5. TRIGONOMETRIC RATIOS
- Introduction of trigonometric ratios using unit circle.
- degree and radians
- values of T-ratios for 30°,45°,60°,90°.
- area of sector and arc-length of circle.
- Concept of allied angles.
6. COMPOUND ANGLES
- Concepts of addition and subtraction of angles.
- Sum and difference formulas.
- Factor formulas.
7. MULTIPLE AND SUB-MULTIPLE ANGLES
- Formulas of multiple angles (2A and 3A) of an angle(A)
- Formulas of sub-multiples(A/2) of an angle(A).
8. GRAPHS
- Graphs of sine and cosine functions
9. PROPERTIES OF TRIANGLE
- sine and cosine formulas.
- Projection formula.
- Tangent Rule.
- formulas of area of a triangle (Δ = 1/2.a.b.sin c) & relations between Δ , R , r
and s.
- Solutions of a triangle.
10. INVERSE TRIGONOMETRIC FUNCTIONS
- Concept and definition.
- Formulas and simple examples
11. HEIGHT & DISTANCE
- Application of Trigonmetry in H & D problems
12. CO-ORDINATE GEOMETRY POINT
- Distance formula between two points in 2-D
- Circum-center of a triangle.
- Area of a triangle.
- Division of a line segment.
- Locus of point.
13. STRAIGHT LINE
- Cartesian equation of a straight line.
- Equation of a straight line in R2: ax+by+c=0.
- Slope of a straight line.
- Intercepts on axis.
- Equation of a straight-line passes through two points (x1, y1) and (x2, y2).
- Equation of straight-line having slope m and passing through the point (x1, y1).
- Equation of st. line having intercepts on y-axis and slope m
- Parallel and perpendicular straight-line relation between their slope. Angle
between two straight lines.
14. CIRCLE
- Definition of a circle
- General equation
- Standard equation
- Formation of equation of a circle
- Tangent & Normal.
15. PARABOLA
16. ELLIPSE
17. HYPARBOLA
18. FUNCTIONS & LIMITS
- Definition of function
- Examples
- Concept & rules of limit
- Evaluation of standard limit of algebraic & trigonometric function
19. DIFFERENTIATION
- Definition.
- Derivation of constant function.
- Formula: Xn, ax, Sin x, ex, etc.
- Formula for sum, product, and quotient of functions.
- Chain rule.
- Derivation of parametric and Implicit functions.
- Second order differentiation.
- Application of derivatives in Velocity, Acceleration, Maxima and minima, Radius
of curvature
20. INTEGRATION
- Introduction to Integration
- Formula for standard functions
- Simple basic rules of Indefinite Integration.
- Evaluation of simple Indefinite Integrals.
- Integration by Substitution.
- Definite Integral, Lower limit, Upper limit & Properties of definite integral.
- Solution of simple problems of definite Integral.
- Application of Integration in area & volume of circle, parabola & ellipse only.
21. LOGARITHM AND EXPONENTS
- Definition and Concepts
- Loarithm rules
- Examples based on rules (without using Logarithmic Tables)
22. VECTOR ALGEBRA
- Vector and Scalar quantities
- Types of vectors (Position vector, Equal vector, Opposite vector,
Coplanarctors, Co-initial vectors)
- Geometrical representation of vectors.
- Addition and scalar multiplication of vectors. in the direction of axis.
- Magnitude of vector and unit vector.
- Direction cosines of vector and unit vectors in the direction of axis.
- Dot and Cross product of vectors.
- Applications (Work done by force and moment of force)
