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Student and Tutor engaged in a Mathematics class, primarily focusing on number theory. They extensively reviewed and practiced concepts such as prime, co-prime, and composite numbers, as well as prime factorization methods using exponents. The session also included a discussion on terminating and non-terminating decimals and basic exponent rules, with the Tutor encouraging the Student to apply learned rules more consistently and suggesting daily practice with number properties as homework.

Student and Tutor engaged in a detailed Mathematics lesson covering fundamental concepts such as divisibility rules, exponents, factors, and the order of operations (PEMDAS). The Student clarified long-held confusions regarding multiplication strategies and the precise definitions of mathematical terms. The Tutor planned to introduce linear algebra and suggested practicing organization of mathematical notes.

The Student and Tutor extensively reviewed fundamental differentiation rules in Calculus. They covered constant, power, sum/difference, constant multiple, product, quotient, and chain rules, along with derivatives of logarithmic and exponential functions and their properties. The session concluded with the Tutor providing a written summary of all rules discussed for the Student's future reference.

Student and Tutor practiced analyzing rational functions, including identifying horizontal and vertical asymptotes, x- and y-intercepts, and potential holes through factorization and synthetic division. They also reviewed the discriminant method for solving quadratic equations to find x-intercepts when direct factorization is not possible. The plan for the next session includes creating short notes and working on questions from test sections 4.1 and 4.2.

The Student and Tutor engaged in a comprehensive session on rational functions. They practiced identifying horizontal and vertical asymptotes, x and y-intercepts, and holes, including a detailed discussion on factoring higher-degree polynomials using synthetic division. The session concluded with a homework assignment for the Student to graph a complex rational function.

The Tutor and Student started with a review of synthetic division and factoring. They then revised horizontal asymptotes for rational functions, defined x and y-intercepts, and introduced vertical asymptotes. The session heavily focused on applying these concepts to two complex rational functions, including calculating all asymptotes and intercepts, and determining the function's graphical behavior around vertical asymptotes using sign analysis. They planned to continue practicing these types of questions due to their importance for exams.