SSLC Maths Formulae

7/25/2019 SSLC Maths Formulae

1/22

Page | 1

CENTURY FOUNDATION MATRIC

HIGHER SECONDARY SCHOOL

TIRUPUR.

STDX

MATHEMATICS

UNIT WISE

FORMULAE AND DEFINITIONS

By

D.Ponnaiyan. M.Sc. B.Ed.

P.G.T in Mathematics

Phone no: 9944200642

www.kalvisolai.com 12/9/2015


2/22

Page | 2



3/22

Page | 3

1. SETS AND FUNCTIONS

Commutative Property:

A B = B A (Set union)

A B = B A (Set intersection)

Associative Property:

A (B C) = (A B) C (Set union)

A (B C) = (A B) C (Set intersection)

Distributive Property:

A (B C) = (A B) (A C) (Intersection distributes over union)

A (B C) = (A B) (A C) (Union distributes over intersection)

De Morgans laws for set difference:

A \ (B C) = (A \ B) (A \ C)

A \ (B C) = (A \ B) (A \ C)

De Morgans laws for complementation:

(A B) = A B

(A B) = A B

Cardinality of sets:

n (A B) = n (A) + n (B)n (A B)

n (A B C) = n (A) + n (B) + n (C)n (A B)n (B C)n (A C) + n (A B C)

Function:

Domain:The set A is called the domainof the function.

Co-Domain:The set B is called the co-domainof the function.

One-One function: (Injective function)

The function is called anone-one function if it takes different elements ofA into different elements of B. In other words f is one-one if no element in B is

associated with more than one element in A.

Onto function: (Surjective function)

The function is called an onto function if every element in B has a

pre-image in A. This is same as saying that B is the range of f.



4/22

Page | 4

One-One and onto function: (Bijective function) (One-One correspondence)

The function is called a one-one and ontofunction if f maps distinctelements of A into distinct images in B and every element in B is an image of some

element in A.

Constant function:

The function is said to be a constantfunction if every element of A has thesame image in B. The range of a constant function is a singleton set.

Identity function:

An identityfunction maps each element of A into itself.

Note:

A setis a collection of well defined objects. The objects in a set are called elements or members

of that set.

Every functioncan be represented by a graph.

If every vertical lineintersects a graph in at most one point, then the graph represents a function.

*****

2. SEQUENCES AND SERIES OF REAL NUMBERS

Arithmetic Progression: (A.P.)

A.P. is, a, a + d, a + 2d, a + 3d, . . .

General term, tn= a + (n-1) d

Number of terms, n=

d

al+ 1

Three consecutive terms, ad, a, a + d.

Four consecutive terms, a3d, a - d, a + d, a + 3d.

Arithmetic Series:

When is given, Sn=2

n la

When is not given, Sn=2n dna 12



5/22

Page | 5

Geometric Progression: (G.P.)

G.P. is a, ar, ar2, ar

3, . . .

General term, tn= a rn - 1

Three consecutive terms,

, a , ar.

Four consecutive terms,3r

a,

, ar, ar3.

Amount (or Appreciation), A = P

nr

100

1

Depreciation, A = P

nr

100

1

Geometric Series:

If r = 1, Sn= na.

If r1, Sn=

1

1

r

ra n

(or) Sn=

r

ra n

1

1

If n = , Sn =r

a

1

Special Series:

The sum of the first n natural numbers,

n

k

k

1

= ( + 1)

2

The sum of the first n odd natural numbers,

n

k

k1

12 = n2

The sum of the first n odd natural numbers (when is given), 1 + 3 + 5 + . . . + l =

2

2

1

l

The sum of squaresof first n natural numbers,

2

1

n

k

k = + 1(2 + 1)

6

The sum of cubesof the first n natural numbers, 23

1 2

1

nnk

n

k

Note:

A sequenceof real numbers is an arrangement or a list of real numbers in a specific order.

In a sequence, if the terms are same then the sequence is called constant sequence.

For example, 1, 1, 1, 1, 1, 1.



6/22

Page | 6

A functionis not necessarily a sequence.

The sequence given by F1= F2= 1and Fn= Fn-1+ Fn-2, n = 3, 4, is called the Fibonacci sequence.Its terms are listed as 1, 1, 2, 3, 5, 8, 13, 21, 34, . . .

An expression of addition of terms of a sequence is called a series.

The sum of infinite number of positive numbers may give a finitevalue.

