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REGULAR TUITION

An opportunity to secure an exceptional score on your resume for a lifetime.

COURSE DELIVERY

  • Tuesdays & Thursdays: Between a window of 3 hours between 4 pm to 7 pm. The maximum batch size would be 8 students.

  • 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 May and portions will be completed by November 1st.

SYLLABUS 

For those serious about this course, we recommend viewing on a laptop for the best experience.

CHAPTER 1: REAL NUMBERS

  • The fundamental theorem of Arithmetic teaches you that every number is built by prime numbers and introduces prime factorization, and application in finding HCF & LCM of a group of numbers.

  • Decimal expansion of Rational numbers depending on the prime factorization of the denominator.

  • Now the last and most frequently asked question is to prove that the square root of non-perfect squares is irrational through a standard algorithm, basically through contradiction.

CHAPTER 2: POLYNOMIALS

  • After being comfortable with working with Algebraic expressions and understanding Polynomials in 9th grade, we first learn how to arrive at the degree of polynomials in one variable from their Geometric representation.

  • Finding zeros of a linear polynomial in one variable.

  • Finding zeros of a quadratic polynomial and proving the relationship between these zeros and the coefficients of the polynomial.

CHAPTER 3: LINEAR EQUATION IN TWO VARIABLE

  • In 9th grade, the study of linear equations in two variables was limited to their geometrical understanding and building equations from word problems, mostly related to practical purposes.

  • In this chapter, we understand the relevance of the solutions due to the interaction of a pair of linear equations in two variables.

  • Next, we move on to one of the most important concepts in Mathematics dealt with in high school. Ratios of coefficients of x, y, and the constant term to determine whether the pair of equations will have a solution, no solution, or infinitely many solutions.

  • Finally, there will also be word problems based on a pair of linear equations dealt in this chapter.

CHAPTER 4: QUADRATIC EQUATIONS

  • After the chapter on Polynomials, the concept of factorization by splitting the middle term is repeated again.

  • The first exercise is on identifying whether the equation given would turn out to be a quadratic equation in one variable, incase the presentation of the equation is not straight forward.

  • Quadratic equations unlike other higher order equations in one variable, have a formula to arrive at the roots or zeros.

  • The method is called the discriminant method and discriminat is the part of the formula.

  • From the discriminant, we can arrive at the type of zeros before arriving at the zeros.

  • And, in most cases, we can approximate a variation between two variables either as a linear or quadratic curve.

CHAPTER 5: ARITHMETIC PROGRESSION

  • This topic is dealt with for the first time in 10th grade.

  • The first exercise deals with identifying an Arithmetic progression and also writing down the missing terms.

  • The second exercise is based on a formula to calculate the nth term of an Arithmetic progression.

  • The third exercise is based on a formula to calculate the Sum to n terms of the same.

  • The final exercise will also test you on the concept for the nth term along with that for the sum to n terms.

  • This chapter unlike the chapters before though all of them have a standard algoritam, but the problems can be demanding.

CHAPTER 6: TRIANGLES

  • The chapter starts with the difference in the concept of congruent and similar figures.

  • The first exercise is based on the Basic proportionality theorem of Thales and this is crucial to arriving at shortcuts to proving two triangles are similar.

  • Next, we look into five shortcuts which are postulates to arrive at the similarity of triangles, which otherwise would take us to prove all three angles are correspondingly equal. The ratio of corresponding sides also has to be a constant.

  • The final exercise is based on the Pythagorean theorem.

CHAPTER 7: COORDINATE GEOMETRY

  • Understanding the introduction to Coordinate Geometry in 9th grade is a prerequisite. 

  • Now, the first exercise introduces a formula using the coordinates of two ends of a line segment to arrive at the distance.

  • The next exercise uses the same coordinate points of a line segment’s ends to arrive at a point that divides the line segment in a ratio.

  • The mid-point formula is a special case where the ratio is 1:1

CHAPTER 8: INTRODUCTION TO TRIGONOMETRY

  • This topic is taken up for the first time in a student's life in his last grade in High school.

  • Here it would be the most abstract treatment of Mathematics so far and Calculus to come after this in senior school for those who opt for Maths.

