Engaging Math lessons from elementary to AP Calculus with creative problem solving

The Student reviewed synthetic division of polynomials with the Tutor, covering factor theorem, polynomial long division, and factorizing quadratic equations. The Student practiced several examples of polynomial division and quadratic factorization. The Tutor suggested focusing on factorizing quadratics in the next session to solidify foundational skills before moving on to more complex problems.

Kitty worked with Madison on various calculus problems, focusing on chain rule, product rule, and quotient rule applications. Madison practiced differentiating composite functions, trigonometric functions, and algebraic expressions, with an emphasis on correct substitution and simplification. They reviewed several homework problems, and Kitty provided detailed explanations and corrections.

Kitty Cyntia Szomyu assisted Anna with practicing problems on perpendicular lines, including finding equations of lines, using slope-intercept and point-slope forms, and determining midpoints. Anna worked through various exercises, and Kitty introduced the midpoint formula. The session ended without assigning specific homework due to Anna's prior commitment.

This lesson focused on differentiation techniques with a student residing in Port St Lucie. The learner practiced simplifying expressions, finding gradients, and determining ranges for increasing/decreasing functions. They reviewed factorization and expanded on the chain and product rules. The student was assigned practice questions on the chain rule and may request an additional lesson if new material is covered in class tomorrow.

Kitty and Anna reviewed linear equations and graphs, including slope, y-intercept, correlation, and rates of change. Anna practiced solving word problems, finding equations of lines, and converting equations to standard form. Kitty will email Anna practice problems on standard form and finding slope.

This lesson involved a comprehensive review of differentiation using first principles, calculating derivatives at a point, and evaluating limits. The learner, a student at California State University, Fullerton, worked through several problems, gaining proficiency with a graphing calculator to visualize functions and identify discontinuities. The discussion also covered strategies for their upcoming test retake, with a strong focus on graphical analysis and a deep understanding of the definitions of continuity.