Mathematics Tutor Specializing in Algebra, Calculus, and Exam Coaching

The tutor and student worked through problems related to hyperbolas, covering their definition, key components (vertices, foci), equations, and graphing techniques for both origin-centered and non-origin-centered hyperbolas. They practiced identifying these elements from equations and vice versa, with plans to review more complex problems in the future.

The Student and Tutor reviewed methods for calculating the angle between vectors using the dot product and magnitudes. They also practiced finding the angle a vector makes with the x-axis by plotting points and applying trigonometric functions, with a plan to cover projectile motion and areas of triangles in future sessions.

The tutor and student worked through advanced calculus topics including implicit differentiation, definite integrals, integration by parts, partial fractions, and an introduction to differential equations. They practiced solving various problems using these techniques and reviewed the steps involved in each method.

The Tutor and Student reviewed the concepts of anti-derivatives and integration techniques, including basic power rule integration, integration of trigonometric and exponential functions, u-substitution, and integration by parts. They practiced solving various integration problems using these methods and discussed potential topics for the next session, including differentiation optimization.

The tutor and student reviewed the properties and equations of parabolas, including their orientation and vertex determination. They then briefly introduced ellipses, focusing on their standard equations and the concept of the major axis, with plans to delve deeper into ellipses in a future session due to internet connectivity issues.

The tutor and student worked through problems involving kinematics, specifically calculating velocity, speed, and intersection points with axes. They also covered methods for finding the area of triangles using trigonometric formulas and Heron's formula, and delved into vector equations of lines, including parametric and rectangular forms.