Math Practice

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

Vectors are quantities with both magnitude and direction, forming an important topic in high school mathematics. In the CSCA exam, vector questions mainly involve basic operations (addition, subtraction, scalar multiplication), coordinate representation, dot product and its applications. Questions typically test linear operations, conditions for parallel and perpendicular vectors, and using vectors to solve geometric problems.

复数

Complex numbers are an extension of real numbers, in the form a + bi (where i is the imaginary unit, i² = -1). In the CSCA exam, complex number questions mainly involve basic concepts, arithmetic operations, geometric representation (complex plane), and modulus and conjugate. Questions typically test algebraic operations, position in the complex plane, and modulus calculations.

立体几何

Solid geometry studies points, lines, planes, and solids in three-dimensional space and the relationships among them. In the CSCA exam, this topic commonly tests surface-area and volume calculations for standard solids (such as prisms, cones, and spheres), the interpretation and reconstruction of solids from orthographic three-view diagrams, and reasoning about the relative positions of lines and planes in space. Questions usually combine diagrams with numerical data, requiring strong spatial visualization and precise use of formulas.

空间直角坐标系

Space coordinates are mathematical tools for describing positions in three-dimensional space. In the CSCA exam, space coordinate questions mainly involve establishing spatial rectangular coordinate systems, the distance formula between two points in space, and coordinate operations of space vectors. Questions typically test coordinate representation of spatial points, distance calculations, and coordinate-based approaches to spatial geometry problems.

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.