REGULAR TUITION
Ensure you adopt a disciplined approach to mathematics starting from this grade, as abstract problems in geometry and algebra can present significant challenges otherwise.
COURSE DELIVERY

Monday & Wednesday: Between a window of 3 hours between 4 pm to 7 pm, batch size of 8 students at the maximum.

The total lecture on a day on something new will be 1.5 hours after everyone has joined the class.

The time before and after the lecture will be for personalized training and tests.

Classes start in June and portions will be completed by December 15th, so students from different schools get ample time to prepare for their last term exam scheduled for different dates during February  March. Also there would be differences in portions from the first term exam..
SYLLABUS
For those serious about this course, we recommend viewing on a laptop for the best experience.
CHAPTER 1: REAL NUMBERS
The chapter starts with an introduction to Rational numbers and this is important for those who are not comfortable with fractions and operations on them.
Next the concept of irrational numbers and especially the square root of nonperfect squares.
√2 is the length of the hypotenuse of a right triangle with equal sides as 1. And it was Hippacus in Greece who came out for the first time on the existence of numbers that was not rational and he is said to have had a sad end to his life.
Next, you have operations on irrational numbers and rational numbers which make up the set of Real numbers.
Next differentiating fractions which are terminating and nonterminating without dividing.
Finally taking exponentiation and extraction of numbers and introducing the law of exponents to simplify arithmetic expressions which follow the VBODMAS rule.
CHAPTER 2: POLYNOMIALS
After understanding of general algebraic equations and understanding polynomials in one variable in 8th grade, we look closely into polynomials in one variable which are linear and quadratic.
Starting with the value of a polynomial, the remainder theorem, and arriving at how to find the zeros of a polynomial through trials.
Next factorization of a quadratic polynomial through splitting the middle term.
Finally, one of the most difficult exercises in 9th grade where you apply identities for factorization of expressions that are quadratic in one, two, and three variables and also cubic expressions in one and two variables.
CHAPTER 3: COORDINATE GEOMETRY
The concept of dividing a 2D plane using two perpendicular axes and representing every point on the plane with two coordinates was put forward by Rene Descartes.
This helped to study more on Geometric figures and also study variations between two variables that could be of any degree.
This chapter is probably one of the easiest chapters since we only need to arrive at the coordinates of a point and represent a point on this coordinate plane or cartesian plane.
This will be a foundation for your study of linear equations to follow and also chapters in 9thgrade Physics.
CHAPTER 4: LINEAR EQUATIONS
An introduction to the Linear equation in two variables.
Framing linear equations from word problems.
Graphical representation of the linear equations based on the chapter on Coordinate Geometry.
Finally, a special case where you understand more about linear equations in one variable through graphical interpretation.
CHAPTER 5: INTRODUCTION TO EUCLID’S GEOMETRY
There was only Euclid Geometry till the 18th century, before people wanted to make maps of the globe for counties that controlled most parts of the world. This new Geometry was called Spherical Geometry.
Now, today there are many Geometric concepts man has come up with to model new developments in especially Physics.
To come up with a particular perspective on Geometry, you need to define the basic elements, common notions and postulates.
This chapter discusses the basic definitions of a point, line etc. Next common notions and five postulates, which forms the foundation for one of the most read works in the history of the world. The “Elements” compiled by Euclid in 300 BC from all that was known in Alexandria, Greece.
Euclid’s geometry is known for its perfect logical order in introducing theorems.
CHAPTER 6: LINES & ANGLES
Starting with definitions of vertically opposite angles, complementary and supplementary angles.
Next relationships between angles like corresponding angles when a transversal intersects two parallel lines. This is based on the 5th postulate that parallel lines never meet and the interior angles on the same side of the transversal sums to 180
This forms the basis for two important rules for triangles.
The angle sum property and exterior angle property.
CHAPTER 7:TRIANGLES
This is one of the crucial chapters in a high school student's life.
This chapter deals with congruency of triangles and based on the fact that every polygon can be divided into triangles, helps one to work on congruent figures in general.
Now this chapter introduces five postulates to simplify the process, compering to otherwise looking for three angles and three corresponding sides to be equal.
Most importantly, this chapter and the next two to follow do not have an algorithm for to solve all questions.
Solving Geometric questions is an art and patience to focus your mind can only take you to the next level, where you start developing problemsolving skills in general
CHAPTER 8: QUADRILATERALS

This chapter takes concepts from lines and angles and congruency of triangles to prove that a diagonal of a quadrilateral with opposite sides parallel or a parrelogram divides the parrelogram into two congruent triangles.

