Mathematics is the study of quantity, structure, space, and change. It originated from practical needs to count and measure, and early forms can be seen in patterns on ancient structures. Important historical figures like Pythagoras, Pascal, and Euler made significant contributions to fields like geometry, calculus, and algebra. Mathematics is divided into pure mathematics, which explores logic and reasoning, and applied mathematics, which uses mathematical methods in fields like science, engineering, and business. Common branches of mathematics include arithmetic, algebra, geometry, sets, probability, and calculus.

1. BY,
S.PRIYADHARSHINI

2. is Mathematics?
What is Mathematics?
• Mathematics is the study of topics such as
quantity, structure, space and change.
• Mathematics is not about numbers, equations,
computations or algorithms: it is about
understanding.

3.  Mathematics first arose from the practical
need to measure time and to count.
 The earliest evidence of primitive forms of
counting occurs in notched bones and scored
pieces of wood and stone.
 Early uses of geometry are revealed in
patterns found on ancient cave walls and
pottery.
 As civilisations arose in Asia and near East
sophisticated number systems, geometry and
algebra began to develop.

4.  Mayans
- had calender 18 months a year and 20
days a month.
 Romans
- invented Roman Numerals.
 Egyptians
- find fractions.
- invented geometry and came close to
develop pi.

5.  Pierre de Fermat – infinitesimal calculus
 Blaise Pascal - probability
 Pythagoras of Samos- pythagoras theorem
 Isaac Newton - calculus
 Thales of Miletus-geometry
 Leonhard Euler-differential calculus
 Joseph Louise Lagrange-calculus
 Euclid- euclidian geometry
 Archimedes- surface and volume of sphere

7. Pure mathematics explores the boundary of
mathematics and pure reason.
 ARITHMETIC :the branch of mathematics
dealing with the properties and manipulation
of numbers.
 ALGEBRA : the part of mathematics in
which letters and other general symbols are
used to represent numbers and quantities in
formulae and equations.

8.  GEOMETRY :the branch of mathematics
concerned with the properties and relations of
points, lines, surfaces, solids.
 SETS : collection of well defined distinct
objects.
 PROBABILITY :is a branch of mathematics that
deals with calculating the likelihood of a given
event's occurrence, which is expressed as a
number between 1 and 0.
 CALCULUS : the branch of mathematics that
deals with the finding and properties of derivatives
and integrals of functions.

9. Applied Mathematics is a branch of
mathematics that deals with mathematical
methods that find use in science,
engineering, business, computer science, and
industry.
 Business Maths: is mathematics used by
commercial enterprises to record and manage
business operations.

10.  Engineering maths : is a branch of
applied mathematics concerning
mathematical methods and techniques that
are typically used in engineering and
industry.

12.  The way Math was taught to them.
 They don’t understand the concepts of Math.
 Math is boring and too hard to learn.
 Too much homework and studying.
 Too many formulas and equations to
remember.
 Confusing.
 Math is not needed beyond schooling.
 I will never need to know this Math when I am
older.

16.  Over 70% of all jobs require maths.
 On average maths graduates earn more than
any other profession.
 Many degrees require maths including
physics, economics, medicine, IT, social
science, psychology, fashion design etc.,
 Without maths we would have no TV,
mobiles, games, CDs, credit cards etc.,
 Florence Nightingale was a mathematician.

18. SQUARING A 2-DIGIT NUMBER ENDING IN 5
 Choose a 2-digit number ending in 5.
 Multiply the first digit by the next
consecutive number.
 The product is the first two digits : XX__ .
 The last part of the answer is always 25 :
__25.

19.  SQUARING 3-DIGIT NUMBER ENDING IN 5
 Example 1: 685 x 685
Step 1:(68 + 1) x 68 = 69 x 68 = 4692
Step 2: 5 x 5 = 25
Step 3: Join the values, 685 x 685 = 469225
 Example 2: 405 x 405
Step 1: (40 + 1) x 40 = 41 x 40 =1640
Step 2: 5 x 5 = 25
Step 3:Join the values, 405 x 405 = 164025

20.  Step 1: Subtract the given multiplicand value by
1.
Step 2: Find the complement of multiplicand
(Base value - Multiplicand value).
Step 3: Append step 1 with step 2.
 Example: 456 x 999 (Multiplicand and Multiplier
Digits are Same)
 Step 1 : 456 -1 = 455
Step 2 : Complement of 456 is 544 (that is 1000
- 456)
Step 3 : 455544 (Its a final answer)

22.  EXAMPLE:
35 x 11
 First split 35 as 3 5
 Add 3 and 5. 3+5=8.
 Put 8 between 3 &5.
 We get an answer 385.

23.  EXAMPLE:
425x11
 First number=4
 Add first and second digit 4+2=6, then
second and third digit 2+5=7.
 Last number=5.
 Answer= 4675

25. How Many Times Can You
Subtract 10 from 100?

26. Think

27. Once. Next time you would be
subtracting 10 from 90.

28. Some months have 30 days and
some have 31 days. Which
month has 28 days?

29. Think

30. All months

31. If there are 6 apples and you
take away 4. How many do you
have?

32. Think

33. The 4 you took

34. An electric train is moving
north at 100 mph and a wind
is blowing to the west at
100mph. Which way does the
smoke blow?

35. Think

36. There is no smoke in an
electric train.

37. How many bricks does it take
to complete a building made
of brick?

38. Think

39. Only one “The Last One”

40.  Math is one of the building blocks of human
knowledge and social progress - without
proper and math conclusions, it is not
possible to estimate or to budget properly.
 The world is nothing without Maths.