GENERAL Track
176 Techniques4 Stages
Complete Mental Maths & Fast Calculation Mastery
Full sequential or self-paced track encompassing all 176 techniques across 14 modules for lifelong mental math proficiency.
Sponsored Learning Partner
Supporting free calculation training for competitive exam aspirants.
Structured Curriculum Stages
4 Stages1
28 techniquesFoundations: Number Sense & Divisibility
TECH-001• Diff 1.5
Place-Value Digit Decomposition
TECH-002• Diff 1.5
Digit Complement to Powers of 10
TECH-003• Diff 1.5
Parity Invariance (Odd/Even Rules)
TECH-004• Diff 2.5
Prime Factor Decomposition Ladder
TECH-005• Diff 2.5
Co-Prime Testing via Euclidean Gap
TECH-006• Diff 2.5
Consecutive Integer Product Properties
TECH-007• Diff 1.5
Perfect Square Benchmark Mapping
TECH-008• Diff 2.5
Perfect Cube Benchmark Mapping
TECH-009• Diff 1.5
Fast HCF via Continuous Difference
TECH-010• Diff 1.5
Fast LCM via Prime Base Scaling
TECH-011• Diff 2.5
Factor Count Formula (Tau Function)
TECH-012• Diff 2.5
Sum of Factors Formula (Sigma Function)
TECH-013• Diff 1.5
Power of 2 Index Scale Recognition
TECH-014• Diff 2.5
Cyclic Last-Digit Periods of Exponents
TECH-015• Diff 1.5
Terminal Digit Divisibility ($2, 5, 10$)
TECH-016• Diff 1.5
Last-k-Digits Divisibility ($4, 8, 16$)
TECH-017• Diff 1.5
Digital Sum Divisibility ($3, 9$)
TECH-018• Diff 1.5
Composite Divisibility Factor Splitting
TECH-019• Diff 1.5
Alternating Digit Sum Test ($11$)
TECH-020• Diff 2.5
Osculator Method for 7 (Subtract $2\times$ Unit)
TECH-021• Diff 2.5
Vedic Osculator Method for 13 (Add $4\times$ Unit)
TECH-022• Diff 2.5
Vedic Osculator Method for 17 & 19
TECH-023• Diff 1.5
Casting Out Nines (Beejank / Digital Root)
TECH-024• Diff 2.5
Remainder Theorem via Polynomial Shift
TECH-025• Diff 2.5
Wilson’s Remainder Theorem for Primes
TECH-026• Diff 2.5
Euler-Totient Power Reduction
TECH-027• Diff 1.5
Modular Negative Residue Arithmetic
TECH-028• Diff 2.5
Last Two Digits via Modulo 100 Expansion
2
54 techniquesRapid Arithmetic: Operations, Powers & Roots
TECH-029• Diff 1.5
Left-to-Right Mental Addition
TECH-030• Diff 1.5
Compensation via Nearest Benchmark
TECH-031• Diff 1.5
Complementary Pairing (Making Tens)
TECH-032• Diff 1.5
Nikhilam Subtraction from Powers of 10
TECH-033• Diff 1.5
Subtraction via Equal Addition Compensation
TECH-034• Diff 1.5
Left-to-Right Subtraction
TECH-035• Diff 2.5
Vinculum Digit Notation (Bar Numbers)
TECH-036• Diff 2.5
Column Aggregation via Deviations
TECH-037• Diff 1.5
Nikhilam Multiplication Below Base
TECH-038• Diff 1.5
Nikhilam Multiplication Above Base
TECH-039• Diff 2.5
Nikhilam Multiplication Mixed Base
TECH-040• Diff 1.5
Anurupyena Sub-Base Multiplication
TECH-041• Diff 1.5
Urdhva-Tiryagbhyam $2 \times 2$
TECH-042• Diff 2.5
Urdhva-Tiryagbhyam $3 \times 3$
TECH-043• Diff 1.5
Antyayor Dashake'pi (Tens Same, Units Sum 10)
TECH-044• Diff 2.5
Units Same, Tens Sum to 10
TECH-045• Diff 1.5
Ekanyunena Purvena ($\times 9, \times 99, \times 999$)
TECH-046• Diff 1.5
Multiplication by 11 (Digit Sliding Addition)
TECH-047• Diff 2.5
Multiplication by 12 (Double & Add Neighbor)
TECH-048• Diff 1.5
Multiplication by 15 (Add Half and Multiply by 10)
TECH-049• Diff 1.5
Multiplication by 25 (Divide by 4, Multiply by 100)
TECH-050• Diff 1.5
Multiplication by 50 (Divide by 2, Multiply by 100)
TECH-051• Diff 1.5
Multiplication by 125 (Divide by 8, Multiply by 1000)
TECH-052• Diff 2.5
Multiplication by 75 ($\times 3 / 4 \times 100$)
TECH-053• Diff 2.5
Multiplication by 101 ($N \times 100 + N$)
TECH-054• Diff 1.5
Difference of Squares Product ($m^2 - d^2$)
TECH-055• Diff 1.5
Doubling & Halving Factor Shift
TECH-056• Diff 1.5