The Frenchmathematician Carl Fredrick Gauss (C.F.Gauss) is known as

Prince of Mathematics.

*****3. ALGEBRA

The Basic Relationship Between

Zeros and Coefficients of a

Quadratic Polynomial

Relationship Between Roots and

Coefficients of a Quadratic Equation

Sum of zeros, + =

Sum of roots, + =

Product of zeros, =

Product of roots, =

A quadratic polynomial is,

p () = 2( + ) + .A quadratic equation is,

2( + ) + = 0.

Relation Between LCM and GCD:

f (x) g (x) = LCM [f (x), g (x)] GCD [f (x), g (x)]

Rational Expressions:

a2b

2 = (a + b) (a - b)

a3+ b3 = (a + b) (a2ab + b2)

a3- b

3 = (a - b) (a

2+ ab + b

2)

a4+ a

2b

2+ b

4 = (a

2+ ab + b

2) (a

2ab + b

2)

(a3+ b3) (a3- b3) = a6b6

Quadratic Formula:

=a

acbb

2

42

Time =



7/22

Page | 7

Nature of Roots:

= b24ac

If > 0(Positive answer), then the roots are Real and unequal.

If = 0, then the roots are Real and equal.

If < 0(Negative Answer), then No real roots.(Imaginary roots)

Relationship Between Roots and Coefficients of a Quadratic Equation:

= 42

2+ 2 = ( + )2- 2

2- 2 = ( + ) 42

3+ 3 = ( + )3- 3 ( + )

3-

3 = ( - )

3+ 3 ( - )

4+

4= [( + )

2- 2]

22()

2

4- 4 = ( + ) ( - ) (2+ 2)

Note: A system of linear equations a1x +b1y = c1, a2x + b2y = c2in two variables is said to be,

Consistent if at least one pair of values of x and y satisfies both equations.

Inconsistentif there are no values of x and y that satisfy both equations.

The system of equations a1x +b1y - c1= 0, a2x + b2y - c2= 0,

If a1b2b1a20or2

1

a

a

2

1

b

b, then the system of equations has a unique solution.

If2

1

a

a=

2

1

b

b=

2

1

c

c, then the system of equations has infinitely many solutions.

If2

1

a

a=

2

1

b

b

2

1

c

c, then the system of equations has no solution.

A set of finite number of linear equations in two variables x and y is called a system of linear

equations in x and y. Such a system is also called simultaneous equations.

Eliminating one of the variables first and then solving a system is called method of elimination.



8/22

Page | 8

The following arrow diagram helps us very much to apply the method of cross multiplication in

solving a1x +b1y + c1= 0, a2x + b2y + c2= 0.

y 1

b1 c1 a1 b1

b2 c2 a2 b2

The method of synthetic divisionis introduced by Paolo Ruffinin 1809.

For any polynomial p(), = a is zero if and only if p(a) = 0.

(- a) is a factor for p() if and only if p(a) = 0.

(- 1) is a factor of p() if and only if the sum of coefficients of p() is 0.

(+ 1) is a factor of p() if and only if sum of the coefficients of even powers of , includingconstant is equal to sum of the coefficients of odd powers of .

There are infinitely many quadratic equations with the same roots.

A quadratic equation can be solved by,

The method of factorization

The method of completing square

Using a quadratic formula.

*****4. MATRICES

Order or Dimension of a Matrices: If a matrix A has m rows and n columns, then wesay that the order of A is m n.

Types of Matrices:Row Matrix:A matrix is said to be a row matrixif it has only one row. A row matrix is alsocalled as row vector. For example, A = 305

Column Matrix:A matrix is said to be a column matrixif it has only one column. It is also

called as column vector. For example, B =

3

0

5



9/22

Page | 9

Square Matrix:A matrix in which the number of rows and the number of columns are equal is

said to be a square matrix. For example, C =

043

332

221

Diagonal Matrix:A square matrix in which all the elements above and below the leading

diagonal are equal to zero, is called a diagonal matrix. For example, D =

100

000

003

Scalar Matrix:A diagonal matrix in which all the elements along the leading diagonal are

equal to a non-zero constant is called a scalar matrix. For example, E =

700

070

007

Unit Matrix:A diagonal matrix in which all the leading diagonal entries are 1 is called a

unit matrix. A unit matrix of order n is denoted byIn. For example,I2=

10

01

Null Matrix or Zero-matrix:A matrix is said to be a null matrix or zero-matrixif each

of its elements is zero. It is denoted by O. For example, O=

00

00

Transpose of a Matrix:The transpose of a matrixA is obtained by interchanging rows and

columns of the matrix A and it is denoted by AT. For example, if A =

4751 , then AT=

4571

Note:

Equality of Matrices:Two matrices A = [aij]m nand B = [bij]m nare said to be equal if ,

They are of the same order and

Each element of A is equal to the corresponding element of B.

