SAT/GCSE Math & Competition Math Specialist | Visual & ADHD-Friendly Teaching | Deep Problem-Solving

The Tutor and Student worked through various calculus problems involving differentiation, including finding derivatives of complex functions, calculating tangent and normal lines, and applying these concepts to rates of change. They also explored optimization problems and related rates, with the student practicing problem-solving techniques for each. The lesson concluded with a plan to continue calculations for an optimization problem in the next session.

The Student and Tutor extensively practiced differentiation, focusing on exponential and logarithmic functions, including those with general bases. They applied chain, product, and quotient rules to various complex expressions, covering a wide range of academic problems. The plan for the next session is to continue solving the remaining practice problems and reinforce the learned concepts through more problem-solving exercises.

Student and Tutor conducted a comprehensive review of derivatives, covering the definition using limits, fundamental rules like the power, product, quotient, and chain rules, and derivatives of trigonometric and exponential functions. The Student actively practiced solving various problems, demonstrating strong understanding and quick application of the concepts. For future sessions, the Tutor plans to incorporate more practice questions, with the Student expressing a preference for algebraic learning over visual aids.

Student and Tutor reviewed the application of derivatives for optimization problems, practicing with a cylindrical can example to minimize surface area given a fixed volume. They also explored the meaning of the second derivative in determining concavity and applied first and second derivative tests to a polynomial function. The session concluded with a review of derivative rules for exponential and logarithmic functions and a plan to slow the class pace by dedicating the next three sessions to review.

Student and Tutor reviewed applications of derivatives, including finding tangent lines, analyzing particle motion (position, velocity, acceleration), and solving optimization problems. They practiced several exercises applying these concepts. The Tutor plans to send 2-3 homework questions for the Student to complete before the next session.

The Student and Tutor engaged in a detailed session on calculus, reviewing logarithmic properties and extensively practicing finding derivatives of natural logarithmic, exponential, and other base logarithmic functions. They also applied derivative rules to trigonometric functions and solved a practical problem involving particle motion. The Tutor inquired about the Student's plans for AP exams and potential interest in exploring other mathematical topics in the future.