Functions & Calculus, Functions & Trigonometry (SL Level)

• Optimization Problems with Functions

  • Investigate real-life scenarios that involve optimization using functions.

• Function Transformations and Applications

  • Study various function transformations (translations, reflections, stretches, etc.) and their applications. Investigate how these transformations affect the graphs of functions such as quadratic, cubic, exponential, or trigonometric functions. 

• Applications of Trigonometric Functions

  • Explore real-world applications of trigonometric functions, such as analyzing waveforms, sound waves, or periodic motion.

  • Investigate how sine, cosine, or tangent functions model these phenomena 

  • connections between the mathematical models and their real-life applications

• Function Composition and Inverse Functions

  • Investigate function composition and inverse functions in practical scenarios. Show how composite functions or inverses model real-life situations. 

• Modeling different real life scenarios using the different functions (linear, quadratics, rational, exponential and logarithmic)

  • projectile motions, optimization, motion and trajectories, interest rate and investments, chemistry reaction rates

Calculus + Modeling (SL Level) 

• study of optimization problems

  • maximum or minimum value of a function, subject to certain constraints. 

• differential calculus to determine the exact rate of growth in a bacterial culture when different variables such as temperature and food source are changed.

• quantifying building materials

  • calculus integration to calculate the amount of material required to complete a construction project

• calculus to calculate the area or volume of shapes of curved structures like domes, sports arenas, suspended bridges, etc

• building storm drains

  • Storm drains used to drain storm waters and open channels systems must have a surface area that is big enough and does not hinder the flow of water. Calculus is used to calculate the derivation of the basic fluid mechanics that has the optimum capacity for the drain.

• Astronomy

  • Calculus is used to calculate the rate at which position of moving bodies change over time to determine their orbits

• Business- credit card payment

  • set payment structures, they consider different variables such as changing interest rates and fluctuating balances to calculate the minimum amount due on a credit card.

• Analyzing Projectile Motion

  • Explore the motion of a projectile (like a thrown ball or a launched object) 

  • derive equations for the trajectory, maximum height, range, time of flight, and velocity components using differentiation and integration.