Key Topics for 12th Math in MHT CET

Algebra
- Quadratic Equations: Roots, nature, and graphical representation.
- Polynomials: Remainder and factor theorem, sketching curves.
- Sequences and Series: Arithmetic and geometric progressions, sum formulas.
Calculus
- Limits and Continuity: Definition, properties, and types of limits.
- Differentiation: Rules, applications in maxima and minima, and tangents.
- Integration: Definite and indefinite integrals, properties, and applications.
Trigonometry
- Trigonometric Ratios: Definitions, identities, and equations.
- Inverse Trigonometric Functions: Concepts and properties.
- Applications: Height and distance problems, angles of elevation and depression.
Coordinate Geometry
- Straight Lines: Slope, intercept form, and equations of lines.
- Conic Sections: Circle, parabola, ellipse, and hyperbola properties and equations.
- Distance and Area: Formulae for distance between points and area of triangles.
Vectors and 3D Geometry
- Vector Operations: Addition, subtraction, dot and cross products.
- 3D Coordinates: Distance, section formula, and equations of lines and planes.
Statistics and Probability
- Measures of Central Tendency: Mean, median, mode.
- Dispersion: Range, variance, and standard deviation.
- Probability: Basic concepts, conditional probability, and Bayes' theorem.
Matrices and Determinants
- Types of Matrices: Row, column, square, and zero matrices.
- Determinants: Calculation and properties, applications in solving linear equations.
- Inverse of a Matrix: Methods and applications in linear algebra.
Linear Programming
- Formulation: Identifying constraints and objective functions.
- Graphical Method: Solving and interpreting feasible regions and optimal solutions.
Complex Numbers
- Representation: Polar and rectangular forms.
- Operations: Addition, subtraction, multiplication, and division.
- De Moivre's Theorem: Applications in finding powers and roots.

Exam Preparation Tips

Practice previous years' question papers.
Focus on time management during the exam.
Understand concepts rather than memorizing formulas.
Use graphical representations where applicable to visualize problems.
Revise key formulas and theorems regularly.

Algebra

Quadratic Equations: Analyze roots using the discriminant; understand nature (real, equal, complex) and sketch the graphical representation of parabolas.
Polynomials: Utilize Remainder and Factor Theorem for polynomial evaluation; practice sketching polynomial curves based on roots and behavior at infinity.
Sequences and Series: Master the formulas for sums of arithmetic (AP) and geometric progressions (GP), recognizing their respective patterns and applications.

Calculus

Limits and Continuity: Grasp the foundational definition of limits, explore properties (limit laws), and differentiate between types, including one-sided limits.
Differentiation: Apply derivative rules (product, quotient, chain) for functions; find maxima and minima to solve optimization problems and determine tangents.
Integration: Distinguish between definite and indefinite integrals; utilize properties like the Fundamental Theorem of Calculus, and understand applications in area calculation and accumulation.

Trigonometry

Trigonometric Ratios: Learn definitions and key identities (Pythagorean, reciprocal, quotient); solve trigonometric equations systematically.
Inverse Trigonometric Functions: Understand concepts and properties for reversibility and useful identities; practice applying them in equations.
Applications: Solve practical problems involving heights and distances using angles of elevation and depression with appropriate trigonometric models.

Coordinate Geometry

Straight Lines: Explore slope-intercept forms and general equations; interpret line behavior through graphical representations.
Conic Sections: Study properties and equations of circles, parabolas, ellipses, and hyperbolas; relate geometric definitions to algebraic forms.
Distance and Area: Apply distance formula between two points; derive area of triangles using determinants or base-height methods.

Vectors and 3D Geometry

Vector Operations: Perform operations (addition, subtraction) and calculate dot (scalar) and cross (vector) products; understand their geometric interpretations.
3D Coordinates: Calculate distance and apply section formula in three-dimensional space; express equations for lines and planes.

Statistics and Probability

Measures of Central Tendency: Calculate mean, median, and mode; recognize their significance in data interpretation.
Dispersion: Evaluate the range, variance, and standard deviation; understand their roles in data spread analysis.
Probability: Familiarize with core concepts, including conditional probability; apply Bayes' theorem for complex probability scenarios.

Matrices and Determinants

Types of Matrices: Identify and categorize matrices (row, column, square, zero) based on dimensions and applications.
Determinants: Calculate determinants using various methods; apply properties for solving linear equations through Cramer’s rule.
Inverse of a Matrix: Learn methods to find matrix inverses (adjoint, row reduction) and their significance in solving linear systems.

Linear Programming

Formulation: Define constraints and objective functions clearly; ensure correct mathematical representation of real-world scenarios.
Graphical Method: Solve linear inequalities graphically; interpret feasible regions and determine optimal solutions based on intersection points.

Complex Numbers

Representation: Understand polar vs. rectangular forms of complex numbers; establish a connection between these representations.
Operations: Perform addition, subtraction, multiplication, and division on complex numbers; interpret results geometrically.
De Moivre's Theorem: Utilize this theorem for finding powers and roots of complex numbers, enhancing understanding of transformations.

Exam Preparation Tips

Regularly practice previous years' question papers; familiarize with exam format and frequently tested topics.
Prioritize time management techniques during practice sessions to improve overall efficiency and performance.
Focus on conceptual understanding over rote memorization of formulas; this aids in better application during exams.
Incorporate graphical representations where applicable to enhance problem visualization and comprehension.
Continuously revise key formulas and theorems to solidify understanding and recall under exam conditions.