What are the knowledge points in the first volume of mathematics in the second day of junior high school?
I. Pythagorean Theorem
1, exploring Pythagorean theorem
Pythagorean theorem: the sum of squares of two right-angled sides of a right triangle is equal to the square of the hypotenuse. If a, b, and c respectively represent two right angles and hypotenuse of a right triangle, then a2+b2=c2.
2. Must it be a right triangle?
(1) If the three-side length a b c of a triangle satisfies a2+b2=c2, then the triangle must be a right triangle.
3. Application of Pythagorean Theorem
Second, real numbers.
1, know the irrational number
① Rational number: it can always be expressed by finite decimals and infinite cyclic decimals.
② Irrational number: infinite cyclic decimal.
2. Square root
① Arithmetic square root: Generally speaking, if the square of a positive number X is equal to A, that is, x2=a, then this positive number X is called the arithmetic square root of A..
In particular, we stipulate that the arithmetic square root of 0 is 0.
③ Square root: Generally speaking, if the square of a number X is equal to A, that is, x2 = a ... then this number X is called the square root of A, also called the quadratic root.
④ A positive number has two square roots; 0 has only one square root, which is 0 itself; Negative numbers have no square root.
⑤ A positive number has two square roots, one is the arithmetic square of A, and the other is-,which are in opposite directions. Together, these two square roots can be recorded as positive or negative.
6 square root: the operation of finding the square root of a number is called square root, and A is called square root.
3. Cubic root
① Cube root: Generally speaking, if the cube of a number X is equal to A, that is, x3=a, then this number X is called the cube root of A, also called the cube root.
② Every number has a cube root, and the cube root of a positive number is a positive number; The cube root of 0 is 0; The cube root of a negative number is a negative number.
③ Square root: The operation of finding the cube root of a number is called square root, and A is called the number to be opened.
Step 4 estimate
(1) estimation, the general result is a complicated decimal, and the estimation has accurate figures.
5. Find the square root by computer
6. Real numbers
① Real number: the collective name of rational number and irrational number.
② Real numbers can also be divided into positive real numbers, 0 and negative real numbers.
③ Every real number can be represented on the number axis, and every point on the number axis corresponds to a real number. On the number axis, the point on the right is always greater than the number represented by the point on the left.
7. Quadratic radical
Meaning: Generally speaking, the formula with the shape (a≥0) is called the quadratic root, and A is called the root sign.
② =(a≥0，b≥0)，=(a≥0，b & gt0)
③ The simplest quadratic root: Generally speaking, the number of square roots does not contain denominator, nor does it contain factors or factors that can be completely opened. Such a quadratic root is called the simplest quadratic root.
④ When simplifying, it is usually required that the denominator in the final result does not contain the root sign, and each quadratic root is the simplest quadratic root.
Iii. Location and coordinates
1, determine the location
① On a plane, generally two data are needed to determine the position of an object.
2. Plane rectangular coordinate system
Meaning: In a plane, two mutually perpendicular axes with a common origin form a plane rectangular coordinate system.
(2) Usually, the two number axes are placed in horizontal and vertical positions respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, and the vertical axis is called Y axis and vertical axis, which are collectively called coordinate axes. Their common origin O is called the origin of rectangular coordinate system.
③ Establish a plane rectangular coordinate system, and the points on the plane can be represented by a set of ordered real number pairs.
④ In the plane rectangular coordinate system, two coordinate axes divide the coordinate plane into four parts, the upper right part is called the first quadrant, and the other three parts are called the second quadrant, the third quadrant and the fourth quadrant counterclockwise, and the points on the coordinate axes are not in any quadrant.
⑤ In the rectangular coordinate system, for any point on the plane, there is a unique ordered real number pair (that is, the coordinates of the point) corresponding to it; Conversely, for any ordered real number pair, there is a unique point on the plane corresponding to it.
3. Axisymmetry and coordinate changes
(1) The coordinates of two points about the X axis symmetry have the same abscissa and the opposite ordinate; With regard to the coordinates of two points symmetrical about the Y axis, the ordinate is the same, and the abscissa is opposite.
Expanding reading: the skill of improving the math score of junior two.
1, form the habit of thinking and strengthen the understanding and memory of knowledge.
Independent thinking is an essential ability to learn mathematics. When studying, students should think while listening to lectures and do problems while reading books. Through your own positive thinking, you can deeply understand mathematical knowledge, sum up mathematical laws, and solve mathematical problems flexibly, so as to turn what the teacher says and what is written in the textbook into your own knowledge. Don't think you understand what you should remember and recite. We should remember the definitions, laws, formulas and theorems of mathematics, and use them to deepen our understanding when solving problems on the basis of memory.
2. Do more exercises and summarize the problem-solving methods.
When learning mathematics, you must do problems and do them properly. The purpose of doing the problem is first to master and consolidate the knowledge learned; Secondly, initially inspire the flexible use of knowledge and cultivate the ability of independent thinking; The third is to achieve mastery through a comprehensive study and communicate different mathematical knowledge. When solving a specific problem, we must carefully examine the problem, firmly grasp all the conditions of the problem and thermal reaction, and don't ignore any condition. There is a certain relationship between a problem and a class of problems. You can think about the general idea and general solution of this kind of problem, but it is more important to grasp the particularity of this problem and how to grasp the difference between this problem and this kind of problem. Is there a simple solution? Think and summarize while doing, and deepen the understanding of knowledge through practice.
3. Be good at asking questions and cultivate your ability.
Being good at finding and asking questions in the process of learning is one of the important signs to measure whether a student has made progress in his study. Experienced teachers believe that students who can find problems and ask questions have a greater chance of success in learning; On the other hand, students who ask three questions and ask any questions themselves can't learn math well. So, how can we find problems and ask them? First, we should observe deeply and gradually cultivate our keen observation ability; Second, you should be willing to use your head instead of thinking about it. Of course, you can't find any questions and you can't ask any questions. After discovering the problem, through your own independent thinking, you should consult teachers, classmates and parents humbly when the problem is still unresolved. Only those who are good at asking questions and learning with an open mind can become real strong learners.