Learning Outcomes

Logic and Set:
 Be acquainted with logical connectives and construct truth tables.
 Prove set identities
 Define interval and absolute value of real numbers
 Find domain and range of a function.
 Find inverse function and calculate composite function of given functions.
 Define odd and even functions, periodicity of a function, monotonicity of a function
 Sketch graphs of Quadratic, Cubic and rational functions of the form \( \frac{1}{ax+b}\) where \(a \ne 0\) trigonometric ( \( a \sin bx ,a \cos bx)\), exponential (\(e^x\)), logarithmic function (\(\ln x, \log x\)).
 Define and classify sequence and series
 Solve the problems related to arithmetic, geometric and harmonic sequences and series
 Establish relation among A.M, G. M and H.M.
 Find the sum of infinite geometric series .
 Obtain transpose of matrix and verify its properties.
 Calculate minors, cofactors, adjoint, determinant and inverse of a square matrix
 Solve the problems using properties of determinants
 Define polynomial function and polynomial equation.
 State and apply fundamental theorem of algebra.
 Find roots of a quadratic equation and establish the relation between roots and coefficient.
 Form a quadratic equation with given roots.
 Define a complex number and solve the problems related to algebra of complex numbers.
 Find conjugate and absolute (modulus) value of a complex numbers and verify their properties
 Find square root of a complex number.
Real numbers:
Function:
Curve sketching:
Sequence and series:
Matrices and determinants:
Quadratic equation:
Complex number:
Scope and Sequence of Contents
1: Algebra (44)
 Logic and Set: Statements, logical connectives, truth tables, theorems based on set operations.
 Real numbers: Geometric representation of real numbers, interval,absolute value
 Function: Domain and range of a function, Inverse function, composite function, introduction of functions; algebraic (linear, quadratic & cubic), Transcendental (trigonometric, exponential, logarithmic)
 Curve sketching: Odd and even functions, periodicity of a function, symmetry (about origin, Xand Yaxis),monotonicity of a function, sketching the graphs of Quadratic, Cubic and rational functions of the form \(\frac{1}{ax+b}\) where \(a \ne 0\), Trigonometric (\(a \sin bx ,a \cos bx\)), exponential (\(e^x\)), logarithmic function (\( \ln x \))
 Sequence and series: Arithmetic, geometric, harmonic sequences and series and their properties A.M, G.M, H.M and their relations, sum of infinite geometric series
 Matrices and determinants: Transpose of a matrix and its properties, Minors and cofactors, Adjoint, Inverse matrix, Determinant, Properties of determinants (without proof)
 Quadratic Equation: Nature and roots of a quadratic equation, Relation between roots and coefficient. Formation of a quadratic equation, Symmetric roots, one or both roots common
 Complex number: Imaginary unit, algebra of complex numbers, geometric representation, absolute (Modulus) value and conjugate of a complex numbers and their properties, square root of a complex number.
2: Trigonometry (12)
 Inverse circular functions.
 Trigonometric equations and general values
3: Analytic Geometry (20)
 Straight Line: Length of perpendicular from a given point to a given line, Bisectors of the angles between two straight lines.
 Pair of straight lines: General equation of second degree in x and y, condition for representing a pair of lines, Homogenous seconddegree equation in x and y, angle between pair of lines, Bisectors of the angles between pair of lines
 Coordinates in space:Points in space,distance between two points, direction cosines and ratios of a line
4: Vectors (12)
 Collinear and non collinear vectors, coplanar and noncoplanar vectors, linear combination of vectors, Linearly dependent and independent
5:Statistics and Probability (12)
 Measure of Dispersion: Standard deviation, variance, coefficient of variation, Skewness, Karl Pearson's coefficient of skewness
 Probability:Independent cases, mathematical and empirical definition of probability, two basic laws of probability (without proof).
