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The Student and Tutor practiced solving systems of equations involving various function types, including linear, quadratic, and a circle. They focused on methods such as substitution, factoring, and the quadratic formula to find intersection points and solutions. The session also included a review of algebraic manipulation techniques like combining terms and simplifying fractions within equations.

The session focused on advanced integral calculus techniques. Student and Tutor reviewed integration by parts with substitution for complex functions, calculated the volume of a solid of revolution using the shell method, and discussed the average value of a function requiring trigonometric identities. They also revisited a multi-curve area problem, emphasizing the critical role of graphical analysis and strategic integration by parts. The Student is expected to review trigonometric identities for future homework.

The Student and Tutor extensively practiced algebraic factorization using binomial expansion patterns and the difference of squares. They also introduced and demonstrated completing the square to solve quadratic equations, alongside simplifying square and cube roots. The Student worked through numerous examples from a worksheet.

Student and Tutor reviewed key calculus concepts, including the product rule, power rule for derivatives, and derivatives of trigonometric functions. They practiced applying these rules to various expressions and briefly introduced the chain rule. The session also clarified foundational concepts such as negative and zero exponents and evaluating trigonometric functions using the unit circle, with a plan to continue with the chain rule in the next session.

The Student and Tutor worked on various mathematics problems, starting with polynomial subtraction and then extensively practicing the simplification and manipulation of radical expressions. They also explored Pascal's Triangle for binomial expansion and critically analyzed the truthfulness of statements involving radical properties. The Student expressed increased comfort with radicals after the session and planned to continue practicing using Khan Academy.

The Student and Tutor practiced advanced mathematics problems covering radicals, rational exponents, polynomial operations, and factoring rational expressions. They focused on applying exponent rules, converting bases, expanding polynomials, and simplifying complex algebraic expressions. The Tutor also provided context on undefined points (holes and asymptotes) in functions based on domain restrictions.