Understand the concepts of set, subset, complement set, intersection and union set;

Understand the meaning of empty set and complete set;

Understand the meaning of belonging, tolerance and equality;

Master related terms and symbols, and use them to represent some simple sets correctly.

Understand the meaning of logical connectives "or", "and" and ";

Understand the four propositions and their relationships; Grasp the significance of necessary and sufficient conditions.

2. Function

Understand the concept of mapping, on this basis, deepen the understanding of the concept of function.

Understand the concept of monotonicity of functions, and master some methods to judge monotonicity of simple functions.

By understanding the relationship between the concept of inverse function and the function image as inverse function, we can find the inverse function of some simple functions.

Understand the concept of fractional exponent and master the operational properties of rational exponent power; Master the concept, image and properties of exponential function.

Understand the concept of logarithm and master the operational properties of logarithm; Master the concept, image and properties of logarithmic function.

We can use the properties of function, exponential function and logarithmic function to solve some simple practical problems.

3. Inequality

Understanding the essence of inequality and its proof.

Master the theorem that the arithmetic mean of two (not extended to three) positive numbers is not less than its geometric mean, and simply apply it.

Master analysis, synthesis and comparison to prove simple inequalities.

Master the solution of quadratic inequality, simple absolute inequality and simple fractional inequality.

Understanding inequality: | a |-| b |≤| a+b |≤| a |+| b |.

4. Trigonometric function (46 class hours)

Understanding the concept of arbitrary angle and the meaning of radian can correctly convert radian and angle.

Master the definitions of sine, cosine and tangent at any angle,

Sine, cosine and tangent will be represented by trigonometric function lines in the unit circle.

Understand the definitions of cotangent, secant and cotangent at any angle;

Master the basic relationship between trigonometric functions and the same angle;

Master the inductive formulas of sine and cosine.

Master the sine, cosine and tangent formulas of the sum and difference of two angles;

Master the sine, cosine and tangent formulas of double angles; Through the derivation of formulas, we can understand their internal relations, thus cultivating the ability of logical reasoning.

Can correctly use trigonometric formula to simplify, evaluate and prove the identities of simple trigonometric functions (including derivative of product and difference, product of sum and difference, half-angle formula, but not memorized).

Understand the significance of periodic function and minimum positive period;

Understand the meaning of parity function; And understand the properties of sine function, cosine function and tangent function through their images; And simplify the drawing process of these function images;

I will use the "five-point method" to draw graphs of sine function, cosine function and function y=Asin(ωx+φ) to understand the physical meaning of a, ω and φ.

The angle will be obtained from the known trigonometric function values and represented by the symbols arcsin x, arccos x and Arctan x.

Master sine theorem and cosine theorem, use them to solve oblique triangle, and use calculator to solve the calculation problem of solving oblique triangle.

5. Plane vector

Understand the concept of vector, master the geometric representation of vector,

Understand the concept of * * * line vector.

Master the addition and subtraction of vectors.

Master the product of real number and vector, and understand the necessary and sufficient conditions for the connection of two vectors.

Understand the basic theorem of plane vector,

Understand the coordinate concept of plane vector,

Master the coordinate operation of plane vector.

Master the product of plane vector and its geometric meaning,

Understand that using the product of plane vector can solve the problems of length, angle and verticality, and master the conditions of vector verticality.

Master the distance formula between two points on the plane,

Master the coordinate formula of fixed point and midpoint of line segment, and use it skillfully;

Master the translation formula.

6. Series

Understand the concept of sequence,

Understand the meaning of the general term formula of sequence;

Knowing the recursive formula is a way to give the sequence, and the first few items of the sequence can be written according to the recursive formula.

Understand arithmetic progression's concept,

Master arithmetic progression's general formula and the first n summation formulas, and can solve simple practical problems.

Understand the concept of geometric series.

Master the general formula of geometric series and the first n summation formulas, and can solve simple practical problems.

7. Equations of straight lines and circles

Understand the concepts of inclination angle and slope of a straight line,

Master the slope formula of a straight line passing through two points,

Master the point inclination formula, two-point formula and general formula of linear equation, and skillfully solve linear equation according to conditions.

Grasp the condition that two straight lines are parallel and vertical,

Master the angle formed by two straight lines and the distance formula from point to straight line;

Can judge the positional relationship between two straight lines according to the straight line equation.

Will use binary linear inequality to represent the plane area.

Understand the simple linear programming problem, understand the significance of linear programming, and apply it simply.

Master the standard equation and general equation of a circle,

Understand the concept of parametric equation, and understand the parametric equation of circle.

8. Conic curve equation

Master the definition of ellipse, standard equation and simple geometric properties of ellipse;

Understand the parametric equation of ellipse.

Master the definition of hyperbola, standard equation and simple geometric properties of hyperbola.

Master the definition of parabola, standard equation and simple geometric properties of parabola.

