CSAT Notes for UPSC with diagrams & examples

Section 01: Number System & Foundational Numeracy

Curriculum Overview

Total Topics: 8 | Total Chapters: 31

Topic Breakdown

Topic T01: Number Classifications & Structure

• 1.1 – Real Numbers & Integer Properties: Classification of real numbers and decode the crucial properties of zero to easily tackle tricky integer questions.
• 1.2 – Recurring Decimals & Fraction Conversions: Quick conversion of recurring decimals into fractions and learn essential mental math shortcuts to avoid common calculation traps.
• 1.3 – Prime and Special Number Categories: Square root primality test, co-prime factorization, and algebraic shortcuts to bypass common mathematical traps number system questions.
• 1.4 – Base 10 & Digit Mechanics: The algebraic mechanics of two-digit and three-digit numbers, quickly solve reversal questions, and bypass common digit-manipulation traps.

Topic T02: HCF & LCM Applications

• 2.1 – Algebraic Relations of HCF LCM: Algebraic relationships of HCF and LCM to quickly calculate co-prime pairs and avoid the three-number fallacy.
• 2.2 – HCF LCM for Non-Integers: Exact formulas and decimal equalization shortcuts to flawlessly solve non-integer HCF and LCM questions and bypass common exam traps.
• 2.3 – HCF and LCM Word Problems: Instantly decode word problems, bypass the deceptive ‘minimum’ keyword trap, and apply spatial grid arrangements accurate answers.
• 2.4 – Cyclic Events & Circular Tracks: LCM applications circular tracks and traffic light synchronizations to quickly bypass common dimensional speed traps.
• 2.5 – LCM Remainder Models: Art of solving complex constant difference and surplus remainder word problems quickly.
• 2.6 – HCF Unknown Remainder Model: Absolute difference shortcut to instantly solve HCF unknown remainder questions and bypass time-consuming calculation traps.

Topic T03: VBODMAS & Simplification

• 3.1 – VBODMAS Rule and Operations Order: Exact hierarchy of mathematical operations to bypass continuous division traps and quickly solve complex simplification questions with complete accuracy.
• 3.2 – Fraction Comparison Techniques: Instantly compare fractions using cross-multiplication and gap methods to save time and avoid calculation traps.
• 3.3 – Digital Sum Calculation Method: Digital Sum method to instantly verify complex calculations, bypass tedious multiplication, and avoid approximation traps.

Topic T04: Factors, Multiples & Prime Factorization

• 4.1 – Prime Factorization and Its Shortcuts: Split-and-merge shortcut to instantly break down large numbers and avoid the common composite base trap questions.
• 4.2 – Calculating Number of Factors: Exact formulas to calculate prime and total factors while bypassing common composite base traps.
• 4.3 – Odd, Even & Square Factors: Quick categorization of odd, even, and perfect square factors to effortlessly bypass calculation traps number system questions.
• 4.4 – Calculating Sum of Factors: Formulas and mental math shortcuts to accurately calculate the sum of total, proper, and conditional factors.

Topic T05: Divisibility Rules & Algebraic Divisibility

• 5.1 – Divisibility By 2 And 5: Tail-end divisibility shortcuts powers of 2 and 5 to instantly solve complex number series and missing digit questions.
• 5.2 – Divisibility Rules: 3 and 9: Algebraic symmetry and the time-saving casting out nines technique to instantly solve complex divisibility questions.
• 5.3 – Divisibility Rule of 11: Alternating digit sum and two-digit block methods to bypass calculation traps missing digit questions.
• 5.4 – Triplet Divisibility: 7, 11, 13: Bypass tedious long divisions by mastering the alternating block sums technique to instantly check divisibility by 7, 11, and 13.
• 5.5 – Algebraic Divisibility Rules X^n±Y^n: Odd-even parity rules of algebraic expressions to effortlessly find remainders and bypass common exponent traps.

Topic T06: Unit & Tens Digit Cyclicity

• 6.1 – Unit Digit: Cycle of 1: Unit digit cyclicity of 0, 1, 5, and 6 to instantly solve complex exponential calculations and avoid negative remainder traps.
• 6.2 – Cyclicity of 4 and 9: Even-odd parity shortcuts calculating the unit digits of bases ending 4 and 9 to bypass time-consuming calculations exponent problems.
• 6.3 – Unit Digit Cyclicity Rules: Modulo four shortcuts to instantly find unit digits of massive exponents and avoid common negative subtraction traps.

Topic T07: Remainder Theorems

• 7.1 – Concept of Negative Remainders: Negative remainder shortcut to instantly solve high-exponent division questions and avoid calculation traps.
• 7.2 – Polynomial Remainders and Expansions: Binomial expansion techniques to instantly solve high-power remainder questions and easily bypass common calculation traps.
• 7.3 – Fermat’s Little Theorem: Exponent reduction method to effortlessly solve large power remainder questions on Fermat’s Little Theorem.
• 7.4 – Successive Division Mechanics: Bottom-up algorithm to quickly solve complex successive division problems and avoid common calculation traps.

Topic T08: Factorials & Power of Primes

• 8.1 – Factorials and Prime Powers: Legendre’s formula to quickly calculate the highest power of primes factorials and avoid common composite number traps.
• 8.2 – Trailing Zeros In Factorials: Successive division shortcut to instantly find trailing zeros complex factorial problems and avoid common calculation traps math.