GROUP: 2

MATHS PRESENTATION

EXPONENT

S

What is an exponent ?

The exponent of an number says how many times to use that number in multiplication.

- KARAN SINGLA

Positive ExponentsWe can have 3/8 * 3/8 * 3/8 = 3\8^3 so if a/b are positive or negative but the exponent is positive . So it is called positive exponents

- KARAN SINGLA

Negative Exponents A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, "x–2" (raise to the minus two) just means "x2, but underneath, as in 1/(x2)".

- KARAN SINGLA

LAWS OF

EXPONENTS

Law : 1

xm *xn= xm+n

• for e.g. : let x=2,m=2 and n=3 then 22*23=22+3

4*8=25

32=32Law : 2xm÷xn=xm-n

≈for e.g. :- let x=3 , m=3 and n=2 then, 33÷32=33-2

27/9=31

3=3- JAYA MENDIRATTA

Law : 3

(xm)n= xm*n

(x-m)n= x-m*n

≈for e.g. :- let x=2 , m=3 and n=2 then, (23)2=23*2

82=26

64=64≈for e.g. :- let x=2 , -m=-3 and n=2 then, (2-3)2=2-3*2

-82=2-6

64=64

Law : 4

- JAYA MENDIRATTA

(a/b)-m =(b/a)m

If a/b is rational number a/b≠0 Therefore, m=positive numberFor e.g. :- let x=2 m=2 and y=3

Then 22 *32 =(2*3)2

4*9=(6)2

36=36

Law : 5

- DEEPALI THAKUR

xm *ym= (xy)m

≈for e.g. : let x=2,m=2 and y=3 then 22*32=(2*3)2

4*9=(6)2

36=36

LAW: 6

- DEEPALI THAKUR

xm÷ym=(x/y)m≈for e.g. :- let x=4

y=3 and m=2 then, 42÷32=(4/3)2

16/9=(4)2/(3)2

16/9=16/9

LAw : 7

- DEEPALI THAKUR

PLAYING WITH

NUMBERS

PLAYING WITH NUMBERSIn this section, we shall learn how to solve sums mathematical puzzles involving two or three digit numbers through illustrative examples. Before doing so, let us first have a brief look on some fundamental rules regarding the placing of digits in two or three digit numbers.

- JASMEET SINGH

The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

A two digit number would have two digits, first at ones place and another at tens place. Digit ‘0’ cannot be placed at tens place in a two digit number.

RULES

- JASMEET SINGH

A two-digit number would have two digits, first at ones place and another at tens place. Digit ‘0’ can not be placed at tens place in a two-digit number.

In general, a 2-digit number forms 10a+b, where a != 0 and b are whole numbers.

e.g.1. 37 = 3 * 10 + 7

= 10 * tens digit + ones digit2. 15 = 1 * 10 + 5

= 10 * tens digit + ones digit- HARDIK GROVER

A 3-digit number would have 3-digits, first at ones place, second at tens place and third at hundreds place. Digit ‘0’ can not be placed at hundreds place in a 3-digit number.

In general, a 3-digit number forms 100a + 10b + c, where a, b and c are whole numbers and a != 0.e.g. 1.132 = 1 * 100 + 3 * 10 + 2

2.257 = 2 * 100 + 5 * 10 + 7

Note : If the digits are reversed in a 3-digit number 100a + 10b + c, then the new number formed is 100c + 10b + a.

- HARDIK GROVER

Divisibility by2A number is divisible by 2 if its ones digit is even

number:2,4,6,8,0Divisibility by3A number is divisible by 3 if sum of digits is a

multiple of 3Divisibility by 5A number is divisible by 5:if its ones digit is either 0

or 5.Divisibility by 9A number is divisible by 9:if sum of digits is a

multiple of 9.

DIVISIBILITY TEST

- DEVANSHI DALAL

Divisibility by 10A number is divisible by 10:if ones digit is 0 EXAMPLES:

Eg.1 =3024 is divisible by 2 as its ones digit contains even number 2Eg.2=16785 is divisible by 3 as its sum of digits is 27,which is a multiple of 3Eg.3=9250 is divisible by 5 as its ones digit is oEg.4=865917 is divisible by 9 as its sum of digits is 36, which is a multiple of 3 as well as of 9.Eg.5=3759210 is divisible by 10, as its ones digit contains 0.

- DEVANSHI DALAL

INTRODUCTION TO

GRAPHS

QUADRANTSThe two lines X-

axis and Y-axis divide the plane (graph paper) into four parts. These parts are called QUADRANTS.

The quadrants are fixed and don’t change their places.

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- DEEPANSHA DATLA

CARTESIAN COORDINATE SYSTEM

P .

This is a system in which a point can be located by giving X value followed by Y value and this is written as (x,y). In the point P(4,2) , 4 is the number on X axis, 2 is the number on Y axis. So 4 is the x-coordinate of P called ABSCISSA and 2 is the Y-coordinate of P called ORDINATE. - DEEPANSHA DATLA

Any point on x axis has y coordinate equal to 0Any point on y axis has x coordinate equal to 0A point lies on x axis ,if its y coordinate is zero A point lies on y axis , if its x coordinate is zero

Quadrants Signs of x coordinate

Signs of y coordinate

1st + +

2nd - +

3rd - -

4th + -

Quadrants and signs of x and y coordinate - DEVANSHI SHARMA

FactsFor any non-zero rational number a, we define a 0 = 1.1 raised to any power is 1.Any number raised to power 1 is the number itselfExponents were first used in the 15 century by a man named Nicolas Chuquet.Robert recorde further developed the system of exponents.Every whole number ,except 0,has exactly one immediate predecessor.Every whole number has exactly one immediate successor.- DEVANSHI SHARMA

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