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

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.

The Tutor and Student reviewed logarithmic and exponential functions, focusing on properties, solving equations and inequalities, and finding inverse functions. They applied these concepts to various practice problems and word problems, including a bacterial growth model and a linear cost function. They plan to continue with another session later.

Student and Tutor practiced solving equations involving logarithms and exponential functions, applying properties to simplify expressions and find unknown variables. They also worked on solving a quadratic equation as part of a logarithmic problem and reviewed the importance of checking solutions against the logarithm's domain. The next session will explore additional logarithm rules and derivatives of logarithms.

Student and Tutor reviewed and practiced solving problems involving common and natural logarithms, including their properties and the power rule. They focused on solving both logarithmic and exponential equations, emphasizing the importance of domain checks. The Tutor offered to prepare materials explaining the significance of base *e* for future discussion.