6:Calculus (48)
 Limits and continuity: Limits of a function, indeterminate forms. algebraic properties of limits (without proof), Basic theorems on limits of algebraic, trigonometric, exponential and logarithmic functions, continuity of a function, types of discontinuity, graphs of discontinuous function
 Derivatives: Derivative of a function, derivatives of algebraic, trigonometric, inverse of trigonometric, exponential and logarithmic functions by definition (simple forms), rules of differentiation. derivatives of parametric and implicit functions, higher order derivatives, geometric interpretation of derivative, monotonicity of a function, interval of monotonicity, extreme values of a function, concavity, points of inflection
 Antiderivatives:Integration using basic integrals,integration by substitution and by parts methods, the definite integral, the definite integral as an area under the given curve, area between two curves
7:Computational Methods (12) or Mechanics
 System of linear equations: Gauss Elimination Method, Gauss Seidel Method
 Linear programming problems (LPP): simplex method (two variables only)
7:Mechanics(12) or Computational Methods
 Statics: Triangle law of forces and Lami's theorem
 Newton's laws of motion and projectile
Sample project works/practical works for grade 12
 Take a square of arbitrary measure assuming its area is one square unit. Divide it in to four equal parts and shade one of them. Again take one not shaded part of that square and shade one fourth of it. Repeat the same process continuously and find the area of the shaded region.
 Truth values of conjunction and disjunction using logic gate circuit
 Write two simple statements related to mathematics and write four compound statements by using them.
 Prepare a model to illustrate the values of sine function and cosine function for different angles which are multiples of \(\pi/2,\pi\).
 Prepare a model to explore the principal value of the function \(\sin^{–1} x\) using a unit circle and present in the classroom.
 Draw the graph of \(\cos^{–1} x\), using the graph of cosx and demonstrate the concept of mirror reflection (about the line y = x).
 Derive the length of perpendicular from (h, k) to line ax+by+c=0
 Derive the condition that general equation of second degree x and y represent pair of line.
 Verify that the equation of a line passing through the point of intersection of two lines \(a_1x + b_1y + c_1 = 0\) and \(a_2x + b_2y + c_2 = 0\) is of the form \((a_1x + b_1y + c_1) + K(a_2x + b_2y + c_2) = 0.\)
 Prepare a model and verify that angle in a semicircle is a right angle by using vector method.
 Collect the scores of grade 10 students in mathematics and English from your school. a. Make separate frequency distribution with class size 10.b. Which subject has more uniform/consistent result?c. Make the group report and present.
 Roll two dices simultaneously 20 times and list all outcomes. Write the events that the sum of numbers on the top of both dice is (a) even (b) odd in all above list. Examine either they are mutually exclusive or not. Also find the probabilities of both events.
 Search the application of derivative in our daily life with example.
 Find the area of circular region around your school using integration.
 Take a metallic bar available at your surrounding and make a rectangular frame. Find the dimension of the rectangular metallic frame with maximum area.
 Find the roots of any polynomial equation by using any ICT tools and present it in the classroom.
 Correlate the trapezoidal rule and Simpson rule of numerical integration with suitable example.
 Find the daily life problem related to motion of a particle in a straight line and solve that problem.
Student Assessment
Evaluation is an integral part of learning process. Both formative and summative evaluation system will be used to evaluate the learning of the students. Students should be evaluated to assess the learning achievements of the students. There are two basic purposes of evaluating students in Mathematics: first, to provide regular feedback to the students and bringing improvement in student learningthe formative purpose; and second, to identify student's learning levels for decision making.
a. Internal evaluation
Internal assessment includes classroom participation, terminal examinations, and project work/practical work (computer works and lab work) and presentation. The scores of evaluation will be used for providing feedback and to improve their learning. Individual and group works are assigned as projects.
The basis of internal assessment is as follows:Classroom participation  Marks from terminal examinations  project work/practical work  Total 
3  6  16  25 
The mark for classroom participation is 3 which is given on the basis of attendance and participation of students in activities in each grade.
(ii) Marks from trimester examinationsMarks from each trimester examination will be converted into full marks 3 and calculated total marks of two trimesters in each grade.
(iii) Project work/practical workEach Student should do at least one project work/practical work from each of seven content areas and also be required to give a 15 minutes presentation for each project work and practical work in classroom. These seven project works/practical works will be documented in a file and will be submitted at the time of practical evaluation. Out of seven projects/practical works from each area any one project work/practical work should be presented at the time of practical evaluation by student.
b. Final/External Examination
Final/external evaluation of the students will be based on the written examination at the end of each grade. It carries 75 percent of the total weightage. The types and number questions will be as per the test specification chart developed by the Curriculum Development Centre.
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