Experienced Mathematics Tutor making Math simple and engaging while boosting their confidence

The Tutor and Student reviewed the properties and operations of rational expressions, including simplification, multiplication, division, addition, and subtraction. They practiced finding values that make expressions undefined and worked through examples of combining expressions with similar and dissimilar denominators by finding the least common denominator. The next session will continue with solving rational equations and simplifying complex fractions.

The Tutor instructed the Student on solving quadratic equations using factoring, the quadratic formula, and completing the square. They practiced identifying coefficients, applying factoring techniques, substituting values into the quadratic formula, and manipulating equations to complete the square. The lesson included various examples and problem-solving steps for each method.

The student and tutor reviewed and practiced solving systems of linear equations using the substitution method. They also covered special cases of systems with no solution and infinite solutions, and how these relate to graphing. The next session was scheduled for the following week.

The tutor and student reviewed topics related to radicals and real numbers, including simplifying square and cube roots. They then focused on solving various types of linear equations, practicing multi-step problems and algebraic manipulations. The next session will likely cover the substitution method for solving systems of linear equations.

The student and tutor worked through various problems involving systems of linear equations. They reviewed methods for solving these systems, including elimination, substitution, and graphical interpretation, practicing algebraic techniques and integer operations. The tutor suggested reviewing integer operations in the next session based on observed difficulties and will ask the student to provide upcoming topics from their classes.

The tutor and student reviewed trigonometric identities, including the difference of squares and Pythagorean identities. They then delved into finding polynomials from their zeros, applying the Complex Conjugate Root Theorem and practicing polynomial multiplication. Finally, they worked on calculating the difference quotient for rational functions, which involved algebraic simplification and understanding function notation. The session concluded with well wishes for the student's upcoming exam and graduation.