Transcript Terms from chapter 8

GOVT. OF TAMILNADU
DEPARTMENT OF SCHOOL EDUCATION
BRIDGE COURSE 2011-2012
CLASS VIII- MATHS
MATHEMATICIANS
PYTHAGORAS
 569
B.C. – 475 B.C.
 Greece
 First pure
mathematician
 5 beliefs
 Secret society
 Pythagorean theorem
ARISTOTLE
 384
B.C. – 322 B.C.
 Greece
 Philosopher
 Studied mathematics
in relation to science
EUCLID
 325
B.C. – 265 B.C.
 Greece
 Wrote The Elements
 Geometry today
AL-KHWARIZMI
 780
A.D.-850 A.D.
 Baghdad (in Iraq)
 1st book on Algebra
 Algebra
 Natural Number
 Equation
Alileanardo-da-Vinci
 1452
A.D. - 1519 A.D
 Italy
 Painter
 Architect
 Mechanic
Galileo-Galili
 1564
A.D.– 1642
A.D.
 Italy
 Teacher
 Mathematician
ALGEBRA
Types of polynomials:
 Polynomials are named according to the number of
terms present in them.
 Monomial:
 Binomial:
 Trinomial
They are special names given to a polynomial.

Classify the following into monomials,
binomials and trinomials:
(A) x + 1
 (B) 3m²
 (C) 2x²- x-4

ALGEBRA
FIND THE VALUE OF THE VARIABLES
31.5 = a - 34.4
 42 + y = 57
 x + 76.31 = 164.89
 x - 32 = 49
 23+ y = 119

AREA
Area measures the surface of something.
1 metre
1 metre
1m2
1 square metre
1 cm
1 cm
1 mm
1cm2
1 mm 1mm2
AREA
OF A RECTANGULAR LAWN
5 metres long
3 metres wide
The area is
15 square metres
= 15 m2
Area of a rectangle = Length x Width
Area of rectangle = Length x Width
65 m
Field
32 m
210 mm
21 cm
Page
Area of field = 65 x 32
= 2080 m2
Area of the page = 30 x 21
= 630 cm2
30 cm
300 mm
Area of the page = 300 x 210
= 63 000 mm2
UNITS OF AREA
1 square centimetre
1 cm
1 cm = 10 mm
1 cm2 = 100 mm2
1 cm
1 cm2 = 102 mm2
UNITS OF AREA
1 square metre
1000 mm 1m 100 cm
1 m = 100 cm
1 m2 = 100 x 100 cm2
1 m2 = 10 000 cm2
1000 mm
1m
100 cm
1 m = 1000 mm
1 m2 = 1000 x 1000 mm2
1 m2 = 1 000 000 mm2
1 m2 = 1002 cm2 = 10002 mm2
PERIMETER
Perimeter of a shape is the total length of its sides.
Perimeter of a rectangle = length + width
+ length + width
length
width
width
length
P = l + w + l + w
P = 2l + 2w
P = 2(l + w)
Example
L-shaped room
3m
Perimeter = 3 + 1.5 + 2.2 + 3
+ 5.2 + 4.5 = 19.4 m
1.5 m
4.5 m
A
2.2 m
B
5.2 m
3m
Area of A = 4.5 x 3
= 13.5 m2
Area of B = 3 x 2.2
Total area = 13.5 + 6.6 = 20.1 m2
= 6.6 m2
VOLUME
is the amount of space occupied by any 3dimensional object.
1cm
1cm
1cm
Volume = base area x height
= 1cm2 x 1cm
= 1cm2
Cuboid
Side 2
Top
Back
Front
Bottom
Length
(L)
Side 1 Height
(H)
Breadth
(B)
THE NET
L
H
B
B
H
H
L
HH
L
B
L
H
B
B
L
B
Total surface Area
L
L
H
L
B
B
H
B
B
H
L
H
L
H
L
H
L
Total surface Area = L x H + B x H + L x H + B x H
+LxB+LxB
= 2 LxB + 2BxH + 2LxH
= 2 ( LB + BH + LH )
CUBE
L
L

L
Volume = Base area x height
=LxLxL
= L3
• Total surface area = 2LxL + 2LxL + 2LxL
= 6L2
Name
Cube
Figure
Volume
L3
Total
surface
area
6L2
Cuboid
LxBxH
2(LxB +
BxH +
LxH)
Sample net
VOLUME OF A CYLINDER
WHAT IS THIS?

