Experienced tutor helping for grade improvement

The Tutor and Student reviewed quadratic equations and then focused on solving systems of linear equations using the matrix inverse method. They practiced converting systems into matrix form, calculating determinants, cofactors, adjugates, and inverses for both 2x2 and 3x3 matrices, and then applied these to find the variable matrices. The next session will involve creating and solving 3x3 systems of equations.

The Tutor and Student reviewed advanced mathematics topics including trigonometric quadrant rules, Taylor series, matrix inversion for solving linear equations, and complex number operations. They practiced problem-solving techniques for these areas, with the Tutor suggesting alternative methods and clarification for complex concepts. The session concluded with an introduction to differential equations.

The session covered De Moivre's theorem for complex number exponentiation and roots, followed by an introduction to Taylor and Maclaurin series. The student practiced applying these formulas to solve problems and was guided on the procedural steps for each concept. The tutor planned for the student to continue practicing these topics.

The Tutor and Student reviewed solving differential equations using substitution and then delved into complex numbers, covering Euler's formula, conversion between rectangular and exponential/polar forms, and operations like multiplication and division. They also briefly touched upon De Moivre's theorem and plotting on the Argand diagram, with plans to potentially review a practice paper before the student's exam.

The tutor and student worked on solving first-order differential equations using both substitution for homogeneous equations and the integration factor method for linear equations. They practiced identifying P(x) and Q(x), calculating integrating factors, and applying initial conditions to find the constant of integration. The tutor assigned specific problems from worksheets for further practice.

The tutor and student worked through various types of differential equations, focusing on integration techniques for exponential functions and solving separable differential equations. They practiced problem-solving methods for integration and substitution, and discussed upcoming topics like transformations and series.