Session 03-06 - Mock Exam 03

Section 03: Functions as Business Models

Dr. Nikolai Heinrichs & Dr. Tobias Vlćek

Welcome

Mock Exam Overview

Today’s Session

Mock Exam 03

  • Format: 90 minutes, 50 points covering Sections 01–03
  • Structure: 2 problems with progressive difficulty
  • Focus: Functions and their business applications
  • Permitted aids: non-programmable calculator, drawing instruments
  • Strategy: Apply systematic approaches to function problems

Time Management

  • Problem 1 (Business Application): ~45 minutes
  • Problem 2 (Function Analysis): ~45 minutes
  • Secure foundation points first, then tackle challenging parts

Success Strategies

Final reminders

  • Read carefully: Every word in the problem matters
  • Show all work: Partial credit is available
  • Label clearly: Units, variables, and graphs
  • Time management: Don’t get stuck on one part
  • Business sense: Results should be realistic

Remember

This exam tests your ability to model and solve business problems using functions. You have all the tools you need!

Coffee Break - 15 Minutes

Homework Presentations

Solutions from Tasks 03-05

20 minutes - discussion and questions

  • Show composition challenges
  • Discuss inverse function strategies
  • Share approaches to multi-step problems
  • Review any complex business models

Section 03 Review

Problem-Solving Framework

Apply this systematic approach

  1. Understand: Read carefully, identify given information
  2. Plan: Choose appropriate function model
  3. Execute: Apply formulas and techniques systematically
  4. Verify: Check mathematical and business validity
  5. Interpret: Explain meaning in context

Core Formulas I

Your essential toolkit

Linear Functions:

  • Slope-intercept: \(y = mx + b\)
  • Equilibrium: Set supply = demand
  • Break-even: \(R(x) = C(x)\)

Quadratic Functions:

  • Vertex: \(x = -\frac{b}{2a}\)
  • Vertex form: \(f(x) = a(x - h)^2 + k\)

Core Formulas II

Your essential toolkit

Transformations:

  • Vertical shift: \(f(x) + k\)
  • Horizontal shift: \(f(x - h)\)

Composition:

  • \((f \circ g)(x) = f(g(x))\)

Next Session

Next Session Preview

Session 04-01: Polynomial Functions

Advanced Functions Begin!

  • Discuss Mock Exam 03 solutions
  • Address any remaining Section 03 questions
  • Introduction to polynomial functions
  • Higher-degree optimization
  • Complex business modeling

After todays Exam

  • Review problems you found challenging
  • Prepare questions for next session