It has 2 equal shapes at the base, but it is not a
prism as it has rounded sides
It
is a Cylinder
EXAMPLE
V
= Base area x Height
=  r2 X h
The Circle
O
CIRCLE
Eg. ball,bangle,lemon.coin
A
CENTRE
B
CENTRE : O
RADIUS : OA
O
RADIUS
A
.
O
In a plane,each point of the circle is at equal
distance from a fixed point.The fixed point is
called the centre of the circle.
CENTRE = O
O
Radius
A
The distance from centre to any point on the
circle is called radius of the circle.
RADIUS = OA
A
D
I
A
O M
E
T
E
R
.
B
A Line segment passing through the centre of
the circle and whose end points lie on the circle
is called the diameter of the circle.
DIAMETER = AB
.
O
The length of the circle or the distance
around it is called circumference of the
circle.
Relation between radius and diameter
RADIUS = DIAMETER
2
A
OB = AB
2
.
O
B
EG. IF DIAMETER OF THE CIRCLE IS 10 CM THEN
FIND ITS RADIUS?
Sol. Radius =diameter / 2
radius=10 cm/ 2
radius =5 cm
A
.
O
Diameter = 10cm
B
LINES AND ANGLES
PARALLEL LINES

Def: line that do not intersect.

Illustration:
B
A
l
m

Notation:
l || m
AB || CD
D
C
PERPENDICULAR LINES


Def: Lines that intersect to form a right angle.
Illustration:
m

Notation: m  n

Key Fact: 4 right angles are formed.
n
TRANSVERSAL

Def: a line that intersects two lines at different points

Illustration:
t
VERTICAL ANGLES

Two angles that are opposite angles.
t
1
2
3 4
6
5
7
8
1   4
2   3
5   8
6   7
VERTICAL ANGLES

Find the measures of the missing angles
t
125 
?
125 
? 
55
55 
SUPPLEMENTARY ANGLES/
LINEAR PAIR

Two angles that form a line (sum=180)
1+2=180
2+4=180
4+3=180
3+1=180
t
1
2
3 4
6
5
7
8
5+6=180
6+8=180
8+7=180
7+5=180
SUPPLEMENTARY ANGLES/
LINEAR PAIR

Find the measures of the missing angles
t
108? 72 
?108


180 - 72
ALTERNATE INTERIOR ANGLES

Two angles that lie between parallel lines on opposite
sides of the transversal
t
1
2
3
4
5 6
7
8
3   6
4   5
ALTERNATE INTERIOR ANGLES

Find the measures of the missing angles
t
82 
98  ?82 
ALTERNATE EXTERIOR ANGLES

Two angles that lie outside parallel lines on opposite
sides of the transversal
t
1
2
3
4
5 6
7
8
2   7
1   8
ALTERNATE EXTERIOR ANGLES

Find the measures of the missing angles
t
120 
60 
?120 
CONSECUTIVE INTERIOR ANGLES

Two angles that lie between parallel lines on the same
sides of the transversal
t
1
2
3
4
5 6
7
8
3 +5 = 180
4 +6 = 180
CONSECUTIVE INTERIOR ANGLES

Find the measures of the missing angles
t
135 
?45 
180 - 135
GRAPH
GRAPH THE FOLLOWING LINES
Y = -4
Y=2
X=5
X = -5
X=0
Y=0
ANSWERS
x = -5
Y
x=5
X
ANSWERS
Y
y=2
X
y = -4
MEAN
DEFINITION
Mean
– the average of a
group of numbers.
2, 5, 2, 1, 5
Mean = 3
MEAN IS FOUND BY EVENING
OUT THE NUMBERS
2, 5, 2, 1, 5
MEAN IS FOUND BY EVENING
OUT THE NUMBERS
2, 5, 2, 1, 5
Copy
right
©
2000
by
Moni
ca
Yusk
MEAN IS FOUND BY EVENING
OUT THE NUMBERS
2, 5, 2, 1, 5
mean = 3
HOW TO FIND THE MEAN OF A
GROUP OF NUMBERS
•
Step 1 – Add all the numbers.
8, 10, 12, 18, 22, 26
8+10+12+18+22+26 = 96
Step 2 – Divide the sum by the
number of addends
= 96/6
= 16
HOW TO FIND THE MEAN OF A
GROUP OF NUMBERS
The mean or average of these
numbers is 16.
8, 10, 12, 18, 22, 26
WHAT IS THE MEAN OF THESE
NUMBERS?
7, 10, 16
11
WHAT IS THE MEAN OF THESE
NUMBERS?
2, 9, 14, 27
13
WHAT IS THE MEAN OF THESE
NUMBERS?
1, 2, 7, 11, 19
8
WHAT IS THE MEAN OF THESE
NUMBERS?
26, 33, 41, 52
38
DEFINITION
Median
– the middle
number in a set of ordered
numbers.
1, 3, 7, 10, 13
Median = 7
HOW TO FIND THE MEDIAN IN
A GROUP OF NUMBERS
Step
3 – If there are two middle
numbers, find the mean of these
two numbers.
21+ 25 = 46
median
23
2) 46
DEFINITION
Mode – the number that
appears most frequently in
a set of numbers.
1, 1, 3, 7, 10, 13
Mode = 1
Find the mode for the following
 7,
4, 5, 1, 7, 3, 4, 6, 7
Find the mode of the following
frequency table:
If the data are
arranged in the form of
a frequency table the
class corresponding to
the maximum
frequency is called the
model class. The value
of the variate of the
model class is the
mode.
x
10
20
30
40
50
60
F
8
15
12
10
9
6