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

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 = 6a ²

      CSA = 4a ²

      Volume = a ³

     Diagonal = a3

CUBOID

        TSA = 2(lb+bh+hl)

         CSA = 2h (l+b)

         Volume = l × b ×h

         Diagonal = l ²+b ² +h ²

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