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The tutor and student worked through problems involving arithmetic progressions, including solving for terms and applying inequalities to find specific terms. They then transitioned to functional transformations, covering shifts, stretches, compressions, and reflections, and practiced identifying these transformations and their effects on coordinates.

The Tutor and Student reviewed the definition and properties of arithmetic sequences and series. They practiced calculating terms, identifying convergence/divergence/oscillation, and solving for unknown terms and common differences using the arithmetic progression formula. The next session will continue with practice problems.

The Student and Tutor continued their study of integration, focusing on calculating the area under curves and between functions. They practiced problems involving polynomial functions, fractions converted to negative exponents, and finding integration limits by solving quadratic equations. The Tutor assigned two practice questions and requested the Student to find the syllabus for their upcoming academic session.

The Student and Tutor reviewed the fundamental concepts of integration, focusing on its application to calculate the area under a curve. They practiced using the basic integration formula for various polynomial and root functions, including cases where integration limits needed to be determined by finding x-intercepts. Follow-up for the next session was scheduled for Wednesday.

The Student and Tutor covered key concepts in quadratic equations, including completing the square, using the quadratic formula, and understanding the discriminant to determine the nature of roots. They also applied the Pythagorean theorem to solve a real-world problem and briefly explored factoring polynomial (cubic) equations. Due to the upcoming exam and extensive syllabus, they planned a longer session for the next class to cover remaining topics.

The Student and Tutor thoroughly reviewed advanced mechanics, specifically a pulley system problem on an inclined plane, including force analysis, friction calculations, and kinematic equations. They then moved to statistics, practicing how to calculate mean, variance, and standard deviation from a frequency density graph. Finally, they worked on a probability problem involving a tree diagram to determine the likelihood of specific outcomes. For follow-up, the Student was asked to find more practice questions, and the next session will cover area under graphs and mensuration.