Distributive Breakup on Ten Boundaries
TECH-057• Diff 1.5
Sequential Multiplier Chaining
TECH-058• Diff 1.5
Cross-Multiplication for Decimals
TECH-059• Diff 1.5
Division by 5 (Double & Shift Decimal)
TECH-060• Diff 1.5
Division by 25 (Multiply by 4 & Shift by 100)
TECH-061• Diff 1.5
Division by 50 (Double & Divide by 100)
TECH-062• Diff 1.5
Division by 125 (Multiply by 8 & Shift by 1000)
TECH-063• Diff 2.5
Nikhilam Division (Divisors Near & Below 10/100)
TECH-064• Diff 2.5
Paravartya Yojayet Division (Divisors Above Base)
TECH-065• Diff 2.5
Dhwajanka (Flag Method / Straight Division)
TECH-066• Diff 1.5
Factor-Based Progressive Division
TECH-067• Diff 1.5
Remainder-Adjusted Divisibility Pruning
TECH-068• Diff 1.5
Division via Benchmark Percentage Approximation
TECH-069• Diff 1.5
Squaring Numbers Ending in 5 (Ekadhikena)
TECH-070• Diff 1.5
Squaring Numbers Near 50
TECH-071• Diff 1.5
Squaring Numbers Near 100 (Yavadunam)
TECH-072• Diff 2.5
Squaring Numbers Near 1000
TECH-073• Diff 1.5
Duplex Method (Dwandwa Yoga) for 2-Digit Squares
TECH-074• Diff 2.5
Duplex Method for 3-Digit Squares
TECH-075• Diff 1.5
Algebraic Identity Squaring ($(a+b)^2$)
TECH-076• Diff 1.5
Difference of Squares Decomposition
TECH-077• Diff 1.5
Perfect Square Root by Inspection (Vilokanam)
TECH-078• Diff 1.5
First-Order Square Root Approximation
TECH-079• Diff 2.5
Newton-Raphson Iterative Square Root
TECH-080• Diff 1.5
Perfect Cube Root by Inspection (Vilokanam)
TECH-081• Diff 2.5
Cube Expansion via Base Deficit
TECH-082• Diff 2.5
First-Order Cube Root Approximation
3
36 techniquesCommercial & Approximation Maths
TECH-083• Diff 1.5
Standard Fraction Benchmark Mapping ($1/2$ to $1/20$)
TECH-084• Diff 1.5
Cross-Multiplication Fraction Comparison
TECH-085• Diff 2.5
Common Difference Fraction Sorting
TECH-086• Diff 1.5
Percentage Splitting ($10\%, 5\%, 1\%, 2.5\%$)
TECH-087• Diff 1.5
Reciprocal Percentage Property ($x\%$ of $y = y\%$ of $x$)
TECH-088• Diff 1.5
Successive Percentage Formula
TECH-089• Diff 1.5
Successive Discounts Equivalent
TECH-090• Diff 1.5
Reverse Percentage (Finding Base Value)
TECH-091• Diff 2.5
Recurring Decimal to Rational Fraction
TECH-092• Diff 1.5
Decimal-to-Percentage Scaling
TECH-093• Diff 1.5
Multiplying by Common Percentage Multipliers
TECH-094• Diff 2.5
Percentage Margin vs Markup Conversion
TECH-095• Diff 1.5
Quick Ratio-to-Percentage Scaling
TECH-096• Diff 1.5
Percentage Error Calculation
TECH-097• Diff 1.5
Compound Ratio Chaining ($A:B$ & $B:C \implies A:B:C$)
TECH-098• Diff 1.5
Cross-Multiplication for Unknown Proportion
TECH-099• Diff 1.5
Assumed Mean Deviation Method
TECH-100• Diff 1.5
Weighted Average Alligation Formula
TECH-101• Diff 1.5
Alligation Cross Rule for Mixtures
TECH-102• Diff 2.5
Replacement Formula for Repeated Dilution
TECH-103• Diff 1.5
Inverse Proportion Speed-Time Duality
TECH-104• Diff 1.5
LCM Unit-Work Method
TECH-105• Diff 1.5
Relative Speed Aggregation
TECH-106• Diff 1.5
Ratio Difference Preservation
TECH-107• Diff 1.5
Compatible Number Rounding
TECH-108• Diff 1.5
Leading-Digit Order-of-Magnitude Estimation
TECH-109• Diff 1.5
Upper & Lower Bounding (Sandwiching)
TECH-110• Diff 2.5
Percentage Differential Adjustment
TECH-111• Diff 1.5
Reciprocal Approximation Formula
TECH-112• Diff 1.5
Binomial Linear Approximation
TECH-113• Diff 1.5
High-Yield DI Ratio Approximation
TECH-114• Diff 2.5
Significant Figure Bounding
TECH-115• Diff 1.5
Option-Spread Sensitivity Analysis
TECH-116• Diff 2.5
Geometric Mean Approximation
TECH-117• Diff 2.5
Summation of Series Integral Bounding
TECH-118• Diff 1.5
Exponential Growth Doubling Time (Rule of 72)
4
