INTERMEDIATE FIRST YEAR MATHEMATICS -IB
COORDINATE GEOMETRY
1 Locus :
1.1 Definition of locus – Illustrations.
1.2 To find equations of locus - Problems connected to it.
2 Transformation of Axes :
2.1 Transformation of axes - Rules, Derivations and Illustrations.
2.2 Rotation of axes - Derivations – Illustrations.
3 The Straight Line :
3.1 Revision of fundamental results.
3.2 Straight line - Normal form – Illustrations.
3.3 Straight line - Symmetric form.
3.4 Straight line - Reduction into various forms.
3.5 Intersection of two Straight Lines.
3.6 Family of straight lines - Concurrent lines.
3.7 Condition for Concurrent lines.
3.8 Angle between two lines.
3.9 Length of perpendicular from a point to a Line.
3.10 Distance between two parallel lines.
3.11 Concurrent lines - properties related to a triangle.
4 Pair of Straight lines:
4.1 Equations of pair of lines passing through origin,
angle between a pair of lines.
4.2 Condition for perpendicular and coincident lines,
bisectors of angles.
4.3 Pair of bisectors of angles.
4.4 Pair of lines - second degree general equation.
4.5 Conditions for parallel lines - distance between
them, Point of intersection of pair of lines.
4.6 Homogenizing a second degree equation with a first
degree equation in X and Y.
5 Three Dimensional Coordinates :
5.1 Coordinates.
5.2 Section formulas - Centroid of a triangle and
tetrahedron.
6 Direction Cosines and Direction Ratios :
6.1 Direction Cosines.
6.2 Direction Ratios.
7 Plane :
7.1 Cartesian equation of Plane - Simple Illustrations.
CALCULUS
8. Limits and Continuity:
8.1.Intervals and neighborhoods.
8.2 Limits.
8.3 Standard Limits.
8.4 Continuity.
9 Differentiation :
9.1 Derivative of a function.
9.2 Elementary Properties.
9.3 Trigonometric, Inverse Trigonometric, Hyperbolic,
Inverse Hyperbolic Function - Derivatives.
9.4 Methods of Differentiation.
9.5 Second Order Derivatives.
10 Applications of Derivatives:
10.1 Errors and approximations.
10.2 Geometrical Interpretation of a derivative.
10.3 Equations of tangents and normal.
10.4 Lengths of tangent, normal, sub tangent and sub normal.
10.5 Angles between two curves and condition for orthogonality of curves.
10.6 Derivative as Rate of change.
10.7 Rolle’s Theorem and Lagrange’s Mean value theorem
without proofs and their geometrical interpretation.
10.8 Increasing and decreasing functions.
10.9 Maxima and Minima.