Course Title:

Pre Calculus  – Foundations for Calculus and Beyond

Course Overview:

• Think of precalculus as the vital link connecting the maths you've already learnt in algebra and geometry to the exciting challenges of calculus and beyond! 

• More than just learning new topics, this course is about actively developing the strong mathematical understanding and sharp analytical skills you'll need to thrive in those advanced subjects. 

• By diving deeper into mathematical concepts and honing your ability to think critically, precalculus builds a solid foundation, directly preparing you for success in calculus, physics, and various applied math fields. 

• It's about getting truly ready for what comes next!

Course Outline:

>> Your Pathway to Calculus and STEM Adventures!

• Pre Calculus  is your essential guide, seamlessly connecting the algebra and trigonometry you already know to the exciting challenges of calculus and advanced fields like science, technology, engineering, and mathematics (STEM).

• This course offers a clear and step-by-step exploration of key mathematical ideas, building a robust foundation for your future studies.

>> What You'll Master:

• A deep and meaningful understanding of core mathematical concepts, including functions, trigonometry, exponential and logarithmic expressions, and analytic geometry.

• The ability to think logically and apply mathematical reasoning to solve practical, real-world problems you might encounter in various aspects of life and other subjects.

• An insightful introduction to the foundational concepts of calculus, giving you a significant advantage as you move into higher-level math courses.

>> Why Precalculus is Your Ideal Choice:

• Flexible and Adaptable:                                                                                                                  The course's modular design can be tailored to different learning styles and teaching approaches, ensuring a good fit for everyone.

• Crystal-Clear Explanations:                                                                                                       

We prioritize making complex ideas understandable with rich examples and easy-to-follow, step-by-step solutions.

• Relevant and Inclusive:                                                                                                                  

The material has been carefully reviewed to incorporate diverse perspectives, making the math relatable and engaging for students from all backgrounds.

• Trusted Accuracy:                                                                                                       

You can rely on the fact that every part of the course has been thoroughly checked by experts for correctness and clarity.

>> Who Will Benefit Most from This Course:

• High school seniors and first-year college/junior college students setting their sights on calculus or STEM-related programs.

• Learners who are seeking a well-structured and easy-to-navigate path through advanced mathematical concepts.

• Instructors who value rigorous, engaging, and inclusive materials that empower students to succeed.

• Precalculus empowers you to see the interconnectedness of mathematical ideas and makes the journey into higher-level math more approachable, relevant, and ultimately, more successful.

Course Objectives:

>> Vision Statement:

• To empower every student to become a mathematically empowered individual who approaches calculus, STEM fields, and real-world problems with confidence, competence, and a critical mindset.

>> Mission Statement:

• To guide all learners, no matter their background, through a clear, welcoming, and challenging precalculus experience. 

• We achieve this by weaving together deep conceptual understanding, sharp analytical skills, and relevant real-life applications within an engaging and supportive learning community, setting them firmly on a transparent and rigorous path.

>> Smart Goals:

• Function Mastery:                                                                                             

Students will understand and apply the properties and behavior of a variety of functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions, demonstrated by achieving 80%+ on unit assessments and problem sets related to these function types.

• Real-World Problem Solving:                                                                                             

Students will accurately solve complex, multi-step real-world problems using appropriate algebraic strategies, as demonstrated through consistent success in applied tasks and project-based assessments.

• Calculus Foundations:                                                                                              

Students will demonstrate a foundational understanding of the concepts of limits and introductory calculus by completing the final module assessment and a reflection journal on these topics.

• Conceptual Fluency & Application:                                                                                     

Students will demonstrate conceptual fluency, analytical thinking, and application skills through individual and group assessments, achieving a minimum average score of 80% across these evaluations.

• Course Completion Timeline:                                                                                              

Students will complete the course within a timeframe of 12–16 weeks, allowing for flexibility in pacing and individual learning styles.

• Function Skill Development:                                                                                              

Supported by clear examples, DEI-focused scenarios, and scaffolded practice, students will master the properties and behavior of different functions within the first 60–75 hours of coursework.

• Complex Problem Solving Proficiency:                                                                             

Reinforced by practice exercises, instructor guidance, and peer collaboration, students will master the ability to solve complex, multi-step equations and real-world word problems by the 100-hour mark.

• Calculus Readiness:                                                                                                   

Understanding and applying various functions and solving real-world problems builds readiness for calculus, physics, and applied math fields.

• STEM Application:                                                                                                                 

Accurately solving complex problems is essential for success in science, technology, and engineering coursework.

• Elementary Calculus Transition (120 to 150 hours):                                           

Demonstrating foundational understanding of limits and introductory calculus directly supports the transition into Calculus I or equivalent, to be completed within 120–150 total learning hours, integrated through conceptual activities and visual representations.