This forms the basis of all rules for a parrelogram.

Next, each of the Rectangle and Rhombus have an extra rule that is not common to each.

Finally, a square has all the properties of a parrelogram and the specific properties of a Rhombus and Rectangle.

Now if you need to solve problems in this chapter you need a solid foundation of the preceding two chapters.
CHAPTER 9:AREAS OF PARRELOGRAMS & TRIANGLES

This chapter is based on the triangles and parrelograms sharing the same base and between two parallel lines.

Triangles and Parrelograms sharing the same base and between two parallel lines have the same area.

Now for a triangle and parrelogram, the area of a triangle is half of that of the parrelogram.

NOTE: Presently this chapter is deleted and it is a challenging chapter like the two chapters preceding this.
CHAPTER 10: CIRCLES

The prerequisite is a solid foundation with Lines & Angles and Triangles and by now the ability to solve problems in Geometry through logic and reasoning.

Now specific theorems discussed in this chapter are based on equal chords of a circle, equal arcs of a circle, and finally relationship between the angles made by a chord or arc on the minor arc, major arc, and the center of the circle.

Finally, properties of a very important figure with a quadrilateral inside a circle, A cyclic quadrilateral.
CHAPTER 11: CONSTRUCTION

Here you study to bisect an angle and draw the perpendicular bisector of an angle.

Next, you learn how to construct a triangle based on three sets of inputs. For example constructing a triangle when its base, the base angle, and the sum of the other two sides are given.
CHAPTER 12: HERONS FORMULA

A powerful formula to arrive at the area of a Triangle given all its sides.

In this chapter, the first exercise deals with just one triangle with length of sides given indirectly and can be found by basic arithmetic skills like ratios and averages.

The last exercise is based on irregular polygons which have practical applications in the measurement of land.

Also designs which have triangles and hence arrive at the area and probably the cost of cloth required to make the design.
CHAPTER 13: SURFACE AREA & VOLUMES

In 8th grade or in lower grades they have introduced the surface area and volumes of cubes, cuboids and cylinders.

Here for the first time surface area and areas of cone and sphere are introduced.

Now the questions will not be straightforward and your ability to develop problemsolving skills over the last chapters will be tested.
CHAPTER 14: STATISTICS

A very good introduction to the purpose of data and a relatively new branch of Mathematics.

Till 8th grade, you had only discrete frequency distribution. The next type of data discussed here has an extra dimension with the frequency of data points, known as a frequency distribution table.

Now we calculate three measures of central tendency: Mean, Mode, and Median.
CHAPTER 15: PROBABILITY

Now Probability of an event can be measured through two approaches.

The first one is theoretical probability which is based on counting the number of outcomes favorable to an event and the number of total outcomes and taking the ratio of these totals. This requires only your logic and reasoning skills and don't have to depend on data. This is suitable for predicting outcomes in gambling

Now in this chapter, we use statical data to arrive at the same ratio and the student is able to understand the combination between the two branches. This is useful in Engineering and Manufacturing where data is available and this can form the basis of quality control.
COURSE SUMMARY

Summary of the course till December

The first four chapters will be completed before the 1st midterm with weightage given to the Real numbers and Polynomials.

The last four chapters will also be taken at a high pace similar to the first four.

Now in between, almost 50% of the training will be on the five chapters on Geometry in between and we at Mathpinnacle want our students to also benefit from the study of Geometry for their Logical Reasoning and Deduction skills.


Final exam preparation schoolwise.

The last term exam is important for all students.

The school will consider passing weak students who have performed badly on the final term exam, which is almost like a board exam in 9th grade.

It is also important for good students, as it will set the foundation for their mindset to start preparations for the 10th grade CBSE board exam.
