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The tutor and student worked on solving various mathematical problems including rational equations, quadratic equations, and word problems involving triangles. They also practiced solving linear inequalities and understood the concept of absolute value in inequalities, with plans to revisit radical form and continue with more inequality problems.

The Tutor and Student worked through various algebra and coordinate geometry problems from a practice test. They covered graphing linear equations, finding x and y intercepts, applying the distance formula, understanding interval notation, and solving linear and quadratic equations. The Tutor assigned practice of these concepts for the next session.

The Tutor and Student reviewed the definition and representations of functions, including tabular, graphical, and relation diagrams. They focused on distinguishing between functions and relations, understanding that relations have a unique output for each input. Various function types like linear, quadratic, modulus, and exponential functions were also introduced.

The tutor and student reviewed exam feedback and then introduced the mathematical concept of functions. They defined functions as mathematical rules producing unique outputs from given inputs, explored notation and examples, and discussed domain, range, and graphical representation. The next session will involve plotting functions on a graph.

The Tutor and Student began a new chapter on how atoms bond and form molecules, focusing on the exchange of electrons. They covered electron dot structures, the formation of ions by gaining or losing electrons, and the definition of ionic bonds. The Student practiced deriving chemical formulas from ion charges, and they plan to continue with metallic bonds in a future session after the Student's exam.

The Student and Tutor reviewed fundamental concepts in quantum physics and atomic structure, including the wave-particle duality of light, the relationship between energy and frequency, and electron behavior within atomic energy levels. They discussed Bohr's atomic model, the shell model, and definitions of atomic number and mass. The next session will begin a new chapter on how atoms bond.