Motivational GCSE Math lessons with problem solving

Nia and a student from Dallas Baptist University in Grand Prairie reviewed the Intermediate Value Theorem, Mean Value Theorem, and implicit differentiation. The learner practiced applying the three-step continuity test and finding the 'c' value in the Mean Value Theorem. They worked through example problems to prepare for an upcoming exam.

Practicing integration by substitution and integration by parts, the learners worked through several example problems. They covered techniques for simplifying integrals and using trigonometric identities. The pair, who call Hollywood home, plan to meet next week at the same time to continue their calculus lesson.

Two students, both attending Bellaire High School in Houston, focused their lesson on related rates problems and interpreting graphs. They practiced finding relationships between variables and using differentiation to solve related rates questions. The learners also reviewed how to interpret the first and second derivatives on a graph to determine increasing/decreasing intervals and concavity. One student provided notes on graph interpretation for the other to review.

Nia tutored a student from St. Pete on definite integrals, practicing various integration problems including polynomial, exponential, and logarithmic functions. The learner worked on finding areas under curves, solving word problems involving rates of change, and determining break-even points. They scheduled future lessons to continue working on calculus concepts.

Nia and Alexanderpaul began their lesson by reviewing the quotient rule before transitioning to implicit differentiation. During this lesson, Alexanderpaul gained proficiency in differentiating equations involving both x and y variables and applying the product rule in such contexts. They also focused on a key application of calculus: identifying points on a graph where the tangent line is horizontal by equating the derivative to zero. Another lesson has been set for Friday at 9 AM to further prepare Alexanderpaul for his upcoming exam.

Nia and Alexanderpaul continued their calculus practice, focusing on applying the chain rule, product rule, and quotient rule to various problems. They also covered derivatives of trigonometric functions. Nia provided notes and will send the document to Alexanderpaul for review. This lesson built upon their previous session where they reviewed fundamental differentiation rules, including the power rule, constant multiple rule, and sum/difference rule. Alexanderpaul, who attends the University of California, Riverside, had previously practiced applying these rules to various functions, including those with fractional exponents and radicals, and worked on finding derivatives at specific points. Homework problems were assigned to reinforce those earlier concepts. They have scheduled another lesson for the following day to continue practicing calculus, with two more lessons planned before an upcoming exam.