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The tutor and student worked through various mathematical problems, starting with fraction operations including converting mixed numbers and performing division and multiplication. They then tackled word problems involving percentages and discounts, followed by algebraic expression evaluation. The focus was on understanding efficient problem-solving methods.

The tutor and student reviewed fundamental differentiation rules and then delved into the derivatives of exponential and logarithmic functions. They practiced applying these rules, particularly the chain rule, to composite functions and introduced logarithmic differentiation for functions of the form f(x)^g(x). The student was encouraged to practice more problems from a provided worksheet.

The tutor and student reviewed techniques for approximating definite integrals using Riemann sums, including cases with unequal subinterval widths. They practiced calculating left and right Riemann sums, analyzed their properties for increasing and decreasing functions, and then transitioned to using the limit definition of the definite integral to set up and evaluate integrals from given functions and summation expressions.

The class focused on the concept of Riemann sums for approximating the area under a curve, exploring left, right, and midpoint sums with a fixed number of sub-intervals. The session then delved into summation notation and its formulas, leading to the evaluation of limits of sums to find exact areas, which connects Riemann sums to definite integrals.

The student and tutor worked through various derivative rules, including the sum, difference, product, quotient, and chain rules. They practiced applying these rules to algebraic and trigonometric functions, and the tutor reviewed the definitions of trigonometric functions using right triangles. Further practice with mixed derivative rules was planned.

The Tutor introduced and the Student practiced applying the product, quotient, and chain rules in calculus. The Student worked through several examples, differentiating functions involving products, quotients, and compositions. The Tutor assigned practice problems involving mixed rule applications for homework and announced plans to cover exponential, logarithmic, and trigonometric functions in the next session.