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Basic Mathematics & Logarithm: Complete Chapter in 1 Video || Concepts+PYQs || Class 11 JEE

JEE Wallah・151 minutes read

A revision session for Class 11th Algebra is being conducted, covering topics like coordinate geometry, trigonometry, and units. Emphasis is placed on practicing questions, understanding algebraic identities, and using the wavy curve method to solve inequalities effectively.

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The session for Class 11th Algebra includes topics like coordinate geometry, trigonometry, and units.
Emphasis is placed on practicing questions to understand concepts and learning algebraic identities thoroughly.
The wavy curve method is explained in detail for solving inequalities, determining critical points, and shading regions based on denominators.
Logarithmic equations are introduced, detailing properties, base changes, and simplification methods, emphasizing the significance of understanding logarithms for solving equations effectively.

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What topics are covered in the Algebra revision session?
Coordinate geometry, trigonometry, and algebraic identities.

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Summary

00:00

"Class 11 Algebra Revision Session with Identities"

Revision session for Class 11th Algebra is being conducted.
Suggestions from students were taken into account for the session.
The session includes topics like coordinate geometry, trigonometry, and units.
Algebra chapter is divided into five parts.
Emphasis on practicing questions to understand concepts.
Importance of learning algebraic identities thoroughly.
Specific identity discussed: a^k + b^k + c^k = 3abc when a + b + c = 0.
Detailed explanation of a question involving algebraic identities.
Advanced level question involving distinct non-zero real numbers and ratios.
Application of algebraic concepts to solve equations and find the sum of roots.

12:58

Solving Equations with Wavy Curve Method

Product of roots equals product of roots plus minus plus minus, then product of roots alpha beta gamma minus off -1 Apav.
If product of roots is one, put one here; if the value becomes three, then the value is three.
Answer is 30, as 10 * 3 equals 30.
Concept of Meius, concept of cubic mix, and question on identity a k + b k + c k = 3abc.
Formula of p k p k k p r k - 3pq aa is p+ aa in p s + k s sp aa s - p k - k aa minus r p.
Value calculated is 72, a great question on identity.
Wavy curve method explained, steps detailed for solving inequalities.
Example given with 3x - 2 = 4, solving using wavy curve method.
Another example with t - 9 t p 7, range of t determined as -7 to 9.
Repeated linear factor explained, steps for wavy curve method with power factors detailed.

29:05

"Critical Points and Logarithmic Properties Explained"

The number of linear factors in the question is crucial for determining critical points.
When dealing with critical points, alternate between writing minus and plus, without changing any other steps.
The power of a critical point is significant, with even powers being circled and odd powers not circled.
Critical points with even powers are circled, while those with odd powers are not circled.
The sign change process involves maintaining the sign on circled points and changing the sign on non-circled points.
The final answer is determined by shading positive areas and closing off negative areas based on the denominator.
The wavy curve method is explained in detail, with specific instructions on shading and closing off regions.
Logarithmic equations are introduced, emphasizing the importance of understanding the properties of logarithms.
Various properties of logarithms are outlined, including rules for multiplication, division, and changing bases.
The base change theorem is explained, detailing how to convert logarithms from one base to another.

43:20

Simplifying Equations Using Logarithms

The power of a log with a base of 'a' is crucial in simplifying equations.
If the base remains the same, everything else changes, leaving only 'n'.
An example is given with 5 to the power of log 7 base 5, simplifying to 'n'.
The property of taking the power of 10 with a base of 10 is highlighted.
The significance of e to the power of 'a' always equalling 'x' is emphasized.
The natural log with base 'e' is discussed, with its value close to 2.71.
The property of power log c of 11 with base B and exponent A is explained.
The log graph is introduced, detailing the graph's behavior based on the base's value.
A practical example is provided to demonstrate simplifying expressions involving logs.
A method to simplify complex log expressions within a square root is shared, showcasing a quick and efficient approach.

58:45

Mathematical Equations and Logarithmic Brain Teaser

7 times 8 equals 56, with 7 as the base and 8 as the exponent.
The expression 7 minus log base 7 of 8 simplifies to 3.
The cube root of 2 is simplified to 2.
The value of 'a' is determined to be 3.
The value of 'b' is found to be 4.
The sum of 'a' and 'b' is 7.
A brain teaser involving logarithms is presented.
The equation involving positive real numbers 'x' and 'v' is solved.
The values of 'x' and 'v' are calculated to be 3^11 and -6 respectively.
The minimum value of 'c' in a logarithmic expression is discussed.

