Topic outline

• • 01 SETS

Sets are used to define the concepts of relations and functions. We are going to study about different types of sets, venn diagrams, and operations on sets.

• 02 RELATIONS AND FUNCTIONS

We will learn how to map pairs of objects from two sets and then introduce the idea of relations between the pair. Finally, we will learn about a special type of relation called a 'function'.

• 03 TRIGONOMETRIC FUNCTIONS

In this chapter we will generalise the concept of trigonometric ratios to trigonometric functions and study their properties.

• 04 PRINCIPLE OF MATHEMATICAL INDUCTION

In this chapter we'll try and learn to prove certain results or statements that are formulated in terms of n with the help of specific technique, known as principle of mathematical induction.

• 05 COMPLEX NUMBERS

In this chapter we'll be extending the real number system to a larger system so as to solve equations which are not possible within the system of real numbers. We will finally get introduced to the infamous 'imaginary numbers' which you will soon realise are as 'real' as the real numbers that you are already quite familiar with. Equipped with this new weapon called complex numbers, we will revisit quadratic equations from a new point of view.

• • 07 PERMUTATIONS AND COMBINATIONS

Let's now learn the art and science of how to count very large numbers without actually counting them. We will start with the fundamental principle of counting and finally demystify two big words 'permutations' and 'combinations' and make them our friends for ever.

• 08 BINOMIAL THEOREM

Let's learn about the Binomial theorem and how to apply it when the powers involved are positive integers.

• 09 SEQUENCES AND SERIES

Let's learn deeper concepts of arithmetic progressions, get introduced to geometric progressions, and the idea of the arithmetic mean and the geometric mean. We will also look at the sum to n terms of a few special series.

• 10 STRAIGHT LINES

If a line makes an angle á with the positive direction of x-axis, then the slope of the line is given by m = tan α, α ≠ 90°. ®Slope of horizontal line is zero and slope of vertical line is undefined.

®Two lines are parallel if and only if their slopes are equal.

®Two lines are perpendicular if and only if product of their slopes is –1.

®Three points A, B and C are collinear, if and only if slope of AB = slope of BC.

®Equation of the horizontal line having distance a from the x-axis is either y = a or y = – a. ®Equation of the vertical line having distance b from the y-axis is either x = b or x = – b.

®The point (x, y) lies on the line with slope m and through the fixed point (xo , yo ), if and only if its coordinates satisfy the equation y – yo = m (x – xo ).

• 11 CONIC SECTIONS

We look at equations of some of curves, such as circles, ellipses, parabolas and hyperbolas.

• 12 INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

The three numbers representing the three distances are called the coordinates of the point with reference to the three coordinate planes. So, a point in space has three coordinates. In this Chapter, we shall study the basic concepts of geometry in three dimensional space

• 13 LIMITS AND DERIVATIVES

Limits are intuitive, yet elusive. Learn what they are all about and how to find limits of functions from graphs or tables of values. Learn about the difference between one-sided and two-sided limits and how they relate to each other.Get comfortable with the big idea of differential calculus, the derivative. The derivative of a function has many different interpretations and they are all very useful when dealing with differential calculus problems. This topic covers all of those interpretations, including the formal definition of the derivative and the notion of differentiable functions.

• 14 MATHEMATICAL REASONING

All of us know that human beings evolved from the lower species over many millennia. The main asset that made humans “superior” to other species was the ability to reason. How well this ability can be used depends on each person’s power of reasoning. How to develop this power? Here, we shall discuss the process of reasoning especially in the context of mathematics. In mathematical language, there are two kinds of reasoning – inductive and deductive. We have already discussed the inductive reasoning in the context of mathematical induction.

• 15 STATISTICS

Let's learn now about variance and standard deviation and also some measures of dispersion.

• 16 PROBABILITY

We've learnt about the experimental and theoretical approach to probability and now we'll learn about the axiomatic approach to probability.

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