#### Topics

##### Sets and Functions

##### Trigonometric Functions

- Concept of Angle
- Introduction of Trigonometric Functions
- Signs of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Trigonometric Functions of Sum and Difference of Two Angles
- Trigonometric Equations
- Truth of the Identity
- Negative Function Or Trigonometric Functions of Negative Angles
- 90 Degree Plusminus X Function
- Conversion from One Measure to Another
- 180 Degree Plusminus X Function
- 2X Function
- 3X Function
- Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications
- Graphs of Trigonometric Functions
- Transformation Formulae
- Values of Trigonometric Functions at Multiples and Submultiples of an Angle
- Sine and Cosine Formulae and Their Applications

##### Relations and Functions

- Cartesian Product of Sets
- Relation
- Concept of Functions
- Some Functions and Their Graphs
- Algebra of Real Functions
- Ordered Pairs
- Equality of Ordered Pairs
- Pictorial Diagrams
- Graph of Function
- Pictorial Representation of a Function
- Exponential Function
- Logarithmic Functions
- Brief Review of Cartesian System of Rectanglar Co-ordinates

##### Sets

- Sets and Their Representations
- The Empty Set
- Finite and Infinite Sets
- Equal Sets
- Subsets
- Power Set
- Universal Set
- Venn Diagrams
- Intrdouction of Operations on Sets
- Union Set
- Intersection of Sets
- Difference of Sets
- Complement of a Set
- Practical Problems on Union and Intersection of Two Sets
- Proper and Improper Subset
- Open and Close Intervals
- Operation on Set - Disjoint Sets
- Element Count Set

##### Algebra

##### Binomial Theorem

##### Sequence and Series

##### Linear Inequalities

##### Complex Numbers and Quadratic Equations

##### Permutations and Combinations

- Fundamental Principles of Counting
- Permutations
- Combination
- Introduction of Permutations and Combinations
- Permutation Formula to Rescue and Type of Permutation
- Smaller Set from Bigger Set
- Derivation of Formulae and Their Connections
- Simple Applications of Permutations and Combinations
- Factorial N (N!) Permutations and Combinations

##### Principle of Mathematical Induction

##### Coordinate Geometry

##### Straight Lines

##### Introduction to Three-dimensional Geometry

##### Conic Sections

- Sections of a Cone
- Concept of Circle
- Introduction of Parabola
- Standard Equations of Parabola
- Latus Rectum
- Introduction of Ellipse
- Relationship Between Semi-major Axis, Semi-minor Axis and the Distance of the Focus from the Centre of the Ellipse
- Special Cases of an Ellipse
- Eccentricity
- Standard Equations of an Ellipse
- Latus Rectum
- Introduction of Hyperbola
- Eccentricity
- Standard Equation of Hyperbola
- Latus Rectum
- Standard Equation of a Circle

##### Calculus

##### Limits and Derivatives

- Intuitive Idea of Derivatives
- Introduction of Limits
- Introduction to Calculus
- Algebra of Limits
- Limits of Polynomials and Rational Functions
- Limits of Trigonometric Functions
- Introduction of Derivatives
- Algebra of Derivative of Functions
- Derivative of Polynomials and Trigonometric Functions
- Derivative Introduced as Rate of Change Both as that of Distance Function and Geometrically
- Limits of Logarithmic Functions
- Limits of Exponential Functions
- Derivative of Slope of Tangent of the Curve
- Theorem for Any Positive Integer n
- Graphical Interpretation of Derivative
- Derive Derivation of x^n

##### Mathematical Reasoning

##### Mathematical Reasoning

##### Statistics and Probability

##### Statistics

- Measures of Dispersion
- Concept of Range
- Mean Deviation
- Introduction of Variance and Standard Deviation
- Standard Deviation
- Standard Deviation of a Discrete Frequency Distribution
- Standard Deviation of a Continuous Frequency Distribution
- Shortcut Method to Find Variance and Standard Deviation
- Introduction of Analysis of Frequency Distributions
- Comparison of Two Frequency Distributions with Same Mean
- Statistics Concept
- Central Tendency - Mean
- Central Tendency - Median
- Concept of Mode
- Measures of Dispersion - Quartile Deviation
- Standard Deviation - by Short Cut Method

##### Probability

#### notes

By using step-deviation method, it is possible to simplify the procedure.

Let the assumed mean be ‘A’ and the scale be reduced to `1/h` times (h being the width of class-intervals). Let the step-deviations or the new

values be `y_i`.

i.e. `y_i = (x_i - A) /h or x_i = A +hy_i` ...(1)

we know that \[\bar{x} =\frac{\displaystyle\sum_{i=1}^{n} f_ix_i}{N} \]

Replacing xi from (1) in (2), we get

\[\bar{x} =\frac{\displaystyle\sum_{i=1}^{n} f_i(A + hy_i)}{N} \]

=\[\frac {1}{N} (\displaystyle\sum_{i=1}^{n}

f_i A + = \displaystyle\sum_{i=1}^{n}

hf_iy_i )\] = =\[\frac {1}{N} (A \displaystyle\sum_{i=1}^{n}

f_i + h = \displaystyle\sum_{i=1}^{n}

f_i y_i) \]

=A .\[\frac{N}{N} + h \frac {\displaystyle\sum_{i=1}^{n} f_iy_i}{N} \]

(because \[\displaystyle\sum_{i=1}^{n} f_i\] = N )

Thus `bar x = A + h bar y` ...(3)

Now Variance of the variable x, \[\sigma_x^2 =\frac {1}{N} \displaystyle\sum_{i=1}^{n}

f_i (x_i - \bar x)^2 \]

=\[\frac {1}{N} \displaystyle\sum_{i=1}^{n}

f_i (A +hy_i - A - h \bar y)^2 \] (Using (1) and (2))

=\[\frac {1}{N} \displaystyle\sum_{i=1}^{n}

f_i h^2 (y_i - \bar y)^2 \]

= \[\frac {h^2}{N} \displaystyle\sum_{i=1}^{n}

f_i (y_i -\bar y)^2 = h^2 × \] variance of the variable y_{i}

i .e.`sigma_x^2 = h^2 sigma_x^2`

or `σ _x = hσ _y` ...(4)

From (3) and (4), we have

σ_{x} = \[{\frac{h}{N}}\sqrt{N\displaystyle\sum_{i=1}^{n} f_i y_i ^2 - (\displaystyle\sum_{i=1}^{n} f_i y_i) ^2 } \] ...(5)