# Matematica Verde 3: A Comprehensive Textbook for High School Mathematics

## Matematica Verde 3: A Comprehensive Textbook for High School Mathematics

Matematica Verde 3 is a textbook for high school mathematics, written by Massimo Bergamini, Anna Trifone and Graziella Barozzi. It is published by Zanichelli, one of the leading Italian publishers of educational books. The textbook covers topics such as equations and inequalities, functions, coordinate geometry, conic sections, trigonometry, complex numbers and vectors. It is part of a series of four volumes that span from the first to the fifth year of high school.

## Matematica Verde 3.pdf

Matematica Verde 3 is designed to help students develop their mathematical skills and competencies, as well as their logical thinking and problem-solving abilities. The textbook offers a variety of exercises, activities, examples and applications that connect mathematics to real-life situations and other disciplines. It also includes online resources such as interactive exercises, video lessons, laboratory worksheets and guided solutions. Moreover, the textbook features a section called Maths in English, which presents some key concepts and terms in English language, to foster students' linguistic competence and intercultural awareness.

Matematica Verde 3 is a valuable resource for students who want to learn mathematics in a rigorous, engaging and meaningful way. It is also a useful tool for teachers who want to plan their lessons and assess their students' progress. Matematica Verde 3 is available in PDF format on the Zanichelli website[^1^] [^2^], as well as on other online platforms[^3^].

In this article, we will review some of the main topics and features of Matematica Verde 3, and provide some examples and exercises to illustrate them.

## Equations and inequalities

An equation is a mathematical statement that asserts the equality of two expressions. An inequality is a mathematical statement that asserts the relation of order between two expressions. Solving equations and inequalities means finding the values of the unknowns that make them true. Matematica Verde 3 covers different types of equations and inequalities, such as linear, quadratic, exponential, logarithmic, trigonometric and goniometric. It also teaches how to solve systems of equations and inequalities, and how to graph them on the coordinate plane.

For example, consider the following system of equations:

$$\begincases x^2+y^2=25 \\ x-y=1 \endcases$$

To solve it, we can use the substitution method. We isolate x from the second equation and substitute it in the first one:

$$x=y+1$$

$$\Rightarrow (y+1)^2+y^2=25$$

$$\Rightarrow y^2+2y+1+y^2=25$$

$$\Rightarrow 2y^2+2y-24=0$$

Then we solve the resulting quadratic equation by using the formula:

$$y=\frac-b\pm\sqrtb^2-4ac2a$$

where $$a=2$$, $$b=2$$ and $$c=-24$$. We get:

$$y=\frac-2\pm\sqrt4+1924$$

$$y=\frac-2\pm\sqrt1964$$

$$y=\frac-2\pm 144$$

So we have two possible values for y:

$$y_1=\frac-2+144=3$$

$$y_2=\frac-2-144=-4$$

To find the corresponding values for x, we substitute y in the second equation:

For $$y_1=3$$:

$$x-3=1 \Rightarrow x=4$$

For $$y_2=-4$$:

$$x-(-4)=1 \Rightarrow x=-3$$

Therefore, the system has two solutions: $$(4,3)$$ and $$(-3,-4)$$. We can verify them by plugging them in the original equations. e0e6b7cb5c