Find n for an < 0]
Session 3 - Q 54:22
How many two-digit numbers are divisible by 3?
Session 3 - Q 67:53
If m times the mth term of an A.P is equal to n times its
nth term, show that the (m + n)th term of the AP is zero.
Test your understanding
Home Assignment
Session 4 - Introduction6:57
nth Term of an AP:
• nth Term of an AP from the End (Last term):
• Middle Term
• problems based on finding the AP and nth term when its two terms are given
• Word problem
Session 4 - Q 13:36
Determine the AP whose 3rd term is 5
and the 7th term is 9.
Session 4 - Q 25:12
Find the middle term of the A.P. 213, 205, 197,.... 37.
Session 4 - Q 33:36
Find the 11th term from the last term
(towards the first term) of the AP: 10, 7, 4, . . . ,– 62.
Session 4 - Q 44:52
A sum of ₹1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an AP? If so, find the interest at the end of 30 years making use of this fact.
Session 4 - Q 53:41
In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?
Test your understanding
Home Assignment
Session 5 - Introduction7:41
Session 5 - Q 12:32
Find the sum of the first 22 terms of the AP: 8, 3, –2 . . .
Session 5 - Q 23:08
Find the sum of :
(i) the first 1000 positive integers
(ii) the first n positive integers
Session 5 - Q 37:35
Solve the equation: 1 + 4 + 7 + 10 + .....+ x = 287.
Session 5 - Q 45:26
Find the sum of first 24 terms of the list of numbers whose nth term is given by an = 3 + 2n?
Session 5 - Q 55:19
The sum of the first terms of an A.P. is given by Sn = 2n2 + 3n. Find the sixteenth term of the A.P.
Test your understanding
Home Assignment
Session 6 - Introduction1:48
Session 6 - Q 13:53
If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.
Session 6 - Q 26:00
How many terms of the AP: 24, 21, 18 . . . must be taken so that their sum is 78?
Session 6 - Q 32:44
Find the sum of the first 15 multiples of 8.
Session 6 - Q 47:35
A manufacturer of TV sets produced 600 sets in the third year
and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find :
(i) the production in the 1st year
(ii) the production in the 10th year
(iii) the total production in first 7 years
Session 6 - Q 55:06
A sum of ₹700 is to be used in give seven 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.
Test your understanding
Home Assignment
Exercise 1 - Q 113:05
In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
The tax if are after each km when the fare is ₹15 for the first km and ₹8 for each additional km.
The amount of air present in a cylinder when a vacuum pump removes 1/4of the air remaining in the cylinder at a time.
The cost of digging a well after every meter of digging, when it costs ₹150 for the first meter and rises by ₹50 for each subsequent meter.
The amount of money in the account every year, when ₹ 10,000 is depositedat compoundInterestat
8%perannum.
Exercise 1 - Q 210:25
Write first four terms of the AP, when the first term a and common difference d are given as follows:
a = 10, d = 10
a=-2,d = 0
a= 4,d =-3
a =-1,d = 1/2
a =-1.25, d =-0.25
Exercise 1 - Q 35:28
For the following APs, write the first term and the common difference.
(i). 3,1,–1,–3, ….…
(ii). –5, –1, 3, 7, ……..
(iii). 1/3, 5/3, 9/3, 13/3…….
(iv). 0.6, 1.7, 2.8, 3.9 ...
Exercise 1 - Q 444:00
Which of the following are APs? If they form an AP, find the common difference d and write three more terms.
2, 4, 8, 16...
2, 5/2, 3, 7/2 ….
−1.2, −3.2, −5.2, −7.2...
−10, −6, −2, 2, ...
3, 3+√2, 3+2√2, 3+3√2, …..
0.2,0.22,0.222,0.2222...
0, −4, −8, −12...
-1/2,-1/2, - 1/2, - 1/2…..
1, 3, 9, 27...
a, 2a, 3a, 4a...
a, a2, a3, a4…….
√2,√8,√18,√32….
√3,√6,√9,√12…
12, 32, 52, 72……
12, 52, 72, 73…..
Exercise 2 - Q 18:47
Find the missing variable from a, d, n and an, where a is the first term, d is the common difference and an is the nth term of AP.
Exercise 2 - Q 23:35
Choose the correct choice in the following and justify:
30th term of the AP: 10, 7, 4,... is
97
77
–77
–87
11th term of the AP:−3, −12, 2,... is
28
22
–38
- 481/2
Exercise 2 - Q 314:59
In the following AP's find the missing terms:
(i) 2, ___, 26
(ii) ___, 13, ___, 3
(iii) 5, ___, ___, 91/2
(iv) –4, ___, ___, ___, ___, 6
(v) ___, 38, ___, ___, ___, –22
Exercise 2 - Q 43:27
Which term of the AP: 3, 8, 13, 18, . . . , is 78?
Exercise 2 - Q 58:11
Find the number of terms in each of the following APs:
(i) 7, 13, 19, , 205 (ii) 18, 151/2, 13, ….., −47
Exercise 2 - Q 65:31
Check whether – 150 is a term of the AP: 11, 8, 5, 2....
Exercise 2 - Q 78:46
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Exercise 2 - Q 87:50
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Exercise 2 - Q 97:17
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Exercise 2 - Q 103:05
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Exercise 2 - Q 117:49
Which term of the AP: 3, 15, 27, 39,…. will be 132 more than its 54th term?
Exercise 2 - Q 129:37
Two APs have the same common difference. The difference between their 100th terms is100, what is the difference between their 1000th terms?
Exercise 2 - Q 139:56
