# Education Material

# High School

### eMath Textbook Series

eMath1 is a repetition of middle school math, with some topics being treated more carefully than before. It gives an overview of the basic number domains and their operation, shows how solve first degree equations, how to work with percentages, roots and powers, and finally explains the important notion of a function.

eMath2 presents first degree and higher degree polynomials. It shows how to solve equations involving polynomials, and how to factories polynomials. It also explains how to solve simultaneous equations as well as inequalities, and how to work with rational expressions.

eMath4 introduces the basic notions of analytic geometry with the cartesian coordinate system. It shows how to describe lines as equations, and how to determine properties of lines, like intersection, orthogonality, distance from points and angles between lines. The book shows how to define and analyse properties of parabolas, circles and other conic sections.

eMath5 gives an overview of vectors and vector spaces. It explains the basic notion of a vector, how to compute with vectors and how to describe them in a coordinate system. Three-dimensional vectors are also described, together with planes and lines in space.

eMath6 gives an overview of the basic notions of probability and statistics. The basic statistical measures are covered, as well as surveys and samples. The concept of probability is explained, together with the basics of combinatorics. The rules of probability are explained, to show how to compute with probabilities, and the notion of a random variable is explained.

eMath7 introduces the basic notions of calculus: continuity, limits, and derivatives. It shows how to compute the derivative of a function. It applies this to describe the behavior of functions, and to find extreme values of functions. Additionally, it includes a chapter on how to work with rational expressions.

eMath8 describes how to work with exponents, logarithms and roots. It explains the notions of compound functions and inverse functions. It introduces exponential functions and logarithmic functions and shows how compute the derivative of these.

eMath9 gives a more in-depth treatment of trigonometry. It covers the basic trigonometric functions, how to compute with these and how to solve equations with trigonometric functions. The book also covers sequences in general, particularly arithmetic and geometric sequences, as well as arithmetic and geometric sums.

The eMath textbooks are interactive mathematics books. The books follow a teaching approach that uses the Structured Derivations methodology, where the idea is that every step has an explicit justification. This makes it easy to follow the examples that explain the theory. At the same time the approach forces the student to reflect on what they are doing. The books also introduce the students to logic, a step often skipped in school, but without which mathematics becomes magic instead of reasonable and understandable. The books cover all the central topics in high school mathematics (grades 10 -12).

The eMath textbooks are developed by Math teachers from Finland, Sweden and Estonia. The eMath textbooks are organised according to the Finnish national curriculum for high school mathematics at advanced level.