01:14:00

"Logarithmic Equations and Properties Explained"

Log A base B and log B base A are discussed
The concept of cutting logs is explained
The importance of common factors in logarithms is highlighted
The equation formation process is detailed
The minimum value of a natural number is explored
The equation involving log C - A - B is analyzed
The sum of digits in a logarithmic equation is calculated
The manipulation of logarithmic properties is demonstrated
Quadratic equations involving logarithms are solved
The product of positive numbers satisfying a logarithmic equation is determined

01:28:53

Solving Infinite Powers of 7 Problem

The problem involves considering alpha, beta, gamma, log x, Lagva, and Log Jad.
The question requires simplifying the expression involving the power of 7.
The process involves understanding the concept of infinite powers of 7.
The solution includes adding powers of 7 up to infinity.
The final step is to simplify the expression involving the power of 7.
The concept of Geometric Progression (GP) is crucial in solving the problem.
The solution involves understanding the sum of an infinite GP.
The correct answer is determined by comparing the expressions.
The problem requires analyzing the characteristics of logarithmic functions.
The solution involves evaluating the logarithmic expressions to determine their validity.

01:41:41

Solving Quadratic Equations and Logarithmic Properties

The quadratic equation x^2 - 3x - 4 is solved to find the values of x, resulting in x = 4 and x = -1.
To extract x1, y1, x2, and y2, x is substituted with 4 to find y, which equals 2^4 and 1.
The next step involves finding the value of log base 2 of x1 * x2^4 * 2^5 - 1.
By simplifying the equation, log base 2 of 7 is obtained, leading to the final answer of 7.
The concept of quadratic equations is highlighted, emphasizing the importance of understanding the process.
A hint is provided for a homework question involving real numbers a and b greater than one.
The proof of a logarithmic property is demonstrated, showcasing the equality between the power root of a and log base b of a.
An objective question is presented, requiring the roots of a quadratic equation to form a new quadratic equation.
The method of substitution is explained to find the new roots of the quadratic equation, showcasing the application of algebraic techniques.
The importance of understanding quadratic equations and logarithmic properties is emphasized for solving complex problems effectively.

01:55:50

"Transforming Equations and Modulus Functions"

The quadratic equation given is y = -2y.
The quadratic equation is transformed to y = -2/x.
Substituting -2 back into the quadratic equation results in -2bava^2 - 5(-2bava) - 3 = 0.
This leads to a new quadratic equation in y, 3y^2 - 10y - 4 = 0.
By replacing y with x, the new equation becomes x^2 - 10x - 4 = 0.
The process demonstrates how objective questions can be created from log and quadratic mixtures.
The text transitions to discussing modulus functions and equations.
The method of opening modulus functions is explained, with examples like mod x = 2 resulting in x = 2 or x = -2.
The shifting of modulus graphs is detailed, showing how the graph moves based on the equation.
The text concludes with a problem-solving approach for modulus equations, emphasizing the importance of making cases for positive and negative values within the modulus.

02:11:49

"Graphical Method for Solving Quadratic Equations"

The text discusses solving a quadratic equation, starting with the equation 10x + 2 = 0.
Two cases are presented for solving the quadratic equation simultaneously.
The first case involves the equation x - 5 * x - 3 = 0, leading to the value of x being 4.
The second case results in x = 2 being rejected due to it being negative overall.
The valid solution is x = 4, satisfying the equation x e 4.
The text delves into using wavy curves to determine the positive area between 5 and 3.
The sum of all roots is calculated to be 9 + √3.
The text emphasizes the importance of solving equations methodically, whether linear or quadratic.
A graphical approach is introduced to find the roots of the quadratic equation.
The graphical method is highlighted as an alternative to solving equations through cases, providing a visual representation of the solutions.

02:26:30

Solving Modulus Equations and Finding Common Solutions

Non-negative is a positive term, and there are four non-negative terms.
For all four terms to be zero, x must satisfy x = 3 mod x = 5 mod x - 1 = 6 mod x - 2.
The sum of positive terms can only be zero if all terms are zero.
The only solution is x = 0, as having all four terms as zero has no solution.
Practice is essential to understand when and how to solve such questions.
Modulus equations involve basic formulas and properties, like mod a = mod a + mod b.
To solve equations involving modulus, apply the quadratic formula and use a trial-and-error approach.
The intersection of sets s and t involves finding common solutions between the two sets.
By testing values like -3, 3, -4, and -5, the common solutions are determined to be x = -4, x = 3, and x = -5.
In an advanced problem involving logarithms and quadratics, the product of positive real values of x satisfying the equation is found to be √5.

02:41:12

"Quadratic and Logarithmic Problem-Solving Techniques"

The text discusses problem-solving involving quadratic and logarithmic concepts.
Various questions mixing quadratic and log concepts are presented for solving.
Specific examples of quadratic equations and logarithmic properties are detailed.
The text emphasizes the importance of understanding and applying properties in solving equations.
Linear equations are formed using the given information in the text.
Practical steps for simplifying equations and solving linear equations are provided.
The text highlights the direct approach to solving equations by multiplying and subtracting terms.
The importance of practicing and attempting questions independently is stressed.
The text concludes with a call for feedback on the session and encourages continued learning and revision.

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