examination syllabus

National Teacher Education Network Alliance Entrance Examination

High school qidiansheng junior college

Mathematics course examination outline

general requirements

This syllabus is the starting point of the high school mathematics examination syllabus of the Network College Alliance, and its purpose is to select qualified students for the Network College.

This outline puts forward three levels and corresponding requirements for the listed knowledge. The three levels are arranged from low to high, and the requirements of the higher level include the requirements of the lower level.

These three levels are:

Understanding requires candidates to have a preliminary understanding of the meaning of the listed knowledge, memorize the relevant content and be able to use it directly.

Understanding, mastering and knowing will require candidates to have a deep understanding of the meaning of the listed knowledge, be able to explain, give examples or deform and infer, and use knowledge to solve related problems.

Flexible application requires candidates to comprehensively use the listed knowledge to solve more complicated mathematical problems.

The first part of the examination content

First, algebra

(1) Numbers, Equations and Equations

1. Understand the concepts of rational number, real number and number axis, reciprocal, absolute value, reciprocal and arithmetic square root, and make relevant calculations.

2. Understand the concepts of algebra, fraction and quadratic root, and master some of their properties and algorithms.

3. Master the solutions of one-dimensional linear equation, quadratic equation, binary linear equation and ternary linear equation; Can solve the equations composed of binary quadratic equation and binary linear equation; Can solve a simple equation composed of two binary quadratic equations.

(2) Function

1. Understand the meaning of set and its representation; Understand the concepts and representation methods of empty set, complete set, subset, intersection, union set and complement set, understand the meaning of symbols, and use these symbols to express the relationship between elements and sets, sets and sets.

2. In order to understand the concept of function, we can find the domain of some common functions.

3. Understand the concepts of monotonicity and parity of functions, and master the image characteristics of increasing function, subtraction function, odd function and even function.

4. Understand the concepts of linear function and inverse proportional function, master their images and properties, and find their analytical expressions.

5. Understand the concept of quadratic function, master the image and properties of quadratic function, and master the relationship between quadratic function and image; Can find the analytic formula and the maximum or minimum value of quadratic function, and can flexibly use the knowledge of quadratic function to solve related problems.

6. Understand the concept of power function, and master the images and properties of power function.

7. Understand the meaning of inverse function, and you will find the inverse function of some simple functions.

8. Understand the concepts of exponent and logarithm, and master relevant algorithms.

9. Understand the concepts of exponential function and logarithmic function, master their images and properties, and use them to solve related problems.

(3) Inequality and Inequality Group

1. In order to understand the essence of inequality, we can use basic inequalities (r) and (r) to solve some simple problems.

2. Being able to solve linear inequalities of one variable, linear inequalities of one variable and inequalities that can be reduced to linear inequalities of one variable; Able to solve quadratic inequality in one variable; Understanding the concept of interval will represent the solution set of inequality or inequality group on the number axis.

3. Understand the essence of absolute inequality, and you will solve the absolute inequality in the form of sum.

4) Series

1. Understand sequences and related concepts.

2. To understand the concepts of arithmetic progression and arithmetic mean term, you will use arithmetic progression's general term formula, the first n terms and formulas to solve related problems.

3. To understand the concept of equal proportion geometric progression and mean term, we will use geometric progression's general term formula, the first n terms and formulas to solve related problems.

Second, the triangle

(A) trigonometric functions and related concepts

1. Understand the concepts of positive angle, negative angle and zero angle, and understand the concepts of quadrant angle and congruent corner.

2. Understand the concept of radian and the conversion between radian and angle.

3. Understand the concept of trigonometric function at any angle, understand the symbols of trigonometric function in each quadrant and the trigonometric function values at special angles.

Transformation of trigonometric function

1. Master the basic relations and inductive formulas between trigonometric functions with the same angle, and use them for calculation, simplification and proof.

2. Master the sine, cosine and tangent formulas of the sum, difference and double angle of two angles, and use them for calculation, simplification and proof.

(3) Images and properties of trigonometric functions

1. Master the images and properties of sine function and cosine function, and use the properties of these two functions (domain, range, periodicity, parity and monotonicity) to solve related problems.

2. Understand the image and properties of tangent function.

3. Find the period, maximum value and minimum value of the function.

4. Understand the concepts of anti-cosine, anti-cosine, anti-tangent and anti-cotangent functions, as well as their definitions and value ranges; Calculate common inverse trigonometric function values.

Three, plane analytic geometry

(A) the plane vector

1. Understand the concept of vector, master the geometric representation of vector, and understand the concept of * * * line vector.

2. Master the addition and subtraction of vectors and the multiplication of numbers and vectors; Understand the conditions of two vector lines.

3. Master the vector product operation, understand its geometric meaning and its application in dealing with length, angle and vertical problems; Understand the conditions of vertical vectors.

4. Master the rectangular coordinates of vectors and their operations.

5. Master the distance formula between two points on the plane and the midpoint formula of the line segment.

(2) Straight line

1. Understand the concepts of inclination and slope of a straight line, and you will find the slope of the straight line.

2. Know how to solve linear equations, and be able to use linear equations flexibly to solve related problems.

3. Master the conditions of parallelism and verticality of two straight lines and the distance formula from point to straight line, and use them to solve related problems; Understand the formula of the angle formed by two straight lines.

(3) Conic curve

1. Understand the relationship between curve and equation, and find the intersection of two curves.

2. Master the standard equation and general equation of circle, master the positional relationship between straight line and circle, and use them flexibly to solve related problems.

3. Understand the concepts of ellipse, hyperbola and parabola, master their standard equations and properties, and use them to solve related problems.

The second part of the examination paper structure

The examination is in the form of closed-book written examination, with a full score of 100 and an examination time of 120 minutes. You can use a calculator during the exam.

First, the content ratio

Algebra accounts for about 65%

The triangle is about 25%

Plane analytic geometry is about 10%

Second, the proportion of questions

About 35% of multiple-choice questions

Fill in the blanks about 25%

About 40% of the answers

Third, the difficulty ratio

Easy to ask about 40%

About 40% of moderately difficult questions

The difficulty is increased by about 20%.

Reference book: Higher Education Press, edited by Zheng, related chapters of the National Adult College Entrance Examination Review Guide Series, the first edition of 12, Senior High School Starting Point and Specialized Mathematics (Literature and History).