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The word 'statistics' is comes from the Latin word 'status' that means ''a state''.
Statistics is a branch of mathematics which deals in collection, analysis, organisation and presentation of data.
In this chapter we will study the three measures that is mean, medium and mode.
Main topics that is discuss in this statistics are-
-introduction
-basic concepts that are related to statistics
-mean of grouped data
-mode of grouped data
-median of grouped data
-graphical representation of cumulative frequency distribution
-summary
POLYNOMIAL The word 'poly' means ''many'' and 'nomial' means ''term'' so it means ''many terms''.
A polynomial is a expression of constants, variables and exponents that combined in using of addition, subtraction, multiplication and division except not division by a variable.
There are three types of Polynomial
Monomial- Which have only one term of algebraic expression is known as monomial.
Binomial- A algebraic expression which have two terms is known as binomial.
Trinomial- A algebraic expression which have three terms is known as trinomial.
A polynomial which have no variable is known as a zero variable.
A polynomial who only have one variable is known as one variable polynomial,
A polynomial who have two variable is known as two variable polynomial.
A polynomial who have three variable is known as three variable polynomial.
The main topics which will be discussed in this polynomial chapter are-
-The basic concepts related to polynomials
-The geometrical meaning of the zeroes of a polynomial
-Relationship between zeroes and coefficients of a polynomial
-Division algorithm for polynomials.
Probability is the chance of something happen. When someone is tells you the probability of something happening, they are sharing with you how likely the chance of that something is.
probability tells you how many choices you have over the number of possible combinations.
A probability is a branch of mathematics that deals with calculating the chances of a given event's occurance, which is expressed as a number between 1 and 0.
A sequence in which each term after the first is obtained by adding a fixed number to the previous term is an arithmetic sequence or arithmetic progression (AP). The fixed number that is added is the common difference. The sequence 3,7,11,15,19.....is an arithmetic sequence since each term after the first is obtained by adding 4 to the previous term.
A finite portion of an arithmetic progression is known as a finite arithmetic progress and the sum of a finite arithmetic progression is known as arithmetic series.
This chapter covers the following topics-
-introduction
-arithmetic progression
-Nth term of an AP
-sum of first N terms of an AP
-summary
This chapter concentrate on the following surface areas and volumes of cubes,cuboid,sphere (including hemisphere), right circular cylinders, cones and frustum. The entire chapter contains many formulas and each exercise is for the better understanding of each shape. Area is defined as two dimensional measurement, which includes basic plane size. There are two types of area-
-total surface area
-curved surface area
Volume is the amount of space, that measured in cubic units that an object occupies.
The chapter surface area and volumes concentrate on certain topics such as-
-introduction
-surface area of a combination of solids
-volume of a combination of solids
-conversation of solid from one shape to another
-frustum of a cone
In this chapter coordinates geometry we will calculating the slope, distance and midpoint to find the measurements of lines and angles. In this chapter we use graphs and coordinates to find the measurements and other useful information about geometric figure.
We get to know how to find the distance between the two points whose coordinates are given, and to find the area of the triangle formed by three given points. We will study how to find the coordinates of the point which divides a line segments joining two given points in a given ratio.
In this chapter we review the concepts of perimeter (circumference) and area of a circle and apply this to finding the areas of two special ''parts'' of a circular region is called sector and segment. we also find the areas of some combinations of plane figures involving circles and parts of circle.
Trigonometry is a greek word where 'trignon' means ''triangle'' and 'metron' means ''measure''.
A trigonometry is a branch of mathematics which help us to understands the relationship involving the length and angles of triangles. There are six functions of an angle commonly used in trigonometry, the names and abbreviation are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
In this chapter we will study the following topics-
-trigonometric ratios
-trigonometric ratios of some specific angles,
-trigonometric ratios of complementary angles,
-trigonometric identities
A triangle have three edges and three vertices. A triangle is a basic shape in geometry.
In this chapter we will cover the following topics related to triangle.
-Similar figures
A similar figures have a same shape but a similar figures not have a same size. In geometry a two circle are similar, two squares are similar etc.
-Similarity of triangles
A similar triangle have two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are proportional.
-Criteria for similarity of triangles
-Area of similar triangles
-Pythagoras
In a right triangle the square of the hypotenuse is equal to the sum of the square of the other two side.
In Circles you will learn the following:
Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.
(Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
(Prove) The lengths of tangents drawn from an external point to circle are equal.
While in Construction you will learn :
Division of a line segment in a given ratio (internally).
Tangent to a circle from a point outside it.
Construction of a triangle similar to a given triangle
Both the chapters are very important in examination point of view.
When an equation is having two variables with every variables in first degree such that variables are not multiplied with each other then it is called as a linear equations in two variables.
This chapter covers the following concepts-
-Pair of linear equations in two variables
-Graphical methods of solution of a pair of linear equations
-Algebraic methods of solving a pair of linear equations- substitution method, elimination method, cross multiplication method
-equations reducible to a pair of linear equations in two variables.