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The class covered algebraic techniques for rationalizing denominators and numerators, followed by an introduction to vector addition in the context of physics. The student practiced solving problems involving these concepts, and the tutor planned to continue with similar topics and potentially introduce angle calculations for vectors in the next session.

The tutor and student reviewed how to find inverse functions and then moved on to exponential functions. They practiced graphing exponential functions by identifying transformations, plotting key points, and determining asymptotes, domain, and range. The session concluded with plans to continue with logarithmic and exponential relationships in the next class.

The Tutor and Student reviewed vector algebra, including magnitude, direction, and resultant vectors. They then delved into quadratic equations, discriminants, and inequalities, followed by calculus concepts such as finding maximum volume via differentiation and determining if a function is increasing. Finally, they analyzed properties of lines, including perpendicularity, to find unknown coefficients and calculate the area of a triangle formed by these lines.

The tutor and student reviewed the concept of one-to-one functions, including their definition, algebraic verification, and graphical representation using the horizontal line test. They then delved into inverse functions, exploring their definition, properties, and how to verify them using function composition. The session concluded with an exercise on graphing a function and its inverse.

The Tutor and Student reviewed and practiced fundamental logarithmic properties and formulas, including the power rule, product rule, and quotient rule. They worked through simplifying and expanding logarithmic expressions, reinforcing the student's understanding through problem-solving exercises.

The student and tutor extensively reviewed exponential functions, their graphs, and the concept of gradients through differentiation. They practiced calculating derivatives of exponential functions and worked through problems involving finding function parameters from given gradients. The session concluded with an introduction to logarithms and their properties, with plans to continue logarithm practice in the next session.