### FSC Math Short Course Overview

The **FSC Math Short Course** is designed to assist students in the Pre-Engineering or ICS (Intermediate in Computer Science) streams who need a focused and concise review of the 1st and 2nd-year mathematics syllabus. The course covers essential concepts from both years, providing a comprehensive yet streamlined learning experience that prepares students for their final board exams.

### Course Objectives

- To reinforce key mathematical concepts in FSC Part 1 and Part 2.
- To provide concise and clear explanations of complex topics.
- To help students master important formulas and problem-solving techniques.
- To focus on exam-oriented preparation by covering high-priority topics.

### Topics Covered

This course covers critical topics from both FSC Part 1 (1st year) and FSC Part 2 (2nd year) mathematics syllabi.

#### FSC Part 1 (1st Year) Topics:

**Number Systems**- Real and complex numbers
- Operations on complex numbers
- De Moivre’s theorem

**Sets, Functions, and Groups**- Set theory: operations on sets
- Functions: types, domain, and range
- Binary operations and groups

**Quadratic Equations**- Methods of solving quadratic equations
- Discriminant and nature of roots

**Matrices and Determinants**- Types of matrices and basic operations
- Determinants and solving systems of equations using Cramer’s rule

**Sequence and Series**- Arithmetic and geometric progressions
- Summation of finite and infinite series

**Trigonometry**- Trigonometric identities and their applications
- Solution of trigonometric equations
- Inverse trigonometric functions

**Coordinate Geometry**- Cartesian plane, equations of lines, and circles
- Distance formula, midpoint formula, and slopes of lines

**Conic Sections**- Parabola, ellipse, and hyperbola: standard equations and properties

**Differentiation**- Limits and continuity
- Basic differentiation techniques
- Applications of differentiation (tangents, normals, rates of change)

**Integration**- Basic integration techniques
- Applications of integration (area under curves)

#### FSC Part 2 (2nd Year) Topics:

**Functions and Limits**- Types of functions and their limits
- Continuity and differentiability of functions

**Differentiation (Advanced)**- Product, quotient, and chain rules
- Higher-order derivatives
- Applications of differentiation in finding tangents, normals, and optimization

**Integration (Advanced)**- Techniques of integration (substitution, by parts)
- Definite and indefinite integrals
- Applications in calculating areas and volumes

**Differential Equations**- First-order and first-degree differential equations
- Solution methods and real-life applications

**Analytical Geometry**- Equations of straight lines, circles, and conics
- Ellipse, hyperbola: properties and equations
- Tangents and normals to curves

**Vector Algebra**- Vector operations: addition, subtraction, scalar multiplication
- Dot product and cross product
- Applications of vectors in geometry and physics

**Partial Fractions**- Decomposing algebraic expressions into partial fractions
- Applications in solving algebraic equations

**Probability and Statistics**- Basic probability theory
- Permutations, combinations, and their application in probability
- Central tendency: mean, median, mode, and dispersion

**Mathematical Induction and Binomial Theorem**- Principle of mathematical induction
- Expansion using the binomial theorem

**Application of Calculus**- Area under curves, volumes of solids of revolution
- Optimization problems using differentiation

### Course Duration

The **FSC Math Short Course** is designed to be completed within **2 to 3 months**, providing students with a comprehensive review of the entire syllabus while focusing on the most critical exam-related topics.

### Who Should Enroll?

This course is ideal for:

**Pre-Engineering**and**ICS students**in FSC Part 1 and Part 2 who are preparing for final board exams.- Students who need a fast-track review of the most important mathematical concepts.
- Learners who want to strengthen their problem-solving skills in calculus, algebra, and geometry.
- Students aiming to improve their exam scores through structured and focused preparation.

### Learning Outcomes

By the end of this short course, students will:

- Have a strong grasp of both basic and advanced mathematical concepts from both years of FSC.
- Be able to solve complex mathematical problems related to calculus, algebra, and geometry with confidence.
- Be well-prepared to handle both theoretical and application-based questions in their board exams.
- Develop analytical thinking and problem-solving skills that are critical for success in higher studies and professional exams.