Induction of compulsory mathematics knowledge points in senior one 1
I. Collection of related concepts
The meaning of 1. set: some specified objects are brought together to form a set, and each object is called an element.
2. Three characteristics of elements in a set:
The certainty of (1) element is as follows: mountains in the world;
(2) The mutual anisotropy of elements, such as the set of happy letters {H, a, p, Y }；;
(3) The disorder of elements: for example, {a, b, c} and {a, c, b} represent the same set.
3. Representation of assembly: {…} For example, {basketball players in our school}, {Pacific Ocean, Atlantic Ocean, Indian Ocean, Arctic Ocean}
(1) Set is expressed in Latin letters: A={ basketball players in our school}, B={ 1, 2, 3, 4, 5};
(2) Representation of sets: enumeration and description.
The set of non-negative integers (that is, the set of natural numbers) is recorded as: n;
Positive integer set: N_ or n+;
Integer set: z;
Rational number set: q;
Real number set: r.
1) enumeration: {a, b, c ...};
2) Description: describes the common attributes of the elements in the set, and is written in braces to indicate the set {x? r | x-3 & gt； 2}，{ x | x-3 & gt； 2};
3) Language description: Example: {A triangle that is not a right triangle}.
4, the classification of the set:
(1) finite set contains a set of finite elements;
(2) An infinite set contains an infinite set of elements;
(3) An example of an empty set without any elements: {x | x2 =-5}.
Second, the basic relationship between sets
1. "Inclusion" relation-subset;
Note: There are two possibilities that A is a part of B (1); (2)A and B are the same set.
On the other hand, set A is not included in set B, or set B does not include set A, which is marked as AB or BA.
2. "Equality" relationship: A=B(5≥5 and 5≤5, then 5=5).
Example: let a = {x | x2-1= 0} b = {-1,1} "Two sets are equal if their elements are the same".
Namely: ① Any set is a subset of itself. Aiya.
② proper subset: If AíB and A 1B, then set A is the proper subset of set B, and it is recorded as AB (or BA).
③ If aí b and bí c, then aí c.
④ If AíB is accompanied by BíA, then a = b.
3. A set without any elements is called an empty set and recorded as φ.
It is stipulated that an empty set is a subset of any set and an empty set is a proper subset of any non-empty set.
4. Number of subsets:
A set of n elements, including 2n subsets, 2n- 1 proper subset, 2n- 1 nonempty subset and 2n- 1 nonempty proper subset.
Third, the operation of the set.
The operation types intersect and set the complement set;
Define a set consisting of all elements belonging to A and B, which is called the intersection of A and B, and it is marked as AB (pronounced as' A crosses B'), that is, AB={x|xA, and XB}.
A set consisting of all elements belonging to set A or set B is called the union of A and B, and it is marked as AB (pronounced as' A and B'), that is, AB={x|xA, or xB}).
Senior one mathematics compulsory one knowledge point induction two.
Structural characteristics of 1, column, cone, platform and ball
(1) prism:
Geometric features: the two bottom surfaces are congruent polygons with parallel corresponding sides; The lateral surface and diagonal surface are parallelograms; The sides are parallel and equal; The section parallel to the bottom surface is a polygon that is congruent with the bottom surface.
② Pyramid
Geometric features: the side and diagonal faces are triangles; The section parallel to the bottom surface is similar to the bottom surface, and its similarity ratio is equal to the square of the ratio of the distance from the vertex to the section to the height.
(3) Prism:
Geometric features: ① The upper and lower bottom surfaces are similar parallel polygons; ② The side is trapezoidal; ③ The sides intersect with the vertices of the original pyramid.
(4) Cylinder: Definition: It is formed by taking a straight line on one side of a rectangle as the axis and rotating the other three sides.
Geometric features: ① The bottom is an congruent circle; ② The bus is parallel to the shaft; ③ The axis is perpendicular to the radius of the bottom circle; ④ The side development diagram is a rectangle.
(5) Cone: Definition: A Zhou Suocheng is rotated with a right-angled side of a right-angled triangle as the rotation axis.
Geometric features: ① the bottom is round; (2) The generatrix intersects with the apex of the cone; ③ The side spread diagram is a fan.
(6) frustum of a cone: definition: a circle rotates with the vertical line of the right trapezoid and the waist of the bottom as the rotation axis.
Geometric features: ① The upper and lower bottom surfaces are two circles; (2) The side generatrix intersects with the vertex of the original cone; (3) The side development diagram is an arch.
(7) Sphere: Definition: the geometry formed by taking the straight line with the diameter of the semicircle as the rotation axis and the semicircle surface rotating once.
Geometric features: ① the cross section of the ball is round; ② The distance from any point on the sphere to the center of the sphere is equal to the radius.
3. Intuition of space geometry-oblique two-dimensional drawing method.
The characteristics of oblique bisection method are as follows: ① The line segment originally parallel to the X axis is still parallel to X, and its length remains unchanged;
② The line segment originally parallel to the Y axis is still parallel to Y, and its length is half of the original.
4. Surface area and volume of cylinders, cones and platforms.
(1) The surface area of the geometry is the sum of all the surfaces of the geometry;
(2) The surface area formula of special geometry (C is the perimeter of the bottom, H is the height, the oblique height, and L is the bus).
One knowledge point induction of compulsory mathematics in senior one 3
1. subset of "inclusive" relation.
Note: There are two possibilities that A is a part of B (1); (2)A and B are the same set.
On the other hand, set A is not included in set B, or set B does not include set A, which is marked as AB or BA.
2. "Equality" relationship: A=B(5≥5 and 5≤5, then 5=5)
Example: let a = {x | x2-1= 0} b = {-1,1} "Two sets are equal if their elements are the same".
Namely: ① Any set is a subset of itself. Answer (answer)
② proper subset: If A(B) and A(B), then set A is the proper subset of set B.
③ If A(B, B(C), then A(C).
④ If A(B) and B(A) exist at the same time, then A = B. ..
3. A set without any elements is called an empty set and recorded as φ.
It is stipulated that an empty set is a subset of any set and an empty set is a proper subset of any non-empty set.
A set of n elements, including 2n subsets and 2n- 1 proper subset.
Expanding reading: what should we pay attention to when learning mathematics?
1. Listen carefully in class and review in time after class.
Accept a new kind of knowledge, mainly in the classroom, so we should pay attention to the learning efficiency in the classroom, find suitable learning methods, follow the teacher's ideas and think positively in the classroom. Review in time after class, ask questions if you don't understand, remember what the teacher explained in class first when you do your homework, and also firmly grasp the formula and reasoning process, and try not to turn over the books. Try to think for yourself, and don't look at the answer in a hurry. We should also summarize and review regularly and combine knowledge points to become our own knowledge system.
2. Do more questions and develop good problem-solving habits.
If you want to learn math well, it is inevitable to do a lot of problems. Only by mastering all kinds of questions can you effectively improve your math scores. At first, we should focus on the exercises in books, lay a good foundation, and then gradually increase the difficulty, open up ideas and practice various types of problem-solving ideas. For error-prone questions, you should record them and contact them repeatedly. When doing problems, we should develop good problem-solving habits and concentrate, so that we can get into the best state and form habits, so that we can use them freely in the exam.