Ninth Standard math introduction

Friends, today we all are going to discuss about the overall syllabus of your grade IX mathematics and also going to talk about the most suitable way to solve such type of problems. Sadly, most students start learning mathematics by assuming it as a bundle of recipes to handle certain problems. Eventually mathematical world is a web of facts, concepts, and logical reasoning and, a more efficient approach to understand it is to focus on the principles and connections rather than on isolated facts.

The first approach to understand this important concept are building mathematics in this what students need to do is to reduce their problem to one that he/she have solved before. This principle is used all around in mathematics. The main sayings of this principle is : in order to understand a piece of mathematics student have to understand what preceded it. Moving forward what student need to do is to introduce concepts in a simple context and then generalize them in such a manner that facts and rules that are true in the simple context always remain true in the more general context. Before student go and attempt the solution of a given problem or starts studying a subject, it is worthwhile to think absolutely about what he/she expect their solutions to look like, or what they expect to learn. In general there are two outputs or we can say that two possibilities that are students expectations are met or they are not. In the second situation what students generally do is they make a mistake and now that they are alert to the fact that they can recover from it.

Now I am going to give you an introduction about your IX grade mathematics syllabus. The ninth grade syllabus mostly includes following topics in most generalized manner. The topics to cover are as follows :

1. Algebra
2. Geometry
3. Statistics
4. Probability
5. Pre calculus
6. Calculus
7. Trigonometry

Firstly discuss about the Algebra topic of ninth standard, This topic typically treated in ninth standard and most of the topics are considered as the part of Algebra 1. It includes exponents, radicals, properties of numbers, patterns, number system, evaluation of expressions involving signed numbers, exponents and roots, properties of the real numbers, absolute value and equations and inequalities involving absolute value, scientific notation, unit conversions, solution of equations in one unknown and solution of simultaneous equations, the algebra of polynomials and rational expressions, word problems requiring algebra for their solution, Pythagorean theorem, algebraic proofs, functions and functional notation, solution of quadratic equations via factoring and completing the square, direct and inverse variation, and exponential growth. Some of the few other topics are Gauss-Jordan elimination and kinds of matrix formation that includes Matrix/vector addition and Matrix/vector multiplication.

Now let's have a brief introduction about how to solve a word problem. What student need to do is to look for the statements in the problems that describe equal quantities. Then use of algebraic phrases and equal signs to write equations that make the same statements of equality.

To solve a difficult problem what student need to do is to solve a simpler problem first and then apply whatever formulas or methodologies that student learn to solve the more difficult problem. If student is going to opt this technique then he/she might have to iterate this technique and try to build whole hierarchy of problems to solve a truly difficult problem.

Moving further let's talk about the next topic in the ninth grade mathematics, that is Geometry. Geometry is an important area of mathematics which deals with the shape, size, relative position of figures, and the properties of space. It is all about shapes and their properties. Geometry is of two types : Plane geometry and solid geometry. Plane geometry deals about the shapes on a flat surface like lines, circles and triangles, shapes that can be drawn on a piece of paper whereas Solid geometry is all about three dimensional objects like cubes, prisms and pyramids. In ninth standard Geometry, we all are going to learn the following sub topics that are : Euclidean theories and algorithms, then we study about properties of geometry and a whole concepts of coordinates and transformations. Another important topic which is used in both Algebra and in Geometry that is Pythagorean theorem which helps in calculating the third side in a right angle triangle. Then we are going to understand the basic concept behind the coordinate system and look towards measurement of Geometry like triangle, square etc. In addition to this we will talk about different Geometric concepts and isoceles triangle theorems and rectangular coordinate system. Another important section comes under Geometry is Rate, distance, time, angle measurement and arc length. Inequality theorem along with angles of triangles and polygons along with unit of measures etc. are some of the important topics of Geometry.
Now the next topic of ninth standard mathematics are Statistics and Probability which are interrelated with each other, so I am going to discuss both the topics together. In lots of statistical analysis, results depend on the probability calculation like in many of the census results depend on probability and to represent probability we need statistics help. Probability and Statistics together play an important role in finding out measures of central value, measures of spread, and helps in comparing of two data. These two branches are basically treated as the tools of data analysis. Statistics is the practice or science of collecting and analyzing numerical data in large quantities. It is basically a study of the collection, organization, analysis and interpretation of the data. Probability is a way of telling or expressing knowledge that an event will occur or has occurred. The probability of an event occurring given that another event has already occurred is called a conditional probability. So in this section we deal with Mean, median, mode, range, standard deviation and variance in the numeric sequences. We are going to find the combinations and permutations among the series of numbers along with this we need to represent the data with the help of Data representation methods. In probability section I am going to discuss about types of events, conditional probability etc. Statistical analysis and methods to make inferences and organizing and displaying data along with making predictions from data are the another important topic of ninth grade mathematics.
Now the other two topics related with each other are Pre-Calculus and Calculus. Calculus is basically a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. Basically it is the study of 'Rates of Change'. There are two main branches of calculus: Differential Calculus and Integral Calculus. Differential calculus determines the rate of change of a quantity and integral calculus finds the quantity where the rate of change is known. In ninth standard Pre-Calculus section I am going to discuss about the following topics that covers topics like describing functions, representing functions along with Arithmetic and geometric series. The calculus section of mathematics branch includes various mathematical models with their applications to solve problems using multiple approaches along with this it also deals with techniques used to study patterns and analyze data and problems related to personal income and credit. It also comes with problems related to polar and rectangular coordinates along with trigonometric form of complex numbers and mathematical induction. Conic section and fundamental theorem of algebra are also the part of Calculus problem.
The last and final sub topic of ninth grade mathematics is Trigonometry. It is one of the important branch of maths and it also plays an important role in the physics branch. Trigonometry is the branch of mathematics that deals with triangles, circles, oscillations and waves. In mathematical term it is the study of triangles and the relationships between their sides and the angles between these sides. Trigonometric functions are the functions of an angle of a triangle, that are used to relate the angles of a triangle to the lengths of the sides of a triangle. The sub topic of ninth standard trigonometry are Degree and radian measures along with various basic trigonometric functions which I already stated above. Special right triangles means triangles placed in different form or angles and trigonometric values of standard angles are the next important topic of mathematics. Justification of Pythagorean identities are also an important section along with different trigonometric equations is also included in the syllabus.
Whenever student is going through several problems then he should go for work on the easy one first. As this might teach the students something that will surely help them to solve the more difficult problems in a faster and in a better manner. Whenever a student is done with their mathematic question, he or she needs to check the answers as there may be some mistakes in the problem or solution obtained is not an appropriate one. So moving further in next class we again start from the first topic of ninth grade mathematics and try to understand the basic concept behind the Algebra.