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

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.

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.

The Student and Tutor reviewed the concept of inverse functions and proved why the symmetry line is y=x. They then introduced logarithmic functions as inverses of exponential functions, practicing conversions between forms and understanding graphical properties, domain restrictions, and vertical asymptotes. The product rule for logarithms was also introduced, and the next session will cover additional logarithmic rules and derivatives.

Student and Tutor covered exponential functions, including their definition, universal formula, and the distinction between growth and decay. They explored the properties of the mathematical constant 'e' and practiced finding derivatives of functions involving it. The session also introduced logarithmic functions as inverses of exponential functions, with plans for more in-depth discussion and exercises in the next class.

Student and Tutor reviewed various calculus differentiation rules, including the power, product, quotient, chain, and basic trigonometric derivative rules. They practiced applying these rules to solve a series of increasingly complex derivative problems and explored graphical interpretations of derivatives, including cases where a derivative does not exist. The Tutor will prepare material on logarithmic and exponential functions for the next session and assign practice homework.

The Tutor and Student reviewed the unit circle and its relationship to sine and cosine. They then explored the graphs of sine and cosine functions and practiced finding their derivatives, including applying the chain rule and product rule to complex expressions. The next session is scheduled for Thursday at 1:00 PM your time.