Pre-Calculus I (16-Week Course Outline)
Course Code:
Credit Hours: 3 (3+0)
Prerequisites: None
Course Learning Outcomes (CLOs):
At the end of the course, students will be able to:
- Understand the concept of functions, their properties, and graphical representations.
- Analyze and solve systems of equations and inequalities.
- Perform matrix operations and use matrices to solve linear systems.
- Apply the concept of determinants and understand their role in solving linear equations.
- Demonstrate understanding of trigonometric identities, functions, and their applications.
- Understand and apply the concepts of conic sections in various coordinate systems (parametric and polar).
16-Week Course Plan
Week 1: Introduction to Sets and Functions
- Defining sets, set representation, and operations
- Introduction to relations and functions
- Domain and range of functions
Assignments:
- Problem set on set operations
Week 2: Functions and Graphical Transformations
- Graphical transformations of one and two-dimensional functions
- Properties of functions
- Piecewise functions: definition and graphical representation
Quiz 1:
- Graphical transformations of functions
Week 3: Inverses, Continuity, and Discontinuity
- Composition of functions and inverse functions
- Continuity and discontinuity of functions
Assignments:
- Continuity and inverse function problems
Week 4: Polynomial Functions
- Polynomials and their properties
- Polynomial long division and synthetic division
- Zeros and intercepts of functions
Quiz 2:
- Polynomial properties and synthetic division
Week 5: Rational Functions and Asymptotes
- Rational functions and their properties
- Asymptotes: Horizontal, vertical, and oblique
Assignments:
- Asymptote identification and graphing problems
Week 6: Exponential and Logarithmic Functions
- Exponential functions and their properties
- Logarithmic functions and their properties
- Graphing exponential and logarithmic functions
Quiz 3:
- Exponential and logarithmic functions
Week 7: Systems of Equations (Part 1)
- Systems of two equations and two unknowns
- Solving systems using substitution and elimination methods
Assignments:
- Solving systems of linear equations
Week 8: Systems of Equations (Part 2)
- Systems of three equations and three unknowns
- Gaussian elimination and Cramer’s rule
Mid-term Exam
Week 9: Introduction to Matrix Algebra
- Matrix operations: addition, subtraction, multiplication
- Properties of matrices
- Introduction to row operations and row echelon forms
Quiz 4:
- Basic matrix operations
Week 10: Determinants and Matrix Inverses
- Determinants of matrices (2×2, 3×3, and higher-order)
- Inverse matrices and their applications
- Solving systems of equations using matrix inverses
Assignments:
- Determinants and inverse matrices problems
Week 11: Trigonometric Functions (Part 1)
- Angles in radians and degrees
- Right triangle trigonometry
- Law of cosines, law of sines, and area of a triangle
Quiz 5:
- Right triangle trigonometry
Week 12: Trigonometric Functions (Part 2)
- Graphs of trigonometric functions
- Graphs of inverse trigonometric functions
Assignments:
- Graphing trigonometric functions
Week 13: Trigonometric Identities
- Basic trigonometric identities: Pythagorean, sum and difference, double angle, and half angle
- Power-reducing identities
Quiz 6:
- Trigonometric identities
Week 14: Solving Trigonometric Equations
- Solving trigonometric equations using identities
- Applications of trigonometric equations in real-world problems
Assignments:
- Trigonometric equation solving problems
Week 15: Conic Sections
- Introduction to conic sections: Parabolas, ellipses, circles, and hyperbolas
- General form of a conic and degenerate conics
Quiz 7:
- Conic sections
Week 16: Parametric and Polar Coordinates
- Parametric equations and their graphs
- Polar coordinates and conversion between polar and rectangular coordinates
Final Exam Review
Teaching Methodology
- Lectures
- Written assignments
- Problem-solving sessions
- Group presentations
- Semester project on real-life applications of course concepts
Assessment Breakdown
- Mid-term Exam: 30%
- Assignments: 20%
- Quizzes: 10%
- Final Exam: 40%
Textbooks:
- Textbook of Algebra and Trigonometry, Class XI, Punjab Textbook Board, Lahore, Pakistan.
- Calculus and Analytic Geometry, Mathematics FSc Part 2, Punjab Textbook Board, Lahore, Pakistan.
Reference Materials:
- Gilbert, S. S., B. C. Andy, and B. Andrew, Linear Algebra and Its Applications, 4th Ed. Thomson Brooks/Cole, Belmont, CA, USA.
- Chung, S. K. (2014). Understanding Basic Calculus. Create Space Independent Publishing Platform.
- Howard, Anton, Irl Bivens, Stephen Davis. Calculus, 10th Ed. John Wiley & Sons, Inc., 2011.
This 16-week course outline ensures a logical flow of topics, allowing students to progressively build their understanding of Pre-Calculus concepts and apply them effectively.