1. Algebra (12 hrs)
1.1 Determinants: Elementary properties of determinants up to 3rd
order, consistency of equations, Crammer’s rule.
1.2 Matrix: Algebra of matrices, Inverse of a matrix, matrix inverse
method to solve a system of linear equations in 3 variables.
2. Co-Ordinate Geometry (18 hrs)
2.1 Equation of straight line in various standard forms (without proof),
inter section of two straight lines, angle between two lines. Parallel
and perpendicular lines, perpendicular distance formula
2.2 General equation of a circle and its characteristics. To find the
equation of a circle, given:
* Centre and radius
* Three points lying on it
* Coordinates of end points of a diameter;
2.3 Definition of conics ( Parabola, Ellipse, Hyperbola) their standard
Equations without proof.
Problems on conics when their foci, directrices or vertices are given.
3. Integral Calculus (34 hrs)
3.1 Integration as inverse operation of differentiation
3.2 Simple integration by substitution, by parts and by partial fractions
(for linear factors only)
3.3 Use of formulas
for solving problems Where m,n are positive integers
3.4 Applications of integration for :
(a) Simple problem on evaluation of area bounded by a curve and axes.
(b) Calculation of Volume of a solid formed by revolution of an area
about axes. (Simple problems).
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4. Vector Algebra (10 hrs)
a) Definition notation and rectangular resolution of a vector.
b) Addition and subtraction of vectors.
c) Scalar and vector products of 2 vectors.
d) Simple problems related to work, moment and angular velocity
5. Differential Equations (06 hrs)
Solution of first order and first degree differential equation by variable
separation method (simple problems)