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Arithmetic
Percentages & Fractions
Fraction-to-percentage tables (1/2 to 1/20), AB constant product rule, and successive percentage change shortcuts.
Master Quantitative Aptitude for CAT, MBA CET & IPMAT with high-density formula cards, Vedic speed math shortcuts, and Level 0 solved foundation examples.
Fraction-to-percentage tables (1/2 to 1/20), AB constant product rule, and successive percentage change shortcuts.
Scaling ratios, Componendo & Dividendo properties, direct & inverse variation, and income-expenditure shortcuts.
Equal distribution model, Net Deviation method, weighted average shortcuts, and group addition/removal rules.
Cost Price, Marked Price, Multiplier Method, and Dishonest Dealer faulty weight formulas.
Alligation Cross Rule (D-M)/(M-C), weighted average shortcut, and repeated liquid replacement V(1-x/V)^n formula.
Distance = Speed x Time, unit conversions, relative speed, and trains crossing rules.
Total Distance / Total Time rule, 2ab/(a+b) harmonic mean for equal distances, and multi-stage journeys.
Crossing poles & platforms, train length addition rules, 5/18 unit conversions, and relative speed crossing times.
Downstream (B+S) and Upstream (B-S) rules, still water boat speed (D+U)/2, and stream speed (D-U)/2 formulas.
Opposite direction S1+S2, Same direction |S1-S2|, Police-thief chase shortcuts, and head-start gap rules.
Total Work LCM Method, Efficiency rates, Man-Days formula, and Alternate days work shifts.
Inlet and outlet pipe rules, Net Filling Rate, Tank Capacity LCM method, and Leakage shortcuts.
Master the Chain Rule formula, group efficiency equivalence, and proportional wage splitting.
Constant interest calculations, Principal/Rate/Time formula rearrangements, and doubling time shortcuts.
Power of compounding, 2-year and 3-year CI-SI difference shortcuts, multipliers, and compounding frequency rules.
Master 2-year P(R/100)² and 3-year P(R/100)²(3+R/100) CI-SI difference shortcuts, compounding frequencies, and growth multipliers.
Standard form ax+b=c (a≠0), balanced scale operations, isolating variables, and word problem translation shortcuts.
Standard form ax²+bx+c=0, discriminant D=b²-4ac rules, quadratic formula x=(-b±√D)/2a, and root shortcuts.
Fundamental log rules, Base Change Theorem, exponential conversions, digit calculations, and CAT shortcuts.
Master the Remainder Theorem, Factor Theorem, Vieta's formulas, cubic root relations, and synthetic shortcuts.
Master the Laws of Indices, surd rationalization, square root of dual surds, and infinite radical shortcuts.
Master Wavy Curve Method, AM-GM-HM inequality chain, Modulus transformations, distance interpretation, and Cauchy-Schwarz.
Master Domain & Range rules, Composite Functions $f(g(x))$, Bijective Inverses $f^{-1}(x)$, Even/Odd symmetry, and Graph Transformations.
Master Quadratic Vertex Optimization, AM-GM Product/Sum bounds, Cauchy-Schwarz, and Modulus Median Minimization.
Cubic expansions, 3-variable golden formula a³+b³+c³-3abc, conditional identities, and value-substitution shortcuts.
Linear Diophantine equations ax+by=c, non-negative integral solutions, Bézout's identity, and Frobenius coin problem shortcuts.
Arrangement rules, factorials, $^nP_r$ formula, circular seating, tie method for restricted seating, and CAT shortcuts.
Selection rules, $^nC_r$ formula, symmetry identity $^nC_r = ^nC_{n-r}$, committee formation, and CAT shortcuts.
Favorable vs total outcomes, Complement Rule $1 - P(\text{None})$, coins, dice & deck of cards rules, and CAT shortcuts.
2-set & 3-set overlap formulas, $n(A \cup B)$ rules, "Only A" logic, "Neither" calculations, and survey shortcuts.
Constant difference $d$, $a_n = a + (n-1)d$ formula, sum of $n$ terms $S_n = (n/2)(a+l)$, and term count shortcuts.
Common ratio $r$, $a_n = a \cdot r^{n-1}$, finite sum $S_n$, infinite sum $S_\infty = a/(1-r)$, and multiplier tricks.
Reciprocal AP conversion rules, $H_n = 1/[a + (n-1)d]$, and Harmonic Mean $2ab/(a+b)$ for average speed.
$(a+b)^n$ expansion rules, general term $T_{r+1} = \binom{n}{r}a^{n-r}b^r$, middle term positions, and Pascal's Triangle.
Sum of natural powers Σn, Σn², Σn³, Arithmetico-Geometric Progression (AGP), telescoping series, and method of differences.
Vedic multiplication, cube roots in 5 seconds, squares up to 50, and Pythagorean Triplets.
Mental squaring algorithms (Base 50/100), 5-second cube root extraction, approximate square roots, and power recall tables.
Vedic Digital Root (Casting out 9s), last digit matrix filtering, and boundary range estimation for non-calculator speed.
Triangles, Circles, Inradius & Circumradius formulas, and 2D/3D Mensuration shortcuts.
Triangle inequalities, similarity & congruence, Incenter, Circumcenter, Centroid, Orthocenter, and Euler line properties.
Circle theorems, chord properties, arc & sector area, direct & transverse common tangents, and alternate segment theorem.
Parallelograms, rhombuses, trapeziums, regular polygons, interior/exterior angle formulas, Varignon's theorem, and area rules.
Distance & section formulas, slope m=tanθ, line equations, perpendicular distances, and Shoelace polygon area formula.
Prime factorization, total factors formula $(a+1)(b+1)(c+1)$, sum & product of factors, even/odd factors, and co-primes.
Product law $ ext{HCF} imes ext{LCM} = A imes B$, fraction rules, bell-ringing & track meeting times, and 4 remainder models.
Euler's Totient $\phi(n)$, Fermat's Little Theorem, Wilson's Theorem, Binomial expansion $(a \pm 1)^n$, and Cyclicity method.
Cyclicity rules (0-9), binomial expansion for last 2 digits, 24/76 power rules, and Euler totient shortcuts.
Positional base notation, conversions between decimal and base $n$, base arithmetic (+, -, ×), and base $n$ divisibility.
Legendre's formula for $E_p(N!)$, factors of 10, highest powers of composite divisors, and reverse factorial questions.
Rules from 2 to 13, composite divisibility shortcuts (72, 88, 99), prime osculators, and unknown digit ($x, y$) solving.
Number classification, Natural, Whole, Integers, Rational ($\mathbb{Q}$) & Irrational numbers, and Number Line properties.