UPTET Maths Marathon Paper 2 & 1 | UPTET Maths PYQ Marathon | Maths All PYQ by Himanshu Sir #2

Welcome and Session Overview

Introduction to the Session

• The session begins with a warm greeting, emphasizing the importance of today's discussion on previous year questions.

• The instructor mentions that yesterday's session was incomplete, covering only six questions, and today aims to complete that discussion.

Focus on Topics and Questions

• Key topics from various years will be discussed along with related questions to provide a comprehensive understanding.

• The session is designed for both Paper One and Paper Two candidates, highlighting its significance for all attendees.

Problem Solving Approach

Question Breakdown

• A question regarding distance traveled by different modes of transport is presented, requiring calculation of total distance based on fractions given.

• The instructor encourages participants to solve the problem using the least common multiple (LCM) method for efficiency.

Solution Methodology

• To find LCM easily among 5, 3, and 4, it’s suggested to multiply them directly if LCM is not clear. This leads to an assumed total distance of 60 km.

• Each fraction of the total distance is calculated:

• Train covers 2/5 which equals 24 km.

• Bus covers 1/3 which equals 20 km.

• Car covers 1/4 which equals 15 km.

This totals up to 59 km traveled by these modes leaving a remaining distance of 1 km walked. Thus confirming that if this represents a real value of 3 km then total distance must be recalculated as 180 km instead of 60. Hence option C is correct.

Algebraic Identity Question

Understanding Algebraic Identities

• A question from UP TET (2017) asks about finding values based on algebraic identities where x + 1/x = 5 . Participants are tasked with finding x^2 + 1/x^2 .

Simplifying Expressions

• The solution involves squaring the given expression and adjusting for constants:

• If positive: square minus two; if negative: square plus two.

• Here it results in 25 - 2 = 23, making option B correct.

Factorization Challenge

Identifying Factors

• Another question from UP TET (2017) requires identifying factors from expressions involving algebraic terms like x + y - x + y. Participants are encouraged to factorize correctly using known identities or simplifications.

Application of Identities

• By applying identities such as factoring out common terms or recognizing patterns in expressions helps simplify calculations leading towards determining valid options effectively within provided choices.

Polygon Diagonal Formula

Diagonal Calculation in Polygons

• A straightforward formula-based question regarding calculating diagonals in polygons appears from UP TET (2018), asking participants what formula applies when given number sides (n). The formula discussed is:

[ n(n -3)/2 ].

Practical Application Example

• An example illustrates how this formula can be applied directly by substituting values such as for decagon (n =10), yielding results efficiently through basic arithmetic operations.

Average Age Problem

Family Age Average Calculation

• A problem posed about average age within a family states five members have an average age of twenty years while one member's current age is ten years old; participants need to determine what their average age was at his birth time?

Logical Reasoning Steps

• It’s explained logically that since they all would have aged back ten years together when considering his birth time means each member's age reduces equally leading back towards an average calculation resulting ultimately in option A being correct at twelve point five years old rather than any other choice made during discussions thus far .

Approach to Problem Solving

Engaging Students in Problem-Solving

• The instructor encourages students to try solving a problem presented, emphasizing that it is not difficult and can be approached with confidence.

• The instructor reassures students that their comments are visible, creating an interactive environment where they can express their thoughts freely.

• Acknowledges the various activities of students during the session, indicating a relaxed atmosphere conducive to learning.

Understanding Prime Numbers

• Introduces a question involving the ages of two brothers, explaining how to determine if their combined ages yield prime numbers through addition and subtraction.

• Demonstrates calculations using hypothetical ages (23 and 8), showing how different operations affect whether the result is prime or not.

• Concludes that option C is correct after verifying both addition and subtraction yield prime results.

Natural Numbers and Ratios

Exploring Natural Number Sums

• Discusses a problem regarding two natural numbers whose sum equals 48, prompting students to identify which ratios cannot exist based on divisibility rules.