Properties of Matrix Addition:

Matrix addition is commutative. That is A + B = B + A.

Matrix addition is associative. That is A + (B + C) = (A + B) + C.

Existence of additive identity. That is A + O = O + A = A, where O is the null matrix.

Existence of additive inverse. That is A + (-A) = (-A) + A = O, whereA is

the additive inverse of A.

Properties of Matrix Multiplication:

Matrix multiplication is not commutative in general. That is AB BA.

Matrix multiplication is always associative. That is (AB) C = A (BC).



10/22

Page | 10

Matrix multiplication is distributive over addition. That is,

(i) A (B + C) = AB + AC (ii) (A + B) C = AC + BC.

Existence of multiplicative identity. That is AI = IA =A.

Existence of multiplicative inverse. That is AB = BA = I.

Reversal law for transpose of matrices. That is (AB)T= BTAT.

A matrixis a rectangular array of numbers in rows and columns enclosed within square brackets or

parenthesis.

A unit matrix is also called an identity matrix with respect to multiplication.

Every unit matrix is clearly scalar matrix. However a scalar matrix need not be a unit matrix.

A zero-matrix need not be a square matrix.

A matrix does not change if the zero-matrix of some order is added to it or subtracted from it.

The additive inverse of a matrix is its negative matrix and it is unique.

Multiplication of two diagonal matrices of same order is commutative.

Some of the square matrices like

64

32do not have multiplicative inverses.

If B is the multiplicative inverse of A, Then A is the multiplicative inverse of B.

If multiplicative inverse of a square matrix exists, then it is unique.

Addition or subtraction of two matrices are possible only when they are of same order.

If A is a matrix of order m nand B is a matrix of order n p, then the product matrix AB is

defined and is of order m p.

(AT)T= A, (A + B)T= AT+ BT.

If AB = O, it is not necessary that A = O or B = O. That is product of two non-zero matrices

may be a zero matrix.

*****5. COORDINATE GEOMETRY

Section Formula:

Midpoint: M(x, y) = M

2,

2

2121 yyxx

Centroid: G(x, y) = G

3,

3

321321 yyyxxx

Internally: P(x,y) = P

ml

myly

ml

mxlx 1212 ,



11/22


12/22

Page | 12

If a point divides the line segment internally in the ratio ml: , thenm

lis positive.

If a point divides the line segment externally in the ratio ml: , thenm

lis negative.

If is the angle of inclination of a straight line l ,then

0 180

For horizontal lines, = 0or 180

For vertical lines, = 90

The slope of x-axis or straight lines parallel to x-axis is zero.

The slope of y-axis or straight lines parallel to y-axis is not defined.

If is acute, then the slope is positive.

If is obtuse, then the slope is negative.

The equation of x-axis is y = 0.

The equation of y-axis is x = 0.

The equation of a straight line parallel to x-axis is y = k, where k is a constant.

If k > 0, then the straight line lies above the x-axis.

If k < 0, then the straight line lies below the x-axis.

If k = 0, then the straight line is nothing but the x-axis.

The equation of a straight line parallel to y-axis is x = c, where c is a constant.

c > 0, then the straight line lies to the right y-axis.

If c < 0, then the straight line lies to the left of y-axis.

If c = 0, then the straight line is nothing but the y-axis.

The general form of equation of a straight line is px + qy + r = 0.

Two straight lines a1x +b1y + c1= 0 and a2x + b2y + c2= 0, where the coefficients are non-zero,

Are parallel if and only if2

1

a

a=

2

1

b

b

Are perpendicular if and only if a1a2+ b1b2= 0.

Three points A(x1, y1), B(x2, y2) and C(x3, y3) are collinear if and only if

The area of triangle is equal to zero.

Slope of AB = Slope of BC.