58 techniquesAdvanced: Algebra, Geometry & Competitive Science
TECH-119• Diff 1.5
Symmetric Sum & Product Substitution
TECH-120• Diff 1.5
Identity Factorization of $a^3 + b^3 + c^3 - 3abc$
TECH-121• Diff 1.5
Completing the Square for Extrema
TECH-122• Diff 1.5
Vieta’s Root-Coefficient Relations
TECH-123• Diff 1.5
Rationalizing Surds via Conjugates
TECH-124• Diff 2.5
Telescoping Series Cancellation
TECH-125• Diff 1.5
Componento & Dividendo Rule
TECH-126• Diff 2.5
Reciprocal Transformation Substitution
TECH-127• Diff 2.5
AM-GM Inequality Bounding
TECH-128• Diff 2.5
Synthetic Division for Polynomial Roots
TECH-129• Diff 1.5
Logarithmic Power & Base-Change Laws
TECH-130• Diff 1.5
Quadratic Discriminant Sign Analysis
TECH-131• Diff 2.5
Paravartya Algebraic Factorization
TECH-132• Diff 2.5
Cyclic Determinant Factorization
TECH-133• Diff 1.5
Standard Pythagorean Triples Scaling
TECH-134• Diff 1.5
Special Triangle Ratios ($30^\circ-60^\circ-90^\circ$ & $45^\circ-45^\circ-90^\circ$)
TECH-135• Diff 1.5
Complementary Trigonometric Pairs
TECH-136• Diff 1.5
Small-Angle Approximations ($\sin \theta \approx \theta$)
TECH-137• Diff 1.5
Area of Triangle via Coordinate Shoelace
TECH-138• Diff 1.5
Distance from Point to Line Formula
TECH-139• Diff 1.5
Area Scale Ratio from Linear Similarity
TECH-140• Diff 2.5
Half-Angle Trigonometric Half-Steps
TECH-141• Diff 2.5
Product-to-Sum Trigonometric Simplification
TECH-142• Diff 2.5
Hero's Formula with Semiperimeter Shortcuts
TECH-143• Diff 1.5
Unit-Digit Last-Digit Elimination
TECH-144• Diff 1.5
Last-Two-Digits Distractor Pruning
TECH-145• Diff 1.5
Parity (Odd/Even) Filter
TECH-146• Diff 1.5
Divisibility Filter on Options
TECH-147• Diff 1.5
Extreme Value Boundary Substitution
TECH-148• Diff 1.5
Dimensional Analysis Inconsistency Filter
TECH-149• Diff 1.5
Order of Magnitude Range Filter
TECH-150• Diff 1.5
Sign Analysis & Quadrant Bounding
TECH-151• Diff 1.5
Direct Option Back-Substitution
TECH-152• Diff 2.5
Symmetry Elimination in Variables
TECH-153• Diff 1.5
"Solve vs Skip" 30-Second Rule
TECH-154• Diff 2.5
Guess-Penalty Neutralization Strategy
TECH-155• Diff 1.5
Scientific Notation Mantissa-Exponent Separation
TECH-156• Diff 1.5
Physical Constant Shortcut Constants
TECH-157• Diff 1.5
Acceleration Due to Gravity Approximations ($g \approx \pi^2 \approx 10$)
TECH-158• Diff 2.5
Logarithmic Decibel & Attenuation Scale
TECH-159• Diff 1.5
Kinetic Energy vs Momentum Relation ($p^2 / 2m$)
TECH-160• Diff 1.5
Parallel Resistance Product-Over-Sum Rule
TECH-161• Diff 2.5
Capacitive & Inductive Impedance Reciprocals
TECH-162• Diff 1.5
Vector Magnitude via Pythagorean Factorization
TECH-163• Diff 1.5
Radioactive Half-Life Power Scaling ($N = N_0 / 2^n$)
TECH-164• Diff 1.5
Wavelength-Energy Duality Shortcut
TECH-165• Diff 2.5
Thermal Expansion Linearization
TECH-166• Diff 2.5
Doppler Frequency Shift Ratio Approximation
TECH-167• Diff 1.5
Projectile Range & Max Height Ratios
TECH-168• Diff 1.5
Lens Maker Shortcut via Relative Refractive Index
TECH-169• Diff 1.5
Mole Calculation Molar Mass Factor Cancellation
TECH-170• Diff 1.5
STP Gas Volume Scaling ($22.4\text{ L/mol} \text{ or } 22.7\text{ L/mol}$)
TECH-171• Diff 1.5
Quick pH from Hydrogen Ion Scientific Notation
TECH-172• Diff 1.5
Dilution Equation ($M_1 V_1 = M_2 V_2$)
TECH-173• Diff 1.5
Equivalent Weight & Normality Duality ($N = M \times n\text{-factor}$)
TECH-174• Diff 2.5
Arrhenius / Rate Constant Doubling Approximation
TECH-175• Diff 1.5
Faraday’s Electrolysis Charge Shortcut
TECH-176• Diff 1.5
Equilibrium Constant Power Scaling
Sponsored Learning Partner
Supporting free calculation training for competitive exam aspirants.