Ocegik / Modern Maths
Modern Maths Formulas for CAT Preparation
Revise modern maths formulas from Ocegik’s formula library, with named identities, expressions and usage notes grouped by topic.
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Modern Maths: formulas by topic
LogarithmsModern Maths
Product ruleloga(XY) = logaX + logaYa = base, X and Y = the values being logged
Quotient ruleloga(X/Y) = logaX − logaY
Power ruleloga(Xk) = k·logaX
Root in baselogakX = 1klogaX
Root of argumentloga(ᵏ√X) = 1klogaX
Fractional-power baseloga1/kX = k·logaX
Identity of 1loga1 = 0
Same base identitylogxX = 1
Reciprocal base swaplogaX = 1logXa
Change of baselogaX = logbXlogba
Exponent inversea(logaX) = X
Default base conventionunmentioned base is taken as 10
Permutations & CombinationsModern Maths
PermutationsnPr = n!(n − r)!
CombinationsnCr = n!(n − r)! r!
Combination–permutation linknCr = nPrr!
Symmetry of combinationsnCr = nCn−r
Sum of all combinationsnC0 + nC1 + … + nCn = 2n
Distributing n identical items among r personsn+r−1Cr−1
Permutations with repeated itemsn!p! q! r!p, q, r items of each repeated kind
Selections from grouped items{(p+1)(q+1)(r+1)…} − 1selecting some or all from p items of one type, q of another, r of another…
Circular arrangements(n − 1)!
Dividing (m+n) things into groups of m, n(m + n)!m! n!
Dividing 2m things into two equal groups(2m)!2!(m!)2
ProbabilityModern Maths
Probability of an eventP(E) = favourable outcomesall possible outcomesP(E) = probability that event E occurs
Complement ruleP(not E) = 1 − P(E)
Odds in favour= favourable cases / unfavourable cases
Odds against= unfavourable cases / favourable cases
Addition Law (general)P(A or B) = P(A) + P(B) − P(A ∩ B)
Addition Law (mutually exclusive)P(A ∩ B) = 0
Independent eventsP(A ∩ B) = P(A) × P(B)
Multiplication LawP(E and F) = P(E) × P(F)E, F independent
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