Transcript Mathematics Mind Map - Slide 1

- Class X
MIND MAP... G. GIRIDHARA GOPAL
KENDRIYA VIDYALAYA KURNOOL
PROVING 3 or 5 + 8 IS AN IRRTIONAL NUMBER
MIND MAP... G. GIRIDHARA GOPAL
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DECIMAL REPRESENTATION
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POLYNOMIALS
Linear polynomial
Zeros: one
Quadratic polynomial
Zeros: two
Cubic polynomial
Zeros: three
Intersects x-axis at one point
Intersects x-axis at two points
Intersects x-axis at three points
C O E F F E C I E N T O F A P O LY N O M I A L S
ax2 + bx + c


QUADRATIC POLYNOMIAL

-b/a
ax3 + bx2 + cx + d



-b/a


c/a
CUBIC POLYNOMIAL


c/a
DIVISION ALGORITHM
p(x)
g(x)
q(x)
r(x)
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
a1x+b1y+c1=0
TEST FOR CONSISTENCY
a2x+b2y+c2=0
Condition
Inference
Consistency
a1/a2 ≠ b1/b2
Unique solution
consistent
intersecting
a1/a2 = b1/b2 ≠ c1/c2
Infinitely many solutions
consistent
coincident
a1/a2 = b1/b2 = c1/c2
No solutions
inconsistent
parallel
Substitution method
Elimination method
Cross- multiplication method
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Geometrical
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circles
THEOREMS
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O
p
p
o
s
i
t
e
s
i
d
e
Trigonometric Ratios
A
A d j a c e n t
1.
2.
s i d e
• Sin (90° - A) = Cos A
• Cos (90° - A) = Sin A
• Tan (90° - A) = Cot A
• Cot (90° - A) = Tan A
Trigonometric Identities
3.
• Sec (90° – A) = Cosec A
• Cosec (90° - A) =Sec A
Cos² A + Sin² A
Sec² A – Tan² A
Value of sin A or cos A never exceeds 1
Value of sec A or cosec A is always greater than 1
=1
=1
Cosec² A – Cot² A = 1
MIND MAP... G. GIRIDHARA GOPAL
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Horizontal level
Line of sight
Theodolite
Theodolite is
an instrument
to find out
horizontal or
vertical angles and thus
enable us to find heights
and distances of objects
in our daily life.
• Line
drawn
from the
eye of an
observer
to the
point in
object
viewed.
Angle of
elevation
Angle of
depression
• Angle
between
line of
sight and
horizontal
level.
• Above
horizontal
• Angle
formed
between
line of
sight and
horizontal
level.
• Below
horizontal
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Mean
Direct
method
Assumed
mean
method
Step
deviation
method
Less
than
Empirical formula of central tendency
3 Median = Mode + 2 Mean
More
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Ogive
curve
Experimental
Theoretical
Number of trials in which the event happened
Total number of trials
(Classical)
Number of outcomes favourable to Event
Number of all possible outcomes of experiment
Elementary event
Tossing 1 coin
• 2¹
•= 2
• 2 outcomes
• (Sample Space)
Tossing 2 coins
• 2²
•= 4
• 4 outcomes
• (Sample Space)
Tossing 3 coins
• 2³
•= 8
• 8 outcomes
• (Sample Space)
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P(E) + P ( ) = 1
= Not E
General form: ax²+bx+c
> 0
descreminant
• Roots are real distinct
•= 0
Roots are distinct
• Roots are real and equal
• Roots are equal
<0
• Roots are not real
Factorisation Method
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Thank
You
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