• Clarifies the question about identifying impossible ratios among pairs of natural numbers summing to 48, reinforcing understanding of ratio concepts.

Identifying Valid Ratios

• Explains that valid ratios must divide evenly into 48; examples are provided for clarity on which combinations work or fail.

• Emphasizes logical reasoning in determining valid pairs by checking divisibility against the total sum.

Two-Digit Number Properties

Analyzing Digit Sums

• Presents a problem where the sum of digits in a two-digit number equals nine; introduces conditions under which adding 27 reverses its digits.

• Encourages elimination of options based on digit sums before testing potential candidates for reversal upon addition.

Efficient Problem Solving Techniques

• Highlights efficient strategies such as focusing on unit digits rather than full calculations when determining possible answers.

Arithmetic Logic Questions

Understanding Basic Arithmetic Operations

• Introduces an arithmetic logic question involving reducing fractions and multiplying by half, leading to an eighth value outcome.

Simplifying Calculations

• Guides through simplification steps while maintaining clarity on basic operations like multiplication and division without overcomplicating processes.

Percentage Change Calculations

Addressing Percentage Decrease Over Time

• Discusses how vehicle values decrease over time due to percentage drops each year; prompts calculation of overall percentage change across multiple years.

Formula Application for Net Percentage Change

• Shares formula for calculating net percentage changes effectively while encouraging practical application over rote memorization.

Rational Numbers Discussion

Properties Between Rational Numbers

• Asks what exists between any two rational numbers, guiding towards understanding infinite possibilities within rational sets.

Infinite Rational Numbers

• Confirms that between any two rational numbers lies an infinite number of other rational numbers, reinforcing foundational concepts in number theory.

Inverse Product Calculation

Finding Inverses

• Introduces finding inverses related to products involving fractions; emphasizes understanding additive inverses alongside multiplicative ones.

Multiplication Steps Explained

• Walkthrough demonstrates how multiplying fractions leads toward finding desired outcomes efficiently while ensuring comprehension at each step.

Algebraic Simplification Techniques

Utilizing Algebraic Identities

• Presents algebraic simplifications using identities; encourages recognizing patterns within expressions for easier resolution.

Finalizing Answers Through Simplification

• Concludes with straightforward methods yielding quick solutions via identity applications rather than lengthy computations.

Preparation Strategies for Exams

Importance of Consistent Study Habits

• Emphasizes the need for diligent preparation to avoid last-minute cramming, which can lead to stress and poor performance.

• Highlights that daily study habits build confidence and interest in the subject matter, making learning more effective.

• Warns against procrastination, as it can create a backlog of material that becomes overwhelming and discouraging.

Understanding Exam Pressure

• Discusses how pressure from upcoming exams can hinder comprehension if students attempt to learn too much at once.

• Stresses the importance of gradual learning over time rather than cramming before exams.

Conversion Between Units: Speed Measurement

Key Concepts in Unit Conversion

• Introduces a simple method for converting kilometers per hour (km/h) to meters per second (m/s), using multiplication by 5/18.

• Explains the reverse conversion from m/s to km/h, requiring multiplication by 18/5.

Memorization Techniques

• Suggests remembering unit sizes: km/h is larger than m/s; thus, when converting downwards, use a smaller fraction (5/18).

• Provides an example calculation demonstrating how to convert units effectively.

Homework Assignment and Upcoming Topics

Homework Instructions

• Assignments are given with instructions on submitting answers in the comments section after the video ends.

Future Class Schedule

• Announces that tomorrow's class will focus on algebra, promising useful tricks for solving exam questions quickly.

Free Resources and Student Performance Recognition

Accessing Free Study Materials

• Informs students about free UP-TET preparation batches available through specific platforms, detailing registration steps.

Celebrating Student Achievements

• Recognizes top-performing students based on their attempts and accuracy in recent assessments.