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The Student and Tutor reviewed geometry proofs involving parallel lines and transversals, practicing how to use angle relationships like corresponding and alternate exterior angles to prove lines are parallel. They also worked on finding unknown variable values that would make lines parallel. The session concluded with the Tutor explaining a classic proof by contradiction, demonstrating that the square root of two is irrational.

The Student and Tutor reviewed and practiced writing linear equations in slope-intercept form. They worked on problems involving calculating slopes from given points, converting between point-slope and slope-intercept forms, and determining equations for lines parallel to a given line. The session concluded with an introduction to solving linear systems using the substitution method.

The Student and Tutor worked on advanced algebra topics, focusing on polynomial division, specifically synthetic division. They also discussed and practiced identifying vertical and horizontal asymptotes, as well as holes in rational functions. Several examples were worked through to solidify the understanding of these concepts.

The Student and Tutor worked through a study guide for a formative quiz, reviewing fundamental geometry concepts, properties, postulates, and definitions. They practiced identifying the justifications for various geometric statements and completing multi-step proofs involving both line segments and angles. The session concluded a few minutes early.

The session focused on advanced calculus concepts, including determining the radius and interval of convergence for power series using the Ratio, Alternating Series, and P-Series Tests. The Student and Tutor also constructed a Taylor polynomial for tan(x) and used it to approximate a value, practicing complex derivative calculations. The Student plans to review the material and re-solve the problems for reinforcement.

Student and Tutor worked through several advanced calculus problems covering derivatives, series summation, and various integration techniques. They practiced identifying components of functions based on their derivatives, calculating arithmetic series sums, and applying u-substitution for complex integrals. The session concluded with a review of finding critical points of functions.