AP ECET 2023 Syllabus for Mathematics (For Diploma Holders)

ANNEXURE - I
ENGINEERING MATHEMATICS
(Common for all branches of Diploma in Engineering)
Unit-I:
Matrices:Matrices of 3rd order: Types of matrices-Algebra of matrices-Transpose of a matrix-
Symmetric, skew symmetric matrices-Minor, cofactor of an element-Determinant of a square
matrix-Properties-Laplace’s expansion-singular and non singular matrices-Adjoint and
multiplicative inverse of a square matrix-System of linear equations in 3 variables-Solutions by
Crammer’s rule, Matrix inversion method .
Partial Fractions: Resolving a given rational function into partial fractions.

Unit –II:
Trigonometry: Properties of Trigonometric functions – Ratios of Compound angles, multiple
angles, sub multiple angles – Transformations of Products into sum or differenceand vice
versa – Simple trigonometric equations – Properties of triangles – Inverse Trigonometric
functions.
Complex Numbers: Modulus and conjugate, arithmetic operations on complex number—
Modulus-Amplitude form (Polar form)-Euler form (exponential form)-Properties- De Movire’s
Theorem and its applications.

Unit – III : Analytical Geometry
Circles-Equation given center and radius-given ends of diameter-General equation-finding
center and radius. Standard forms of equations of Parabola, Ellipse and Hyperbola – simple
properties.

Unit – IV : Differentiation and its Applications
Functions and limits – Standard limits – Differentiation from the First Principles –
Differentiation of sum, product, quotient of functions, function of function, trigonometric,
inverse trigonometric, exponential, logarithmic, Hyperbolic functions, implicit, explicit and
parametric functions – Derivative of a function with respect to another function-Second order
derivatives –Geometrical applications of the derivative (angle between curves, tangent and
normal) – Increasing and decreasing functions – Maxima and Minima (single variable
functions) using second order derivative only – Derivative as rate measure -Errors and
approximations - Partial Differentiation – Partial derivatives up to second order – Euler’s
theorem.

Unit – V : Integration and Its Applications
Indefinite Integral – Standard forms – Integration by decomposition of the integrand of
trigonometric, algebraic, exponential, logarithmic and Hyperbolic functions – Integration by
substitution – Integration of reducible and irreducible quadratic factors – Integration by parts
– Definite Integrals and properties, Definite Integral as the limit of a sum – Application of
Integration to find areas under plane curves and volumes of Solids of revolution – Mean and
RMS value.

Unit – VI: Differential Equations
Definition of a differential equation-order and degree of a differential equation- formation of
differential equations-solution of differential equation of the type first order, first degree,
variable-separable, homogeneous equations, exact, linear differential equation of the form
dy/dx + Py = Q, Bernoulli’s equation, nth order linear differential equation with constant

coefficients both homogeneous and non homogeneous and finding the Particular Integrals for
the functions , , Sin ax, Cos ax.

ANNEXURE - II
MATHEMATICS (Common Syllabus)

Number of Questions to be Set Unit Wise (Total 50)

UNIT NO TOPICS MARKS
Matrices 05
I
Partial Fractions 02
Trigonometry 10
II
Complex numbers 02
III Analytical geometry 06
IV Differentiation and its applications 10
V Integration and its applications 08
VI Differential equations 07
TOTAL 50

ANNEXURE - III
MODEL QUESTIONS FOR MATHEMATICS

1. The maximum value of 5+8Cos +6Sin is
1) 25
2) 19
3) 15
4) 5

2. The value of Cos100Cos500Cos700 is
1)

2)

3)

4)

3. If Sec2 then the general solution

1) 2nπ ±

2) nπ ±

3) nπ ±
4) 2nπ ±
4. The eccentricity of the ellipse 3x2 +2y2 =6 is
1)
2)

3)

4)

5.

1)
2) e-2

3)
4) e-1