7. • Real numbers
• Quadraticequation
• Arithmeticprogression
• Introductionto trigonometry
• Applicationof trigonometry
• Construction
• Surface area and volume
• Probablity
8. Simple fraction have been used by Egyptians around 1000BC,in the
‘VADIC’ Pulbah Sutra” (The rules of cords) in 900 BC, include what
may be the first used of irrational numbers. The concept of irrational
numbers was empathically accepted by early Indian mathematician
since Manawa {750 – 690 BC},who were aware that sequence roots of
certain number such as √2 and √61 could not be exactly determined.
Around 500 BC, the Greek mathematicians led by Pythagoras realized
to need for irrational number, in particular the irrationality of the √2
15. REL-LIFE PROBLEM
Description the
problem in
mathematical way
Solve the
problem
Interpret the
solution in the
real-life problem
Does the solution
capture the real life
problem
y
e
s
Modeling
18. An arithmetic progression (AP) or arithmetic sequence is a sequence
of numbers such that the difference between the consecutive terms is constant.
For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression
with common difference of 2.
If the initial term of an arithmetic progression is and the common difference of
successive members is d, then the nth term of the sequence is given by:
and in general
A finite portion of an arithmetic progression is called a finite arithmetic
progression and sometimes just called an arithmetic progression. The sum of
a finite arithmetic progression is called an arithmetic series.
The behavior of the arithmetic progression depends on the common
difference d. If the common difference is:
•Positive, the members (terms) will grow towards positive infinity.
•Negative, the members (terms) will grow towards negative infinity
What
this??
19. median is the numerical value separating the higher half of a data sample,
a population, or a probability distribution ,from the lower half. The median of a finite
list of numbers can be found by arranging all the observations from lowest value to
highest value and picking the middle one.
In individual series (if number of observationis very low) first one must arrange all the
observations in ascending order. Then count(n) is the totalnumber of observationin given data.
If n is odd then Median (M) = valueof ((n + 1)/2)th item term.
If n is even then Median (M) = value of [((n)/2)th item term + ((n)/2 + 1)th item term ]/2
Meaning
of
20. The mode is the value that appearsmost often in a set of data.
The mode of a sample is the element that occurs most often in the collection.For
example, the mode of the sample [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] is 6
the arithmetic mean or simply the mean or average when the context is clear,
is the sum of a collection of numbers divided by the number of numbers in the
collection.
21. Shape Volume formula Variables
Cube a = length of any side (or edge)
Cylinder r = radius of circular face, h = height
Prism B = area of the base, h = height
Rectangular prism l = length, w = width, h = height
Sphere
r = radius of sphere
which is the integral of the surface
area of a sphere
Ellipsoid a, b, c = semi-axes of ellipsoid
Pyramid
B = area of the base, h = height of
pyramid
Cone
r = radius of circle at base, h =
distance from base to tip or height
Write down
formulas of
22. Surface areas
Shape Equation Variables
Cube s = side length
Rectangular prism ℓ = length, w = width, h = height
All Prisms
B = the area of one base, P = the
perimeter of one base, h = height
Sphere r = radius of sphere
Closed cylinder
r = radius of the circular base, h =
height of the cylinder
Lateral surface area of a cone
s = slant height of the cone,
r = radius of the circular base,
h = height of the cone
Full surface area of a cone
s = slant height of the cone,
r = radius of the circular base,
h = height of the cone
Pyramid B= area of base, P = perimeter of
base, L = slant height
