Mathematik Übungen

基本初等函数

Basic elementary functions are the foundation of mathematics, mainly including power functions, exponential functions, logarithmic functions, trigonometric functions and inverse trigonometric functions. In the CSCA exam, this part of the content often appears in the form of function image transformation, property analysis, equation solving, etc. Candidates are required to be proficient in definitions, images and basic properties, and be able to apply them flexibly to problem solving.

数列

A series is a sequence of numbers in a certain order in mathematics, mainly including arithmetic sequences and geometric sequences. In the CSCA exam, series questions often involve the general formula, the calculation of the sum of the first n terms, and the application of series properties in geometric and algebraic problems. Mastering the basic formulas and applying them flexibly is the key to solving the questions.

函数

Functions are a central concept in mathematics that describe correspondences between variables, and basic questions such as domain of definition, parity, and analytic form are often covered on the CSCA exam. Questions often require analyzing the properties of a function or calculating specific parameters based on its expression, and require proficiency in algebraic operations and characterization of basic function types.

导数与微积分

Derivatives and calculus are core tools of mathematical analysis, focusing on the rate of change of functions, the slope of tangents, and area calculations. In the CSCA exam, this part of the content usually appears in the form of calculation and application questions, requiring candidates to master the basic rules of derivatives, the geometric significance of derivatives and simple integral operations. The questions are of moderate difficulty and focus on the application of basic formulas and computational accuracy.

平面解析几何

Plane analytic geometry is the branch of mathematics that investigates the properties of geometric figures through coordinate systems, and deals with the representation of equations and their interrelationships for graphs such as lines, circles, and conic curves. In the CSCA exam, this part of the questions often test the application of basic formulas, the judgment of the relationship between the position of graphs (e.g., parallel and perpendicular), and the correspondence between standard equations and geometric properties. The format of the questions is based on calculations and derivation of equations, and requires proficiency in the standard equations and geometric properties of various types of curves.

向量

Vektoren sind Größen mit Betrag und Richtung und bilden ein wichtiges Thema der Oberstufenmathematik. In der CSCA-Prüfung beinhalten Vektorfragen hauptsächlich Grundoperationen (Addition, Subtraktion, Skalarmultiplikation), Koordinatendarstellung, Skalarprodukt und dessen Anwendungen.

复数

Komplexe Zahlen sind eine Erweiterung der reellen Zahlen in der Form a + bi (wobei i die imaginäre Einheit ist, i² = -1). In der CSCA-Prüfung beinhalten Fragen zu komplexen Zahlen hauptsächlich Grundkonzepte, arithmetische Operationen, geometrische Darstellung (komplexe Ebene) sowie Betrag und Konjugierte.

立体几何

Spatial geometry is the branch of mathematics that deals with the study of points, lines, surfaces, and bodies and their relationships in three-dimensional space. In the CSCA exam, this section often involves the calculation of surface area and volume of common three-dimensional (e.g., columns, cones, and spheres), the identification and reduction of three-view drawings, and the determination of spatial positional relationships. The questions usually incorporate graphs and data, requiring candidates to have strong spatial imagination and formula application skills.

空间直角坐标系

Raumkoordinaten sind mathematische Werkzeuge zur Beschreibung von Positionen im dreidimensionalen Raum. In der CSCA-Prüfung beinhalten Raumkoordinatenfragen hauptsächlich die Einrichtung räumlicher kartesischer Koordinatensysteme, die Abstandsformel zwischen zwei Punkten im Raum und Koordinatenoperationen von Raumvektoren.

不等式

Inequalities are central to comparing numerical magnitude relationships in mathematics, and are often examined in conjunction with functions, sets, and absolute value in the CSCA exam. The questions usually require solving the set of inequalities, determining the conditional relationship or analyzing the range of inequalities corresponding to the image of a function. Mastering the basic solution method and understanding the idea of combining numbers and shapes is the key to dealing with these problems.

集合

A set is a basic concept in mathematics that describes a group of objects and mainly involves operations such as element, subset, union, intersection, and complement. In the CSCA exam, set questions are often combined with inequalities and function definition domains, requiring candidates to accurately understand the meaning of symbols and skillfully perform set operations. Mastering the representation of sets and operations is the key to solving the questions.

概率与统计

Probability and statistics is an important branch of mathematics that deals with random phenomena and data patterns. In the CSCA exam, the section focuses on the application of fundamental concepts, such as the normal distribution, probability calculations and game fairness analysis. Questions often incorporate life situations and require candidates to apply formulas and data analysis to solve real-world problems, testing understanding of core statistical ideas.