What are the content and requirements of math knowledge about combinatorics in the high school program in Vietnam?

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Content

Requirements to be met

4

Combinatorics

Counting rules (addition rules, multiplication partial permutation, permutations, combinations) and practical applications

- Apply addition and multiplication rules in some simple situations (for example, counting the number of possible heads/tails when tossing some coins, etc).

- Calculate the number of simplie partial permutation, permutations, combinations.

- Calculate the number of partial permutation, permutations, combinations by hand calculator.

Newton binomial with exponents no more than 5

- Identify Newton binomial ( a + b ) ⁿ ;

- Expand the Newton binomial ( a + b ) ⁿ , with exponent n = 4, by using combinations.

- Expand the Newton binomial ( a + b ) ⁿ with exponent n = 5 by using combinations.

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Content

Requirements to be met

5

Trigonometry of triangles.

Vectors

Trigonometry of triangles. The cosine theorem. The definition of sine. Formula for calculating the area of ​​a triangle. 

- Recognize the trigonometric value of an angle from 0° to 180°.

- Calculate the trigonometric value (true or approximate) of an angle from 0° to 180° using a handheld calculator.

- Explain the relationship between trigonometric values ​​of complementary and supplementary angles.

- Recognize the basic quantification systems in triangles: theorem of cosine, theorem of sine, formula for calculating area of ​​triangle.

- Explain the basic quantification systems in triangles: theorem of cosine, theorem of sine, formula for calculating area of ​​triangle.

- Describe how to solve a triangle and apply it to solving some problems with practical content (for example, determining the distance between two places when encountering obstacles, determining the height of objects when unable to meet obstacles). direct measurement, etc).

Vectors, operations (sum and difference of two vectors, product of a number and vector, dot product of two vectors) and some applications in Physics

- Recognize the concept of vectors, vectors are equal, vector-zero.

- Express some quantities in practice by vectors.

- Can perform operations on vectors (sum and difference of two vectors, product of a number with vector, dot product of two vectors) and describe geometric properties (three collinear points, midpoint of line segment). , the centroid of the triangle,...) is equal to the vector.

- Use vectors and operations on vectors to explain some phenomena related to Physics and Chemistry (for example, problems related to force, to motion,...).

- Apply knowledge of vectors to solve some geometry problems and some practical problems (for example, determining the force acting on an object,...).

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Content

Requirements to be met

6

Coordinate method in the plane

Coordinates of a vector with respect to a coordinate system. Coordinate expressions of vector operations. Application to the problem of solving triangles

- Recognize the coordinates of a vector with a given coordinate system.

- Find the coordinates of a vector, the length of a vector when knowing the coordinates of its start point and end point.

- Use coordinate expressions of vector operations in calculations.

- Apply the coordinate method to the problem of solving triangles.

- Apply knowledge of vector coordinates to solve some practical problems (for example, position of objects on the coordinate plane,...).

Line in the coordinate plane. General equations and parametric equations of straight lines. Distance from a point to a line

- Recognize the general equation and the parametric equation of the line in the coordinate plane.

- Set up the equation of the line in the plane knowing: a point and a normal vector; know a point and a direction vector; know two points.

- Identify two intersecting, parallel, overlapping and perpendicular lines by coordinate method.

- Calculate the angle between two lines based on the calculation formula.

- Calculate the distance from a point to a line using the coordinate method.

- Explain the relationship between the graph of the first order function and the line in the coordinate plane.

- Apply knowledge of straight line equations to solve some practical problems.

Circle in coordinate plane and application

- Set up the equation of a circle when knowing the coordinates of the center and radius; know the coordinates of the three points that the circle passes through; The center and radius of a circle can be determined when the equation of the circle is known.

- Set up the equation of the tangent to the circle when the coordinates of the point of contact are known.

- Apply knowledge of circle equations to solve some practical problems (for example, the problem of circular motion in Physics,...).

Three conic lines in the coordinate plane and application

- Identify three conic lines geometrically.

- Identify the canonical equations of three conic lines in the coordinate plane.

- Solve some practical problems associated with three conic lines (for example, explaining some phenomena in Optics,...).