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In eMath1, students can review the principles of percentage calculation, learn to use proportionality in problem solving, deepen their understanding of fractions, and revise the rules for exponents. In addition, students can strengthen their understanding of the concept of functions and the principles of solving equations and systems of equations. The book also introduces students to different software tools for plotting function graphs, making interpretations, and solving equations.
In eMath2, students learn how to create mathematical models of phenomena using polynomial, rational, and root functions, as well as to understand their properties and solve related equations. They also learn about the relationship between the zeros of a polynomial function and the factors of the polynomial. In addition, the book teaches students how to solve simple polynomial inequalities. The book also introduces students to the use of software tools for exploring polynomial, rational, and root functions, as well as for solving polynomial, rational, and root equations and polynomial inequalities in connection with applications.
In eMath3, students practice representing and describing information about space and shapes in both two- and three-dimensional situations. They learn to apply similarity, the Pythagorean theorem, and trigonometry in right-angled and oblique-angled triangles. Students also practice formulating, justifying, and applying theorems that contain geometric information. The book further introduces students to the use of software tools for exploring figures and solids, as well as the geometry related to them.
In eMath4, students are introduced to how analytic geometry connects geometric and algebraic concepts. They review their understanding of the geometric meaning of an equation and learn to solve absolute value equations. Students are introduced to the concept of vectors and learn how to perform calculations with them, as well as how to use vectors to examine points, distances, and angles in the two-dimensional coordinate system. In addition, they learn to solve plane geometry problems using vectors. The book also introduces students to the use of software tools for exploring curves and vectors, as well as for solving related applied problems.
In eMath5, students are introduced to how mathematical models can be created using sine and cosine functions, as well as exponential and logarithmic functions. They explore sine and cosine functions through the symmetries of the unit circle, gain more practice in solving trigonometric equations, and learn to apply relationships between the sine and cosine functions. Students also learn about the properties of exponential and logarithmic functions and how to solve related equations. The book helps students deepen their understanding of how to use software tools to explore functions, solve equations, and work on applied problems.
In eMath6, students explore the properties of mathematical models of various phenomena through the concept of the derivative. The book helps students build a clear understanding of a function’s limit and continuity, as well as the interpretation of the derivative as the rate of change of a function. Students learn how to determine the derivative of simple functions, differentiate composite functions, and use derivatives to analyze the behavior of functions and find their extreme values within a closed interval. The book also introduces students to the use of software tools for exploring limits, continuity, and derivatives in connection with applications.
In eMath7, students are introduced to the concept of the antiderivative and learn how to determine antiderivatives of simple functions. They learn to understand the concept of the integral and its connection to area, as well as how to determine an integral using a numerical method. In addition, students learn how to calculate areas and volumes using integrals and become familiar with applications of integral calculus. The book also introduces students to the use of software tools for exploring the properties of functions, finding antiderivatives, computing integrals in applied contexts, and performing numerical integration.
In eMath8, students learn how to represent a discrete statistical distribution and determine and interpret its key figures. They also learn to visualize a distribution involving two variables and to calculate the correlation coefficient and regression curve. Students are introduced to combinatorial methods and become familiar with the concept of probability. In addition, they explore the concept of a discrete probability distribution, learn how to determine its expected value, and interpret its meaning.