Grasp the basic properties of the plane and draw the vertical view of the horizontally placed plane figure by oblique survey;

Can draw a graph of various positional relationships between two straight lines in space, straight lines and planes, and can imagine their positional relationships according to the graph.

Master the judgment theorem and property theorem of two straight lines parallel and vertical;

Master the concepts of the angle and distance formed by two straight lines (for the distance of straight lines in different planes, only the given common perpendicular is required to calculate the distance).

Master the judgment theorem and property theorem of parallel lines and planes;

Master the judgment theorem and property theorem of vertical line and plane;

Master the concepts such as the projection of oblique line on the plane, the angle formed by straight line and plane, and the distance between straight line and plane;

Understand the three vertical theorems and their inverse theorems.

Master the judgment theorem and property theorem of parallel two planes;

Master the concepts of dihedral angle, plane angle of dihedral angle and distance between two parallel planes;

Master the judgment theorem and property theorem of two planes perpendicular.

If you are familiar with reduction to absurdity, you will use reduction to absurdity to prove simple problems.

Understand the concepts of polyhedron and convex polyhedron.

Understand the concept of prism, master the properties of prism, and draw a direct view of straight prism.

Understand the concept of pyramid, master the nature of regular pyramid, and draw a direct view of regular pyramid.

Understand the concept of regular polyhedron and Euler formula of polyhedron.

Understand the concept of the ball, master the properties of the ball, and master the formulas of the surface area and volume of the ball.

10. permutation, combination and binomial theorem

Master the principles of classified counting and step counting, and use them to analyze and solve some simple application problems.

Understand the meaning of permutation, master the calculation formula of permutation number, and use it to solve some simple application problems.

Understand the meaning of combination, master the formula and properties of combination number, and use them to solve some simple application problems.

Master the properties of binomial theorem and binomial expansion, and use them to calculate and prove some simple problems.

1 1. Possibility

Understand the statistical law of random events and the significance of random event probability.

In order to understand the significance of the probability of equal possibility events, we will use the basic formula of permutation and combination to calculate the probability of some equal possibility events.

In order to understand the meaning of mutually exclusive events, we will use mutually exclusive events's probability addition formula to calculate the probability of some events.

Knowing the meaning of independent events, we will use the probability multiplication formula of independent events to calculate the probability of some events.

The probability that the event will occur k times will be calculated in n independent repeated tests.

Elective course Ⅰ

1. Statistics

Understand the significance of random sampling and stratified sampling, and use them to sample simple practical problems;

The sample frequency distribution is used to estimate the overall distribution,

Will use samples to estimate the expectation and variance of the population, and know how to extract information from the data and make statistical inference.

2. Derived creatures

Understand that derivative is the limit of average change rate; Understand the geometric meaning of derivatives.

Mastering the derivative formula of function, we can find the derivative of polynomial function.

Understand the concepts of maximum, minimum, maximum and minimum,

Derivative can be used to find the monotone interval, maximum and minimum of polynomial function and the maximum and minimum in closed interval.

Elective course Ⅱ

1. Probability and statistics

Understand the meaning of discrete random variables,

You can find some simple distribution lists of discrete random variables.

Knowing the meaning of expectation and variance of discrete random variables, we can get expectation and variance according to the distribution table of discrete random variables.

Random sampling, systematic sampling, stratified sampling and other common sampling methods will be used to extract samples from the population.

The sample frequency distribution will be used to estimate the overall distribution.

Understand the significance and main properties of normal distribution.

Understand the method and simple application of linear regression.

Step 2 limit

To understand the principle of mathematical induction, we can prove some simple mathematical propositions by mathematical induction.

Understand the concepts of sequence limit and function limit from the changing trend of sequence and function.

Four algorithms to master the limit; Will find the limits of some sequences and functions.

Understand the meaning of continuity and intuitively understand the properties of continuous functions with maximum and minimum values in closed intervals with the help of geometry.

3. Derivative

Understand some practical background of the concept of derivative (such as instantaneous velocity, acceleration, slope of tangent of smooth curve, etc.). );

Master the definition of the derivative of a function at a point and the geometric meaning of the derivative;

Understand the concept of derivative function.

Memorize the basic derivative formula (derivative of c, xm(m is a rational number), sin x, cos x, ex, ax, ln x, logax);

Master the derivation rules of sum, difference, product and quotient of two functions;

Knowing the law of derivative of compound function, we will find the derivative of some simple functions.

Will intuitively understand the relationship between monotonicity of differentiable functions and their derivatives from geometry; Understand the necessary and sufficient conditions for the derivative function to obtain the extreme value at a certain point (the sign of the derivative is different on both sides of the extreme value point); You will find the maximum and minimum of some practical problems (generally referring to unimodal functions).

4. Extension of number system-complex number

Understand the related concepts of complex numbers;

Master the algebraic representation and geometric meaning of complex numbers.

Master arithmetic in complex algebraic form, and can add, subtract, multiply and Divison complex algebraic form.