# Class 9 math’s

for some reason is called the basic foundation to the next big thing, which is the 10th board exam. Every concept and each topic learned during the 9th class math is important as these are the same content that evolves and gets challenging in the 10th boards. Parents find it difficult and strenuous to help their kids stay focused on this subject and this, especially for working parents, is a huge nightmare.

**Number System**

Number system defines a set of values used to represent quantity, let us consider any quantity and this quantity is represented by the decimal. Number Seven, Three, Nine Two is in decimal (7392)

_{10}We can also represent the same quantity in any other number system like binary, octal, duodecimal, hexadecimal. The decimal number system is the most popular and common number system which we use in our daily life. If we have to measure the distance, weigh something, or count our money, we use the decimal number system.

There are ten different digits in decimal number system from 0 to 9. 0 1 2 3 4 5 6 7 8 9 these are the 10 different digits in the decimal number system.

In case of the binary number system, we have two different digits and 2 is the base for the binary number system. Now, what is this base, the base of a number system is also called as radix the base is also called as heretics.

**Polynomials **

A polynomial is a blend of numerous terms. It’s sort of like a chain of terms that are altogether connected together utilizing expansion or subtraction. The terms themselves contain augmentation, yet each term in a polynomial must be joined by either expansion or subtraction. Furthermore, polynomials can be produced using any number of terms consolidated, however there are a couple of particular names that are utilized to depict polynomials with a specific number of terms.

- Only one term (which isn’t really a chain) then we call it a “monomial” because the prefix “mono” means “one”.
- Two terms, then we call it a “binomial” because the prefix “bi” means “two”,
- Three terms, then we call it a “trinomial” since the prefix “tri” means “three”.
- Beyond three terms, we usually just say “polynomial” since “poly” means “many”, and in fact, it’s common to simply use the term “polynomial” even when there are just 2 or 3 terms.

Okay, so that’s the basic idea of a polynomial. It’s a series of terms that are joined together by addition or subtraction.

**Linear Equation**

Well if you were to take the set of all of the xy pairs that satisfy any equation and if you were to graph them on the coordinate plane, you would actually get a line. That’s why it’s called a linear equation. So, for example, the equation y is equal to two x minus three, this is a linear equation.

y = 2x – 3 (it is a linear equation)

for any x value that you put here and the corresponding y value, it is going to sit on the line.

**Euclid’s Geometry**

Euclid’s Geometry is based on various definitions let us look at those definitions

- A point is that which has no part.
- A line is a breadth less length.
- The end of the line are points.
- The edges of a surface are the line.
- A surface is that which has a length and breadth only.
- A straight line is a line which lies evenly with the point on itself.
- A plane surface is a surface which lies evenly with the straight line on itself.

Properties of Euclid’s Geometry

The properties of Euclid’s geometry didn’t require any proof as they were obvious universal truths. He divided these properties into two different types

- with assumptions which were made strictly on the basis of geometry and
- where the assumptions were based on in general mathematics and not specifically based on geometry.

The strict geometry is named as Postulates and the others unknown as Axioms.

**Angles**

Parallel lines are lines that will never cross, even if they go on forever… but what if I take one of our lines and give it a little nudge? Now the lines aren’t parallel anymore. In fact, they cross at a point. Let’s name it Point P. When lines cross at a point like this, we say that they intersect, and we call the point an ‘intersection’.

And when lines intersect, they form ‘angles’. You can think of the angles of the spaces, or shapes, that are formed between the intersecting lines. These intersecting lines form four angles

Generally, there are 3 types of angles:

- Right angles,
- Acute angles,
- Obtuse angles.

**Triangles **

You may remember from the lesson about polygons that triangles are special polygons that always have 3 sides and 3 angles. And that’s what the word ‘triangle’ means. “tri” means 3 and “angles” means angles. 3 sides, 3 angles, but what else is there to know about triangles? Well for starters, we’re going to learn how to classify triangles.

There’s two different way to classify (or organize) triangles. They can be classified by their sides and they can be classified by their angles. Let’s start by classifying triangles by their angles

You may remember from angles that there are 3 types of angles: Right angles, Acute angles, and Obtuse angles. Well! If we use the third line in each of these angles to form closed shapes. We get a triangle. These triangles are in the name of the angles it forms namely

- Right Triangle
- Acute Triangle
- Obtuse Triangle

**Quadrilaterals**

A quadrilateral is just a fancy math word for a polygon that has exactly 4 sides and 4 angles. A square is a special kind of quadrilateral. It’s a quadrilateral because it has 4 sides, and it’s special because all 4 of those sides are exactly the same length, and all 4 of its angles are exactly the same size. In fact, they’re all right angles. Notice also that a square is formed by two pairs of parallel sides. These two opposite sides are parallel, and these two opposite sides are parallel.

The rectangle is another form of quadrilaterals. A rectangle is a quadrilateral that still has 4 equal angles, but it does NOT have 4 equal sides.

A rhombus is a quadrilateral that still has 4 equal sides, but it does NOT have 4 equal angles. And once again, just like the square and rectangle, the rhombus is made from two pairs of parallel sides.

Another form of quadrilaterals is a parallelogram because, even though it’s sides are not all equal, and its angles are not all equal, it’s still made from two pairs of parallel sides.

“A quadrilateral that’s made from two pairs of parallel sides”, then wouldn’t all these other shapes be parallelograms too? Exactly! All of these shapes are parallelograms, just like they are all quadrilaterals.

A quadrilateral that has only ONE pair of parallel sides is called… a trapezoid.

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