Math Formulas Chart For A level and Competitive Exams PPSC

LCM and HCF- Formula Sheet

Definition:

LCM (least Common Multiple): Smallest numbers divisible by given numbers

HCF (Highest common Factor): Greatest number that divides the given numbers

Methods to Find HCF and LCM

Prime Factorization Method

Division Method

Important Formula

LCM × HCF = product of two numbers

Fraction Formulas

HCF of Fractions =

LCM of Fractions =

Relation for Two Numbers

If a=LCM, b=HCF

Numbers = a × x , a × y (where x, y are co-prime)

TYPES OF NUMBERS

              Natural Numbers: 1, 2, 3, …

             Whole Numbers: 0, 1, 2, 3, …

             Integers: …… 3, 2, 1, 0, 1, 2, 3, 4……..

             Rational Numbers: (q≠0)

PROPERTIES OF NUMBERS

Commutative Law: a+b=b+a, axb =bxa

Associative Law: (a+b)+c=a+(b+c)

Distributive Law: a(b+c) = ab + ac

IDENTITIES

Additive Identity: a + 0 = a

Multiplicative Identity: a x 1 = a

EVEN & ODD NUMBERS

Even = 2n

Odd = 2n +1

PRIME & COMPOSITE NUMBERS

Prime: exactly two factors (2,3,5,7 … )

Composite: more than two factors

DIVISIBILITY RULES

By 2 last digit even

By 3 sum of digits divisible by 3

By 5 last digit 0 or 5

By 9 sum of digits divisible by 9

MENSURATION & FORMULA SHEET

CUBE

TSA = 6a²

CSA = 4a²

Volume = a³

Diagonal = a3

CUBOID

TSA = 2(lb+bh+hl)

CSA = 2h (l+b)

Volume = l × b ×h

Diagonal = l²+b² +h²

CYLINDER

TSA = 2πr(h+r)

CSA = 2πrh

Volume = πr²h

CONE

CSA = πrl

TSA = πr (1+r)

Volume = π r²h

l = r² +h²

SPHERE

TSA = 4πr²

Volume = πr³

SEMISPHERE

TSA = 3πr²

CSA = 2πr²

Volume= πr³

IMPORTANT TRIANGLE FORMULAS

Area = ×b×h

Heron’s Formula = s(s-a)(s-b)(s-c)

CIRCLE FORMULAS

Area = πr²

Circumference = 2πr

Area of semicircle = πr²