*****



13/22

Page | 13

6. GEOMETRY

Basic Proportionality Theorem or Thales Theorem:If a straight line is drawn parallelto one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

=

Converse of Thales Theorem:If a straight line divides any two sides of a triangle in the sameratio, then the line must be parallel to the third side.

Angle Bisector Theorem:The internal (external) bisector of an angle of a triangle divides theopposite side internally (externally) in the ratio of the corresponding sides containing the angle.

=

Converse of Angle Bisector Theorem:If a straight line through one vertex of a triangledivides the opposite side internally (externally) in the ratio of the other two sides, then the line

bisects the angle internally (externally) at the vertex.

Criteria for Similarity of Triangles:

AA (Angle-Angle) Similarity.

SSS (Side-Side-Side) Similarity.

SAS (Side-Angle-Side) Similarity.

Similarity Results:

The ratio of the areas of two similar triangles is equal to the ratio of the squares of their

corresponding sides.

If a perpendicular is drawn from the vertex of a right angled triangle to its hypotenuse, then the

triangles on each side of the perpendicular are similar to the whole triangle.

If two triangles are similar, then the ratio of the corresponding sides is equal to the ratio of their

corresponding altitudes.

If two triangles are similar, then the ratio of the corresponding sides is equal to the ratio of the

corresponding perimeters.

Pythagoras Theorem (Baudhayan Theorem):In a right angled triangle, the square ofthe hypotenuse is equal to the sum of the squares of the other two sides.

`BC2= AB2+ AC2



14/22

Page | 14

Converse of Pythagoras Theorem:In a triangle, if the square of one side is equal to thesum of the squares of the other two sides, then the angle opposite to the first side is a right angle.

Tangent-Chord Theorem:If from the point of contact of tangent (of a circle), a chord isdrawn, then the angleswhich the chord makes with the tangent line are equal respectively to the

angles formed by the chord in the corresponding alternate segments.

Converse of Tangent-Chord Theorem:If in a circle, through one end of a chord,a straight line is drawn making an angle equal to the angle in the alternate segment, then

the straight line is a tangent to the circle.

Componendo Rule: Ifd

c

b

a ,then

d

dc

b

ba

is called componendo rule.

Tangent and Point of Contact:A straight line which touches a circle one point iscalled a tangent to the circle and the point at which it touches the circle is called its point of contact.

Circles and Tangents Results: A tangent at any point on a circle is perpendicular to the radius through the point of contact.

Only one tangent can be drawn at any point on a circle. However, from an exterior point of

a circle two tangents can be drawn to the circle.

The lengths of the two tangents drawn from an exterior point to a circle are equal.

If two circles touch each other, then the point of contact of the circles lies on the line

joining the centres.

If two circles touch externally, the distance between their centres is equal to the sum of their radii.

If two circles touch internally, the distance between their centres is equal to the difference

of their radii.

If AB and CD are two chords of a circle which intersect each other internally at P or intersect

each other externally at P, then the proof is PA PB = PC PD.

*****7. TRIGONOMETRY

Trigonometric Identities:

sin2+ cos2= 1 sec2- tan2= 1 cosec2- cot2= 1

sin2= 1 - cos2 sec2= 1 + tan2 cosec2= 1 + cot2

cos2= 1 - sin2 tan2= sec21 cot2= cosec2- 1

cosec . sin = 1 sec . cos = 1 cot . tan = 1



15/22

Page | 15

sin =eccos

1 cosec =

sin

1

cos =sec

1 sec =

cos

1

tan =

cossin cot =

sincos

tan =cot

1 cot =

tan

1

sin (90- ) = cos cosec (90- ) = sec

cos (90- ) = sin sec (90- ) = cosec

tan (90- ) = cot cot (90- ) = tan

Heights and Distances:

{(Old Henry) (And His) (Old Aunty)}

sin =

(Old Henry) cosec =

(Henry Old)

cos =

(And His) sec =

(His And)

tan =

(Old Aunty) cot =

(Aunty Old)

Trigonometric Ratios of Some Special Angles:

Ratio 0 30 45 60 90

sin 01

2

2

1

2

3 1

cos 12

3

2

1

1

2 0

tan 03

1

1 3 notdefined()

Opposite Side

Hypotenuse Side

Adjacent Side



16/22

Page | 16

Componendo and Dividendo Rule:

Ifd

c

b

a , then

dc

dc

ba

ba

2= 1.414

3= 1.732

*****8. MENSURATION

Cylinder: If thebase of a cylinder is not circular then it is called oblique cylinder.