  • The fundamental purpose is to define six ratios for one of the two acute angles in a right-angled triangle and introduce the value of the ratios for standard angles : 0, 30, 45,60, and 90.

  • The purpose of this treatment will be reflected in the next chapter on Applications of Trigonometry.

  • The final exercise would be the most difficult exercise in High school to master for someone looking forward to scoring a perfect 100 in the board exam. It is based on just three identities, though it will take your skill as a mathematician to find patterns while solving so that you can simplify them. 

CHAPTER 9: APPLICATIONS OF TRIGONOMETRY

  • This chapter will answer questions asked by many adults around you, on why studying Trignomtery for life. 

  • Now here we use trigonometric ratios of standard angles to calculate distances and heights or depths.

  • Now say we need to calculate the height of a huge building, it is more practical to measure the distance from the building and use surveying equipment to arrive at the angle of elevation. In case the angle is 45 degrees, the height of the building will be equal to the distance.

CHAPTER 10: CIRCLES

  • The congruency of Triangles and the chapter on Circles dealt in 9th grade is a prerequisite for someone planning to master this chapter.

  • This is a very easy chapter compared to the one in 9th grade. There are only two basic theorems considered here based on Tangents to a circle.

  • One exercise based on the result is that the angle between a tangent and the radius at the point of intersection is 90 degrees.

  • The second one is based on the result that the measure of two tangents from an exterior point is equal.

CHAPTER 11: CONSTRUCTION

  • This is a very easy chapter on the division of a line segment and the construction of Tangents to a circle.

  • This chapter may be deleted.

CHAPTER 12 : AREAS RELATED TO CIRCLES

  • Areas of all standard figures dealt upto 9th grade is a prerequisite to this chapter.

  • The first part is based on the perimeter and areas of circles and sectors, where a semi-circle is a special case.

  • Next, you have areas of a segment of a circle, usually made by standard angles.

  • Finally, to master this chapter, you need to apply formulas all major 2-D entities you have studied so far to find areas of complicated designs and problems with probably squares and segments.

CHAPTER 13: SURFACE AREA & VOLUMES

  • The formulas for Surface area & Volumes dealt in 9th grade of Cube, Cuboid, Cylinder, Cone, and Sphere is a prerequisite.

  • With this, there are questions based on Surface area and Volumes of a combination of solids.

  • Finally, there can also be questions about converting a solid to another by melting or cutting.

CHAPTER 14: STATISTICS

  • The understanding of Statistics in 9th grade is a prerequisite. 

  • 9th-grade Statistics was on calculating the mean, mode, and median of data which was either discrete or in the form of a frequency distribution table.

  • Now, in 10th grade, we solve for mean, median, and mode of grouped frequency distribution.

  • Here the entire range of data is divided into equally spaced classes and when you have a median or mode falling within a class, you have formulas to calculate the precise solution which lies between the lower and upper limit of the class.

  • Also when the class limits are high, we use two methods to simplify calculations for the mean.

CHAPTER 15: PROBABILITY

  • Now probability can be applied to two types of data: Experimental & Theoretical.

  • 9th grade probability was based on Experimental data, whereas in the 10th grade it is based on theoretical data.

  • Theoretical approach arrives at the ratio of number of outcomes supporting the event and the total number of outcomes.

  • This demands you to apply your logic and reasoning to count these outcomes and assuming that all events have equal likelihood, you arrive at the probability of the event.

  • Questions will be based on coins, dice, cards, and balls of different colors in a bag.

  • Now in higher grades where Mathematics is an optional subject, you have counting tools like Permutation & Combination.

  • Summary of the course till November.

    • The first five chapters will be completed at the earliest so that our students have a good attempt on the first mid-term.

    • The next three chapters on Triangles, Introduction to Trigonometry and its Application will be slow-paced. An introduction to 9th-grade Geometry is essential and Trigonometry is dealt with in a student's life for the first time. 

    • The following chapters are relatively easy after all this training and will be completed by November 1st, even if we need a few extra classes.

  • Final preparation for CBSE Board exam.

    • Mathpinnacle has been training both students who take Basic and Standard in the same classroom.

    • We train each student according to his/her weaknesses and strengths through personalized question banks and like all other centers we try to have mock exams on Sundays.

COURSE SUMMARY

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