Grade 12 Mathematics

Unit 1: Algebra (44)

  1. Permutation and combination
    1. Basic principle of counting
    2. Permutation of (a) set of objects all different (b) set of objects not all different (c) circular arrangement (d) repeated use of the same objects
    3. Combination of things all different, Properties of combination
  2. Binomial Theorem
    1. Binomial theorem for a positive integer, general term, Binomial coefficient
    2. Binomial theorem for any index (without proof), application to approximation
    3. Euler's number, Expansion of \( e^x,a^x \log(1+x)\) (without proof)
  3. Complex numbers
    1. Polar form of complex numbers
    2. De Moivre's theorem and its application in finding the roots of a complex number
    3. Properties of cube roots of unity
    4. Euler's formula
  4. Sequence and series
    1. Sum of finite natural numbers, sum of squares of first n-natural numbers, Sum of cubes of first n-natural numbers
    2. principle of mathematical induction and use it to find sum.
  5. Matrix based system of linear equation
    1. Solution of a system of linear equations by Cramer's rule up to three variables
    2. Solution of a system of linear equations by matrix method (row-equivalent and inverse) up to three variables

Unit 2: Trigonometry (12)

  1. Properties of a triangle (Sine law, Cosine law, tangent law, Projection laws, Half angle laws)
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  2. Solution of triangle (simple cases)
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Unit 3: Analytic Geometry (20)

  1. Conic section:
    1. Condition of tangency of a line at a point to the circle
    2. Tangent and normal to a circle
    3. Standard equation of parabola, equations of tangent and normal to a parabola at a given point
    4. Standard equations of Ellipse and hyperbola

Unit 4: Vectors (12)

  1. Product of Vectors: Scalar product of two vectors, angle between two vectors, geometric interpretation of scalar product, properties of scalar product, application of scalar product in geometry and trigonometry, vector product of two vectors, geometrical interpretation of vector product, properties of vector product, application of vector product in geometry and trigonometry.
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Unit 5:Statistics and Probability (12)

  1. Correlation and Regression: Correlation, nature of correlation, correlation coefficient by Karl Pearson's method, interpretation of correlation coefficient, properties of correlation coefficient (without proof), rank correlation (only elementary concept), regression equation, regression line of y on x and x on y
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  2. Probability: Dependent cases, conditional probability (without proof).
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Unit 6:Computational Methods (12) or Mechanics

  1. Numerical computation: Roots of algebraic and transcendental equation (bisection and Newton-Raphson method)
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  2. Numerical integration:Trapezoidal rule and Simpson's rule
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Unit 7:Mechanics(12) or Computational Methods

  1. Statics: Forces and resultant forces, parallelogram law of forces, composition and resolution of forces, Resultant of coplanar forces acting on a point.
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  2. Dynamics: Motion of particle in a straight line, Motion with uniform acceleration, motion under the gravity, motion down a smooth inclined plane.
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Math 12 Curriculum

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