Solving Real-world Problems Involving Functions (including Modelling) Interactive Videos

Explore the differentiation of trigonometric functions and their applications in calculus. Focus includes solving for tangents and analyzing oscillating behaviors, with an emphasis on mastering the chain rule and identifying common errors. Develop skills to handle complex mathematical challenges with confidence.

Explore exponential functions with a focus on initial amounts, growth and decay rates, and their real-life applications. Enhance understanding of exponential growth and decay, develop problem-solving abilities, and distinguish between linear and exponential scenarios.

Explore cubic functions with a focus on examining stationary points, analyzing end behavior, and understanding root characteristics. Gain insights into identifying and interpreting crucial features of cubic functions to enhance problem-solving abilities in polynomial equations.

Explore the differentiation of logarithmic and exponential functions by mastering principles such as the power property and the application of the product rule. Gain an understanding of deriving derivatives for various bases, enhancing problem-solving skills in calculus.

Explore the application of complex numbers in solving puzzles within discrete mathematics, particularly in relation to subset sums and generating functions. Gain an understanding of how generating functions serve as tools for encoding mathematical problems. Discover the ways in which complex numbers provide deep insights into discrete mathematics challenges. Develop skills in mathematical problem-solving and theoretical analysis through the integration of complex numbers and generating functions.

Explore the application of function composition in real-world scenarios, such as using coupons in restaurants. Understand how the order of applying discounts affects outcomes and develop strategies to maximize savings.

Explore key optimization concepts in calculus, focusing on the identification of maxima and minima within various functions. Develop skills in the application of calculus, enhancing the understanding of geometric optimization problems, and recognizing the significance of critical points in function analysis.

Gain an understanding of the fundamental principles of function notation and the evaluation of linear and non-linear functions. Develop the ability to translate equations into function notation, calculate outputs based on specific inputs, and interpret mathematical relationships. These skills are crucial for enhancing mathematical reasoning and problem-solving capabilities.

Explore linear functions through equations, graphs, and tables. Develop skills in identifying and interpreting variable relationships, analyzing graph characteristics, and applying linear function concepts to real-world situations.

Explore the application of differential equations in modeling real-world physical systems with a focus on using unit step functions to address sudden changes. Gain proficiency in constructing functions with multiple discontinuities and applying the Laplace transform to analyze shifts, thereby enhancing mathematical modeling skills.

Explore numerical integration with the trapezoidal rule, focusing on estimating areas under curves and solving practical problems such as water accumulation. Strengthen understanding of calculus applications and improve skills in estimating and evaluating integrals across various scenarios.

Explore the potential of gaming to enhance problem-solving skills and apply these techniques to address real-world challenges. Learners will discover how gaming can be leveraged to navigate complex issues while cultivating skills such as urgent optimism and blissful productivity.

Explore geographical relationships and navigational course angles between locations such as Milwaukee and Grand Haven. Gain skills in interpreting trigonometric functions in maritime navigation, enhancing geographical spatial awareness. Apply trigonometric concepts to practical navigation, developing abilities to determine angles, courses, and paths in real-world scenarios.

Explore mathematical functions with a special emphasis on area calculations and their applications in real-world scenarios. Learners will develop skills in interpreting graphs, assessing substance quantities over time, and using formulas to calculate areas, enhancing their understanding and analytical capabilities in mathematics.

Explore advanced calculus concepts by mastering the application of the Chain Rule, Product Rule, and Quotient Rule. The focus is on enhancing problem-solving skills and gaining insights into evaluating derivatives of complex functions. Learners will determine equations of tangent lines, fostering a comprehensive understanding of these core calculus principles.

Explore the use of trigonometry to find missing angles in right triangles, integrating skills such as diagram labeling, setting up trigonometric ratios with SOHCAHTOA, and employing inverse functions. Develop the ability to solve for angles in both mathematical and real-world problems, enhancing problem-solving and analytical skills through practical application.

Explore how graph theory can be applied to logical reasoning challenges, specifically in identifying individuals based on provided statements. Enhance critical thinking and gain insights into applying mathematical concepts effectively in real-world contexts.

Explore the use of quadratic functions in optimizing revenue, illustrated through real-life examples such as adjusting movie theater ticket prices. Learn to identify the vertex of a quadratic graph and comprehend its importance in maximizing outcomes across various scenarios.

Explore the application of arithmetic progressions to solve real-world problems by understanding how evenly spaced deposits relate to arithmetic sequences. Achieve skills in pattern identification, calculating total distances using arithmetic progression formulas, and applying these concepts to practical scenarios.

Investigate the principles of inverse and direct variation through identifying formulas and solving problems. Develop the ability to differentiate between types of variation and calculate constants, enhancing comprehension of mathematical relationships in real-world contexts.