If the base is circular but not perpendicular to the axis of the cylinder, then the cylinder is called

circular cylinder.

If the axis is perpendicular to the circular base, then the cylinder is called right circular

cylinder.

Cone:

If the base of a cone is not circular, then it is called oblique cone.

If the base of a cone is circular then, it is called circular cone.

If the vertex is directly above the centre of the circular base, then it is a right circular cone.

Right Angled Triangle Cone

2

Base Radius

Height (h) Height (h)

Sector Cone

Radius () Slant height ()Arc length (L) Perimeter of the base (2r)

Area (

360r2) C.S.A ()

Slant height, = 22 rh

Height, h =22

rl

Radius, r =22

hl



17/22

Page | 17

Frustum of a Cone: Let us consider a right circular solid cone and cut it into two solids so as to obtain a smaller

right circular cone. The other portion of the cone is called frustum of the cone.

In other words, if a solid right circular cone is sliced with a plane parallel to its base, the part

of the cone containing the base is called a frustum of the cone. Thus a frustum has two

circular discs, one at the bottom and the other at the top of it.

The Latin word frustum means piece cut off and its plural is frusta.

Sphere: If a circular disc is rotated about one of its diameter, the solid thus generated is called sphere.

Thus sphere is a 3dimensional object which has surface area and volume.

Volume: Volume is literally the amount of space filled .

S.No Solid Name

L.S.A (or)

C.S.A

(sq.units)

T.S.A

(sq.units)

Volume

(cu.units)

1.Cylinder

2rh 2r (h+r) r2h

2.Hollow Cylinder

2h (R + r) 2(R + r) (Rr + h) h (R2r2)

3.Cone

r r (+ r)1

3r2h

4.Frustum

- - - - - - - -- - - - - -1

3h (R2

+ r2

+ Rr)

5.Sphere

4r2 - - - - - - -4

3r3

6.Hollow Sphere

- - - - - - - - - - - - - -4

3(R3- r3)

7.Hemisphere

2r2 3r22

3r3

8.Hollow Hemisphere

2(R2+ r2) (3R2+ r2)2

3(R3- r3)

9. Internal surface area of the cylinder (Hollow) 2r h

10. External surface area of the cylinder (Hollow) 2R h

11. Inner surface area of the sphere (Hollow) 2r2

12. Outer surface area of the sphere (Hollow) 2R2

13. Volume of water discharged Cross section area (r2) Speed Time

14. Conversions

1 m = 1000 litres

1 d.m3 = 1 litre

1000 cm3 = 1 litre

1000 litres = 1



18/22

Page | 18

King Henrys Daughter Makes Delicious Choco Mittai

*****

9. PRACTICAL GEOMETRY Two tangents can be drawn to a circle from an external point.

Diameters subtend 90on the circumference of a circle.

*****10. GRAPHS

Quadratic Graphs:Let us consider the quadratic polynomial, cbxaxy 2 ,

If a > 0, then the curve is open upward.

If a < 0, then the curve is open downward.

Special Graphs: Direct variation, ky x

Indirect variation, x

ky

*****11. STATISTICS

Measures of dispersion:

Measures of dispersion give an idea about the scatteredness of the data of the distribution.

Range (R), Quartile Deviation (Q. D), Mean Deviation (M. D) and Standard Deviation (S. D) are the

measures of dispersion.

Range:

Range is the simplest measure of dispersion. Range of a set of numbers is the difference

between the largest and the smallest items of the set.

Range = Largest valueSmallest value

Range = LS.

The coefficient of range =+



19/22

Page | 19

Standard Deviation ():

Data Direct MethodActual Mean

Method

Assumed Mean

Method

Step Deviation

Method

Ungrouped

22

n

x

n

x

n

d 2

d = xx

22

n

d

n

d

d = Ax

2

2

n

d

n

d c

d =c

Ax

Grouped - - - - - - -

f

fd2

22

f

fd

f

fd

22

f

fd

f

fd c

Standard Deviation of the first n natural numbers is, =12

12 n

Coefficient of variation, C.V = 100x

Note:

A better way to measure dispersion is to square the differences between each data and the mean

before averaging them. This measure of dispersion is known as the Variance and the positive

square root of the Variance is known as the Standard Deviation.

The term Standard Deviation was first used by Karl Pearson in 1894 as a replacement

of the term mean error used by Gauss.

