Mainly examines set operations, related concepts of functions, domain, value range, analytical expression, limit, continuity and derivative of functions.

This part is the focus but not the difficulty of the college entrance examination. It mainly contains some basic questions or intermediate questions.

This part is the focus and difficulty of the college entrance examination. It mainly consists of some comprehensive questions.

It mainly examines the solution and proof of inequalities, and rarely examines them individually. It mainly focuses on comparing the size of the answers to the questions. It is the focus and difficulty of the college entrance examination

This part has a greater connection with our lives and is an application question.

Mainly to prove parallel or perpendicular, find angles and distances

The difficulty of the college entrance examination requires a lot of calculations and usually contains parameters.

Key points of inspection

Key points of inspection

Key points of inspection

Key points of inspection

Key points of inspection

Key points of inspection

Do not leave any blank spaces in the entire test paper when scoring parts.

Coordinate systems are the basis of analytic geometry. In the coordinate system, an ordered real array can be used to determine the position of a point, and then equations can be used to describe geometric figures. In order to describe geometric figures or describe natural phenomena using algebraic methods, different coordinate systems need to be established. Polar coordinate system, cylindrical coordinate system, spherical coordinate system, etc. are different coordinate systems from the rectangular coordinate system. For some geometric figures, choosing these coordinate systems can make the equations established simpler.

Parametric equation is an equation that uses parameter variables as an intermediary to express the coordinates of points on the curve. It is another representation of the curve in the same coordinate system. Some curves are more conveniently represented by parametric equations than by ordinary equations. Learning parametric equations helps students further appreciate the flexibility of mathematical methods in solving problems.

Generally, in the plane rectangular coordinate system, if the coordinates x and y of any point on the curve are functions of a certain variable t, x=f(t), y=g(t)

For each allowable value of t, the point M(x,y) determined by the above equations is on this curve, then the above equation is the parametric equation of this curve, and the variable t connecting x and y is called a variable Parameters, referred to as parameters. Compared with parametric equations, equations that directly give the relationship between the coordinates of points are called ordinary equations. (Note: The parameter is a bridge connecting the variables x and y. It can be a variable with physical and geometric meaning, or it can be a variable with no practical meaning.

round

oval

hyperbola

Preparation method

substitution method

discriminant method

inequality method

inverse function method

monotonicity method

Number-shape combination method

Grasp the definition of monotonicity of functions

Be proficient in the monotonicity of basic elementary functions and their monotonic intervals

Elective textbooks for senior high school students include derivatives and their applications. It is generally very simple to use derivatives to find the monotonic interval of a function.

Attention should be paid to applications of function monotonicity, such as finding extreme values, comparing sizes, and problems related to inequalities.

periodic function

Graphics of Trigonometric Functions

domain of trigonometric functions

y=arcsin(x)

y=arccos(x)

y=arctan(x)

sin(arcsin x)=x

arcsin(-x)=-arcsinx

arccos(-x)=π-arccosx

arctan(-x)=-arctanx

arccot(-x)=π-arccotx

arcsinx arccosx=π/2=arctanx arccotx

sin(arcsinx)=x=cos(arccosx)=tan(arctanx)=cot(arccotx)

When x∈[—π/2, π/2], arcsin(sinx)=x

When x∈[0,π],arccos(cosx)=x

x∈(—π/2, π/2),arctan(tanx)=x

x∈(0,π), arccot(cotx)=x

x〉0,arctanx=π/2-arctan1/x, arccotx is similar

If (arctanx arctany)∈(—π/2, π/2), then arctanx arctany=arctan(x y/1-xy)

Clever "transformation" - returning the conditions that appear in the form of "quantity product of vectors, plane vectors collinear, plane vectors perpendicular" and "linear operations of vectors" to their true colors, into "the relationship between corresponding coordinate products"

Cleverly dig out the "conditions" - use the implicit condition "the boundedness of the sine function, the cosine function," to transform the constant establishment problem of the inequality into an equation containing the parameter ψ, and find the value of the parameter ψ, so that the function of the function can be found Analytic

Make use of the "properties" - make use of the monotonicity, symmetry, periodicity, odd-evenness of the sine function and the cosine function, as well as the overall substitution idea, you can find their symmetry axis and monotonic interval

The graphs of the function y=Asin(wx φ) and the function y=Acos(wx φ) are axially symmetrical about the straight line passing through the maximum point and parallel to the y-axis.

The graphs of the function y=Asin(wx φ) and the function y=Acos(wx φ) are respectively centrally symmetrical about their middle zero points.

The symmetry properties of the function y=Atan(wx φ) and the function y=Acot(wx φ) can also be obtained by using images.