How many three-digit numbers are divisible by 7?
Exercise 2 - Q 145:21
How many multiples of 4 lie between 10 and 250?
Exercise 2 - Q 157:09
For what value of n, are the nth terms of two APs: 63, 65, 67,... and 3, 10, 17,.... equal?
Exercise 2 - Q 168:59
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Exercise 2 - Q 176:53
Find the 20th term from the last term of the AP: 3, 8, 13,...., 253.
Exercise 2 - Q 1812:53
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Exercise 2 - Q 198:23
Subba Rao started work in 1995 at an annual salary of ₹ 5000 and received an increment of ₹ 200 each year. In which year did his income reach ₹ 7000?
Exercise 2 - Q 208:09
Ramkali saved ₹ 5 in the first week of a year and then increased her weekly savings by ₹ 1.75. If in the nth week, her weekly savings become ₹ 20.75, find n.
Exercise 3 - Q 112:30
Find the sum of the following AP's.
(i) 2, 7, 12, ..., to 10 terms. (ii) –37, –33, –29, ..., to 12 terms.
(iii) 0.6, 1.7, 2.8, ..., to 100 terms. (iv) 1/15, 1/12, 1/(10 ), …, to 11 terms.
Exercise 3 - Q 214:51
Find the sums given below:
(i) 7 + 101/2 + 14 +……+ 84
(ii) 34 + 32 + 30 + … + 10
(iii) –5 + (–8) + (–11) + ... + (–230)
Exercise 3 - Q 346:35
In an AP
(i) Given a = 5, d = 3, an = 50, find n and Sn.
(ii) Given a = 7, a13 = 35, find d and S13.
(iii) Given a12 = 37, d = 3, find a and S12.
(iv) Given a3 = 15, S10 = 125, find d and a10.
(v) Given d = 5, S9 = 75, find a and a9.
(vi) Given a = 2, d = 8, Sn = 90, find n and an.
(vii) Given a = 8, Sn = 210, find n and d.
(viii) Given an = 4, d = 2, Sn = -14, find n and a.
(ix) Given a = 3, n = 8, S = 192, find d.
(ix) Given l = 28, S = 144, and there are total of 9 terms. Find a.
Exercise 3 - Q 410:29
How many terms of the AP: 9, 17, 25,... must be taken to give a sum of 636?
Exercise 3 - Q 55:10
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Exercise 3 - Q 66:24
The first and the last terms of an AP are 17 and 350 respectively. If, the common difference is 9, how many terms are there and what is their sum?
Exercise 3 - Q 75:36
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Exercise 3 - Q 86:08
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Exercise 3 - Q 99:33
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
Exercise 3 - Q 108:18
Show that a1, a2,……, an,…. form an AP where an is defined as below:
(i) an = 3 + 4n
(ii) an = 9 - 5n
Also find the sum of the first 15 terms in each case.
Exercise 3 - Q 1114:48
If the sum of the first n terms of an AP is (4n – n2), what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.
Exercise 3 - Q 123:56
Find the sum of the first 40 positive integers divisible by 6.
Exercise 3 - Q 133:22
Find the sum of the first 15 multiples of 8.
Exercise 3 - Q 144:35
Find the sum of the odd numbers between 0 and 50.
Exercise 3 - Q 156:07
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being
₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
Exercise 3 - Q 168:47
A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If, each prize is ₹ 20 less than its preceding term, find the value of each of the prizes.
Exercise 3 - Q 176:21
In a school, students thought of planting 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 the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of class II will plant two trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?
Exercise 3 - Q 189:50
A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... What is the total length of such a spiral made up of thirteen consecutive semicircles. (Take π = 22/7)
[Hint: Length of successive semicircles is l1, l2, l3, l4,.... with centers at A, B, A, B, . . ., respectively.]
Exercise 3 - Q 1915:35
200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and soon. In how many rows are the 200 logs placed and how many logs are in the top row?
Exercise 3 - Q 2010:15
In a potato race, a bucket is placed at the starting point, which is 5 meters from the first potato, and the other potatoes are placed 3 meters apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: To pick up the first potato and the second potato, the total distance (in meters) run by a competitor is 2 × 5 + 2 × (5 + 3)]
Exercise 4 - Q 19:03
Which term of the AP: 121, 117, 113,. . ., Is its first negative term?
[Hint : Find n for an< 0]
Exercise 4 - Q 214:42
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Exercise 4 - Q 39:20
A ladder has rungs 25 cm apart (see figure). The rungs decrease uniformly in length from 45 cm, at the bottom to 25 cm at the top. If the top and the bottom rungs are 21/2 m apart, what is the length of the wood required for the rungs?
[Hint: Number of rungs = 250/25 + 1]
Exercise 4 - Q 413:51
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
[Hint: Sx – 1 = S49 – Sx]
Exercise 4 - Q 511:03
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1/4 m and at read of 1/2 m (see figure). Calculate the total volume of concrete required to build the terrace.
[Hint : Volume of concrete required to build the first step = 1/4 × 1/2 × 50 m3]