0 xx

xnx

xnx

Assumed mean method and step deviation method are just simplified forms of direct method.

S.D of a collection of data remains unchanged when each value is added or subtracted by a

constant.

S.D of a collection of data gets multiplied or divided by the quantity k , if each item is

multiplied or divided by k .

The S.D of any nsuccessive terms of an A.P. with common difference dis, =12

12 nd

The S.D of any n consecutive even(or odd) integers is, =12

12

2 n

Variance is the square of Standard deviation.



20/22

Page | 20

The coefficient of variation helps us to compare the consistency of two or more

collections of data.

When the C.V is more, the given data is less consistent.

When the C.V is less, the given data is more consistent.

C.V is also called as a Relative Standard Deviation.

*****12. PROBABILITY

Experiment:Any process of observation or measurement is called an experiment. For example,

tossing a coin.

Random experiment:A random experiment is one in which the exact outcome cannot be predicted beforeconducting the experiment. However, one can list out all possible outcomes of the experiment.

Sample space:The set of all possible outcomes of a random experiment is called its sample space

and it is denoted by the letter S.

Trail:Each repetition of the experiment is called a trail.

Event:A subset of the sample space S is called an event.

Equally likely events:Two or more events are said to be equally likely, if each one of them has an equal

chance of occurrence. Mutually exclusive events:

Two or more events are said to be mutually exclusive events, if the occurrence

of one event prevents the occurrence of other events. In other words, if A and B are mutually

exclusive events, then A B = . Complementary events:

LetEbe an event of a random experiment and S be its sample space. The set

containing all the other outcomes which are not in E but in the sample space is called the

complimentary event of E. It is denoted by E . Thus, E = S - E. Note that E and E are mutuallyexclusive events.

Exhaustive events:Events E1, E2,, En are exhaustive events if their union is the sample space S. Sure event:

The sample space of a random experiment is called sure or certain event as any one

of its elements will surely occur in any trail of the experiment. The probability of the sure event is 1.

That is P(S) = 1.

Impossible event:An event which will not occur on any account is called an impossible event.

It is denoted by . The probability of an impossible event is 0. That is P() = 0.



21/22

Page | 21

Favourable outcomes:The outcomes corresponding to the occurrence of the desired event are called

favourable outcomes of the event. For example, if E is an event of getting an odd number in

rolling a die, then the outcomes 1, 3, 5 are favourable to the event E.

Probability:

)()()(

SnAnAP . This is not applicable if the number of possible outcomes is infinite and the

outcomes are not equally likely.

The probability of an eventAlies between 0 and 1, both exclusive. That is 0 P(A)1. )(1)( APAP

Addition theorem on probability: P (A B) = P (A) + P (B)P (A B). The event A B is said to occur if the eventA occurs or the eventB occurs or both A and B

occur simultaneously.

The event A B is said to occur if both the events A and B occur simultaneously.

If A and B are mutually exclusive events, then A B = . Thus, P(A B) = P(A) + P(B). P(A B) = 0.

A B is same asA \B in the language of set theory.

Important sample spaces: Tossing one coin, S = {H, T}

n (S) = 2

Tossing two coins, S = {HH, HT, TH, TT}

n (S) = 4

Tossing three coins, S = {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}

n (S) = 8

Rolling one die, S = {1, 2, 3, 4, 5, 6}

n (S) = 6

Rolling two dice, S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n (S) = 36

Rolling three dice, n (S) = 216. (Sample space is not necessary).



22/22

Page | 22

A leap year,

S = {(Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun)}

n (S) = 7

A non leap year,

S = {Sun, Mon, Tue, Wed, Thu, Fri, Sat}

n (S) = 7

Playing cards, S = {52 cards}

n (S) = 52

Red colour cards = 26

Black colour cards = 26

Spade cards = 13

Hearts cards = 13

Clavor cards = 13

Diamond cards = 13

Number cards = 04

(each number)

*****

~~~ Yes. Now we are 100% knowledgeable

students in Mathematics ~~~

Mathematics is the alphabet with which

God has written the Universe

Spade

(Black)

Hearts

(Red)

Clavor

(Black)

Diamond

(Red)A A A A

2 2 2 23 3 3 3

4 4 4 4

5 5 5 5

6 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

10 10 10 10

J J J J

Q Q Q Q

K K K K


SSLC Maths Formulae

Documents

Transcript of SSLC Maths Formulae