MATHEMATICS
ICSE XII > MATHEMATICS

# 1. Determinants and Matrices

 (i) Determinants - Order. I.1Minors - Cofactors I.2.Expansion. I.3.Properties of determinants I.4.Simple problems using properties of determinants (ii) Matrices - Cramer's Rule

# 3. Conics

 3.0.As a section of a cone. Definition of Foci, Directrix, Latus Rectum. PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix. 3.0.As a section of a cone. Definition of Foci, Directrix, Latus Rectum. PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix. 3.0.As a section of a cone. Definition of Foci, Directrix, Latus Rectum. PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix. 3.0.As a section of a cone. Definition of Foci, Directrix, Latus Rectum. PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix. (i) Parabola (ii) Ellipse (iii) Hyperbola

# 5. Calculus

 (i) Differential Calculus (i) Differential Calculus (ii) Integral Calculus

# 6. Correlation and Regression

 6.1.Definition and meaning of correlation and regression coefficient. 6.2.Coefficient of Correlation by Karl Pearson. 6.3.Rank correlation by Spearman’s (Correction included). Lines of regression of x on y and y on x.

# 7. Probability

 7.1.Random experiments and their outcomes. 7.2.Events: sure events, impossible events, mutually exclusive events, independent events and dependent events. 7.2.Events: sure events, impossible events, mutually exclusive events, independent events and dependent events. Definition of probability of an event. Laws of probability: addition and multiplication laws, conditional probability (excluding Baye’s theorem). Laws of probability: addition and multiplication laws, conditional probability (excluding Baye’s theorem).

# 8. Complex Numbers

 8.1.Argument and conjugate of complex numbers. 8.1.Argument and conjugate of complex numbers. 8.2.Sum, difference, product and quotient of two complex numbers 8.3.Additive and multiplicative inverse of a complex number. 8.4Simple locus question on complex number; 8.5.Triangle inequality. 8.6.Square root of a complex number. 8.7.Demoivre’s theorem and its simple applications. 8.8.Cube roots of unity: 1,?,?2 ; application problems.

# 9. Differential Equations

 9.1.Differential equations, order and degree. 9.2.Solution of differential equations. 9.3.Variable separable. 9.4.Homogeneous equations and equations reducible to homogeneous form. 9.5.Linear form

# 10. Vectors

 10.1.Scalar (dot) product of vectors. 10.2.Cross product - its properties - area of a triangle, collinear vectors. 10.3.Scalar triple product - volume of a parallelopiped, co-planarity. 10.3.Scalar triple product - volume of a parallelopiped, co-planarity. 10.3.Scalar triple product - volume of a parallelopiped, co-planarity. 10.4.Proof of Formulae (Using Vectors) - Sine rule. 10.4.1.Cosine rule 10.4.2.Projection formula 10.4.3.Area of a ? = ½ ab sin C

# 11. Co-ordinate Geometry in 3-Dimensions

 (i) Lines - Cartesian and vector equations of a line through one and two points. I.1.Coplanar and skew lines. I.1.Coplanar and skew lines. I.2.Conditions for intersection of two lines. I.3.Shortest distance between two lines. (ii) Planes - Cartesian and vector equation of a plane. (ii) Planes - Cartesian and vector equation of a plane. II.1.Direction ratios of the normal to the plane. II.2.One point form. II.3.Normal form. II.4.Intercept form. II.5.Distance of a point from a plane. II.6.Angle between two planes, a line and a plane. II.7.Equation of a plane through the intersection of two planes

# 12. Probability

 12.1.Baye’s theorem; 12.2.theoretical probability distribution, 12.3.probability distribution function; 12.4.binomial distribution - its mean and variance.

# 13. Discount

 13.1.True discount; 13.1.True discount; 13.2.banker's discount; 13.3.discounted value; 13.4.present value; 13.5.Cash Discount 13.6. Bill of Exchange

# 14. Annuities

 14.1. Meaning 14.1. Meaning 14.2.formulae for present value and amount; 14.3.deferred annuity 14.4.applied problems on loans 14.5.sinking funds 14.6.scholarships. NOTE: Annuity due is required to be covered.

# 15. Linear Programming

 15.1.Introduction 15.2.definition of related terminology such as constraints 15.3.objective function 15.4.optimization 15.5.iso profit 15.6.iso cost lines 15.7. advantages of linear programming; limitations of linear programming; 15.8.application areas of linear programming 15.9.different types of linear programming (L.P.) 15.10.problems, mathematical formulation of L.P problems 15.11.graphical method of solution for problems in two variables 15.12.feasible and infeasible regions, feasible and infeasible solutions 15.12.feasible and infeasible regions, feasible and infeasible solutions 15.13.optimum feasible solution.

# 16. Application of derivatives in Commerce and Economics

 16.1.Cost function 16.2.average cost 16.3.marginal cost 16.4.revenue function and break even point.

# 17. Index numbers and moving averages

 17.1.Price index or price relative. 17.2.Simple aggregate method. 17.3.Weighted aggregate method. 17.4. Simple average of price relatives - Weighted average of price relatives (cost of living index, consumer price index).