April 2023 Math Advanced Lecture for Year 11

Introduction

• Lecturer: Cisha
• Company: AAR Notes
  • Established in-person lectures at UTS from 2016-2019.
  • Shifted to online lectures in 2020, expanded reach.
  • Currently trying pre-recorded lectures, with live Q&A.
• Free resources offered by AAR Notes: lectures, forums, newsletters, ATAR calculator.
• Paid resources: T Smart tutoring, study guides, Ed Unlimited.

Personal Introduction

• Cisha graduated in 2021 with an ATAR of 95.85.
• Subjects: Math Advanced, Extension 1, Chemistry, Physics, DT, English Advanced.
• Currently studying Veterinary Science.
• Hobbies: Animal fostering, rock climbing.

Lecture Overview

• New content will focus on introduction to calculus.
• Topics include differentiation, rules of differentiation.
• Aim to eliminate silly mistakes by using structured problem-solving techniques.

Frequently Asked Questions

1. Study Time for Math: No set answer, varies by student.

   • Advise: Do math homework first after school, reflect on mistakes.
   • Advise studying 6 hours a week, excluding homework.

2. Study Method for Math: Reflect on mistakes, use a mistake diary.

   • End of week review of new and old content.
   • Use past papers and topic tests for practice.

3. Considering Dropping to Standard Math:

   • Don't drop due to difficulty; drop if you dislike advanced math content.
   • Standard math might be harder due to application-focused questions.

4. Avoiding Silly Mistakes: Use the framing technique.

   • Steps: Read questions carefully, recall formulas, solve methodically, check answers.

Study Techniques

• Mind Maps: Visualize connections between concepts.
• Hierarchical Maps: Organize information from broad to specific.
• Consistent Practice: Regular review and practice to solidify understanding.

Differentiation

• Notation: f'(x), y', dy/dx.
• Continuous Functions: No holes, asymptotes, or jumps.
• Differentiation by First Principles: Formula explained, example provided.
• Basic Differentiation Rules
  • Power rule: f(x) = x^n, f'(x) = nx^(n-1).
  • Sum rule: Differentiate terms separately.
  • Constant multiple rule: Constant coefficients remain in derivatives.
• Finding Gradient: Use derivative function to find gradient at specific points.

Differentiation Rules

• Product Rule: For functions multiplied together.

  • Formula: y' = vu' + uv'.
  • Example given.

• Chain Rule: For composite functions.

  • Formula: y' = nf'(x)[f(x)]^(n-1).
  • Example given.

• Quotient Rule: For functions divided by one another.

  • Formula: y' = (vu' - uv')/v^2.
  • Example given.

Tangents and Normals

• Tangent: Line that touches curve at one point, same slope as the curve.
• Normal: Line perpendicular to the tangent.
• Gradient of Normal: Negative reciprocal of tangent gradient.
• Point-Gradient Formula: y - y1 = m(x - x1) for finding equation of tangent or normal.
• Examples provided to find tangents and normals.

Study Tips

1. Ask Questions: Clarify doubts immediately.
2. Diversify Resources: Use textbooks, past papers, topic tests.
3. Create Formula Sheets: Highlight important formulas, especially those not on official sheets.
4. Be Consistent: Regular practice ensures skill retention.

Exam Tips

• Reading Time: Skim through the paper to allocate time effectively.
• Mark Maximization: Write something for every question, use framing technique.
• Stay Calm: Maintain focus and confidence throughout the exam.

---

Lecture concluded with a reminder to enjoy the holidays and prepare for the next term.