Expert maths tutor with dynamic teaching style for interactive learning and exam success.

The tutor and student worked through problems involving finding stationary points, maxima, and minima of functions using first and second derivatives. They practiced differentiation techniques, including the quotient rule, and analyzed the behavior of functions at critical points. The student was assigned practice problems from a worksheet for further review.

The session focused on understanding and identifying even and odd functions through various examples. Subsequently, the Student and Tutor delved into the definitions of domain and range, practicing how to determine these for functions presented both algebraically and graphically, including common function types and the greatest integer function. The Tutor indicated that the first chapter's topics are nearing completion.

The session focused on various types of functions, including absolute value, greatest integer, even, and odd functions. Student and Tutor defined these functions, explored their graphical representations, and practiced identifying and graphing different function types. Homework was assigned to determine if given functions are even or odd, with domain and range planned for the next session.

The session focused on applying economic concepts to solve quadratic equations in business contexts. Student and Tutor worked through problems involving demand and supply functions, calculating total revenue, total cost, and profit, determining break-even points, and finding equilibrium price and quantity. The Student also practiced graphing quadratic functions and was assigned homework to plot several quadratic equations.

The Student and Tutor focused on quadratic functions, covering their definition, the calculation of the discriminant, and its implications for the nature of roots. They extensively practiced finding roots using the quadratic formula and graphing parabolas by identifying key features like shape, intercepts, and vertex. The session also included an application of quadratic equations to solve a profit maximization problem, with further application-based questions deferred to the next session.

The session focused on graphing various functions, including square root and cubic functions. The Tutor then introduced piecewise functions, demonstrating how to graph them by considering different rules over specified intervals. Student and Tutor also reviewed interval notation and inequality symbols to correctly interpret inclusion or exclusion of boundary points on graphs. Homework was assigned to practice plotting piecewise functions, with the Student instructed to share their solutions for checking.