Requirements

Basic knowledge of fundamental operations - addition, subtraction, product, and division.
Basic elementary math knowledge.
Each chapter includes prerequisite knowledge classes in which the child gains extensive knowledge and a thorough understanding of the chapters.

Description

This course is carefully designed to explain various areas of Algebra.
It has 325 lectures spanning around 44 hours of on-demand videos that are divided into 4 sections, and each chapter is a section and further divided into simple sessions. The course is divided into a simplified day-by-day learning schedule.
Each topic is divided into simple sessions and explained extensively by solving multiple questions. Each session contains a detailed explanation of the concept.
An online test related to the concept for immediate assessment of understanding.
Session-based daily home assignments with a separate key. The students are encouraged to solve practise questions and quizzes provided at the end of each session.
This course will give you a firm understanding of the fundamentals and is designed in a way that a person with little or no previous knowledge can also understand it very well.
It covers 100% video solutions of various problems and situations.
Our design meets the real classroom experience by following classroom teaching practices. We have designed this course by keeping in mind all the needs of students and their desire to become masters in Algebra. This course is designed to benefit all levels of learners and will be the best gift for board-appearing students. Students love these easy methods and explanations. They enjoy learning math and never feel that math is troublesome.

Topics covered in the course:

Polynomials
Pair of Linear Equations in Two Variables
Quadratic Equations
Arithmetic Progressions

With this course you'll also get:

Perfect your mathematical skills on Algebra for better scores.

A Udemy Certificate of Completion is available for download.

Feel free to contact me with any questions or clarifications you might have.

I can't wait for you to get started on mastering the Algebra.

I look forward to seeing you on the course! :)

Benefits of Taking this Course:

On completion of this course, one will have detailed knowledge of Algebra and be able to easily solve all the problems, which can lead to scoring well in exams with the help of explanatory videos ensure complete concept understanding.

Downloadable resources help in applying your knowledge to solve various problems.

Quizzes help in testing your knowledge. In short, one can excel in math by taking this course.

Who this course is for:

This course has been designed for students of Grade 10th CBSE, ICSE, SSC, GCSE, IGCSE, SAT, ACT, GRE, and other board-appearing students.
Students studying for the public or other competitive examinations as well as job aspirants.
Home-school parents are looking for extra support with the fundamentals.
Anyone interested in revising or learning the basics of mathematics should.
Students in junior high and high school/secondary schools.
Anyone who wants to proficient mathematics and the solving different real life situations as well.
Anyone who wants to study math for fun after taking a break from school.
It will also benefit schools who wish to run classes in the absence of a teacher and make learning fun for their students.
It will also benefit teachers and schools who wish to improve their teaching skills and make learning fun for their students.
For 11th, 9th, and 8th grade students, this will help as a bridge course.
These are the people whose jobs require them to solve basic daily math-related problems.

Mastering Algebra: A Comprehensive Guide for All

What you'll learn

Explore related topics

Course content

Polynomials58 lectures • 6hr 43min

Pair of Linear Equations in Two Variables109 lectures • 16hr 10min

Quadratic Equations72 lectures • 10hr 2min

Arithmetic Progressions86 lectures • 11hr 9min

Requirements

Description

Who this course is for: