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Unit

Major learning outcomes
(in the cognitive domain)

Topics and Sub-topics

Unit - I

Algebra

1. Solve the given simple problem based on laws of the logarithm.

1b. Calculate the area of the given triangle by the determinant method.

1. Solve given system of linear equations using matrix inversion method and by Cramer’s rule.
2. Obtain the proper and improper partial fraction for the given simple rational function.

1.1 Logarithm: Concept and laws of logarithm

1.2 Determinant and matrices

a. Value of determinant of order 3x3

b. Solutions of simultaneous equations in three unknowns by Cramer’s rule.

c. Matrices, algebra of matrices, transpose adjoint, and inverse of matrices. Solution of simultaneous equations by matrix inversion method.

d. Types of partial fractions based on nature of factors and related problems.

Unit - II

Trigonometry

2a. Apply the concept of Compound angle, allied angle, and multiple angles to solve the given simple engineering problem(s).

1. Apply the concept of Submultiple angle to solve the given simple engineering-related problem(s).
2. Employ the concept of factorization and de-factorization formulae to solve the given simple engineering problem(s).
3. Investigate given simple problems utilizing inverse trigonometric ratios.

2.1Trigonometric ratios of Compound, allied, multiple, and sub-multiple angles (without proofs)

2.2Factorization and de-factorization formulae(without proofs)

2.3Inverse trigonometric ratios and related problems.

2.4Principle values and relation between trigonometric and inverse trigonometric ratio.

Unit - III

Coordinate Geometry

1. Calculate the angle between the given two straight lines.
2. Formulate an equation of straight lines related to given engineering problems.
3. Identify perpendicular distance from the given point to the line.
4. Calculate perpendicular distance between the given two parallel lines.

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3.1 Straight line and slope of straight line

a.   The angle between two lines.

b. Condition of parallel and perpendicular lines.

3.2            Various forms of straight lines.

a.   Slope point form, two-point form.

b.   Two points intercept form.

c.   General form.

d.   Perpendicular distance from a point on the line.

e.   Perpendicular distance between two parallel lines.

Unit - IV

Mensuration

4a. Calculate the area of the given triangle and circle.

4b. Determine the area of the given square, parallelogram, rhombus, and trapezium.

4c. Compute surface area of given cuboids, sphere, cone, and cylinder.

4d. Determine the volume of given cuboids, sphere, cone, and cylinder.

4.1Area of regular closed figures, Area of triangle, square, parallelogram, rhombus, trapezium, and circle.

4.2Volume of cuboids, cones, cylinders, and spheres.

Unit - V

Statistics

1. Obtain the range and coefficient of range of the given grouped and ungrouped data.
2. Calculate the mean and standard deviation of discrete and grouped data related to the given simple engineering problem.

5c. Determine the variance and coefficient of variance of given grouped and ungrouped data.

1. Justify the consistency of given simple sets of data.

5.1Range, coefficient of range of discrete and grouped data.

5.2Mean deviation and standard deviation from the mean of grouped and ungrouped data, weighted means

5.3Variance and coefficient of variance.

5.4Comparison of two sets of observations.