The second volume of the first day of junior high school mathematics review knowledge points
rational knowledge
1, monomial: The product of numbers and letters is called monomial.
2. Polynomial: The sum of several monomials is called polynomial.
3. Algebraic expressions: monomials and polynomials are collectively referred to as algebraic expressions.
4. The number of monomials: The sum of the indices of all the letters in the monomials is called the number of monomials.
5. Degree of Polynomial: The degree of the degree term in a polynomial is the degree of this polynomial.
6. Complementary angle: The sum of two angles is 90 degrees, and these two angles are called complementary angles.
7. Complementary angle: The sum of two angles is 180 degrees, and these two angles are called complementary angles.
8. Relative vertex angles: two corners have a common vertex, and two sides of one corner are opposite to the extension lines of two sides of the other corner. These two angles are antipodal angles.
9. Common angle: In the "three-line octagon", the angles at the same position are common angles.
10, internal angle: in the "three-line octagon", the angle sandwiched between two straight lines is the internal angle.
1 1, ipsilateral inner angle: in "trilinear octagon", the angle on the same side of trilinear is ipsilateral inner angle.
12, significant number: an approximation, starting with the first number on the left that is not 0 and ending with the exact 1, all numbers are significant numbers.
13, probability: the probability of an event is the probability of this event.
14, triangle: A figure composed of three line segments that are not on the same line is called a triangle.
15, Angle bisector of triangle: In a triangle, the angle bisector of an inner angle intersects its opposite side, and the line segment between the intersection of the vertex and this angle is called the angle bisector of triangle.
16, triangle midline: the line segment connecting the vertex and the midpoint of the opposite side of the triangle is called the midline of the triangle.
17. Height line of triangle: Draw a vertical line from one vertex of triangle to the line where its opposite side is located, and the line segment between vertex and vertical foot is called height line of triangle.
18, congruent graphics: two graphics that can overlap are called congruent graphics.
19, variable: the number of changes is called variable.
20. Independent variable: If there is an active change in the amount of change, it is called an independent variable.
2 1, dependent variable: the quantity that changes passively with the change of independent variables is called dependent variable.
22. Axisymmetric figure: If a figure is folded along a straight line and the parts on both sides of the straight line can overlap each other, then this figure
This is called an axisymmetric figure.
23. Symmetry axis: A straight line folded in half in an axisymmetric figure is called symmetry axis.
24. perpendicular bisector: The line segment is an axisymmetric figure, and its symmetry axis is perpendicular to this line segment and divides it into two parts. Such a straight line is called the midline of this line segment. (refers to the middle vertical line)
Summary of Mathematics Knowledge Points in Volume II of Grade One of Beijing Normal University Edition
intersection line
One vertex has a common * * *, one side has a common * * *, and the other side is an extension line opposite to each other. Such two angles are called adjacent complementary angles.
There are four pairs of adjacent complementary angles when two straight lines intersect.
There is a vertex with a common * * *, and both sides of the corner are opposite extension lines. These two angles are called antipodal angles.
Two straight lines intersect and have two opposite angles.
The vertex angles are equal.
Two straight lines intersect, and one of the four corners is a right angle, so the two straight lines are perpendicular to each other. One of the straight lines is called the perpendicular of the other straight line, and their intersection point is called the vertical foot.
Parallel lines and their determination
Property 1: Two straight lines are parallel and equal to the complementary angle.
Property 2: Two straight lines are parallel and the internal dislocation angles are equal.
Property 3: Two straight lines are parallel and complementary.
Properties of parallel lines
Property 1 Two parallel lines are cut by a third line, and the congruence angles are equal. To put it simply: two straight lines are parallel and have the same angle.
Property 2 Two parallel lines are cut by a third straight line, and their internal angles are equal. To put it simply: two straight lines are parallel and their internal angles are equal.
Property 3 Two parallel lines are cut by a third straight line and complement each other. Simply put, two straight lines are parallel and complementary.
translate
Translate one unit length to the left and you can get the corresponding point (x-a, y).
Translate b unit lengths upwards, and you can get the corresponding point (x, y+b).
By translating down by b unit lengths, the corresponding point (x, y-b) can be obtained.
Review method of mathematics in grade one of junior high school
Main knowledge points of junior one mathematics:
Basic knowledge of algebra
1. Algebraic expression: the expression of the number of connections, and the letters indicating this number with the operation symbol "+-×℉ ..." are called algebraic expressions. Note: There are certain restrictions on using letters to represent numbers. First, the number obtained by letters should ensure that its formula is meaningful; second, the number obtained by letters should also make it meaningful in real life or production; A single number or letter is also algebraic.
2. Several important algebraic expressions: (m and n represent integers)
(1) The square difference between A and B is: A2-B2; The square of the difference between a and b is: (a-b) 2;
(2) If a, b and c are positive integers, the two-digit integer is 10a+b and the three-digit integer is10a+10b+c;
(3) If both m and n are integers, the quotient m is divided by 5, and the remainder n is 5m+n; Even number is 2n, and odd number is 2n+1; Three consecutive integers are: n- 1, n, n+1;
(4) If b>0, positive number is: a2+b, negative number is: -a2-b, non-negative number is: a2, and non-positive number is: -a2.
rational number
Any number that can be written in q/p form (p, q is an integer, p≠0) is a rational number. Positive integers, 0 and negative integers are collectively referred to as integers; Positive and negative scores are collectively called scores; Integers and fractions are collectively called rational numbers. Note: 0 is neither positive nor negative; -a is not necessarily negative, and +a is not necessarily positive; P is not a rational number;
Rational number addition rule:
(1) Add two numbers with the same symbol, take the same symbol, and add the absolute values;
(2) Add two numbers with different symbols, take the symbol with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value;
(3) Adding a number to 0 still gets this number.
Arithmetic of rational number addition;
The commutative law of (1) addition: a+b = b+a; (2) The associative law of addition: (a+b)+c=a+(b+c).
Rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number; That is, a-b=a+(-b).
Rational number multiplication rule:
(1) Multiply two numbers, the same sign is positive, the different sign is negative, and the absolute value is multiplied;
(2) Multiply any number by zero to get zero;
(3) When several numbers are multiplied, one factor is zero and the product is zero; Each factor is not zero, and the sign of the product is determined by the number of negative factors.
Arithmetic of rational number multiplication;
(1) The commutative law of multiplication: ab = ba(2) The associative law of multiplication: (AB) C = A (BC);
(3) Distribution law of multiplication: a(b+c)=ab+ac.
Rational number division rule: dividing by a number is equal to multiplying the reciprocal of this number; Note: Zero cannot be divisible.
Addition and subtraction of algebraic expressions
Monomial: in algebraic expressions, if only multiplication (including power) operations are involved. Or algebraic expressions that contain division but do not contain letters in division are called monomials.
Coefficient and times of single item: the non-zero numerical factor in single item is called the numerical coefficient of single item, referred to as the coefficient of single item for short; When the coefficient is not zero, the sum of all the letter indexes in a single item is called the degree of the item.
Polynomial: The sum of several monomials is called polynomial.
Number and degree of polynomials: the number of monomials contained in a polynomial is the number of polynomial terms, and each monomial is called a polynomial term; In polynomial, the degree of the degree term is called the degree of polynomial; Note: (If A, B, C, P and Q are constants) ax2+bx+c and x2+px+q are two common quadratic trinomials.
Algebraic expression: An algebraic expression without division or with division but without letters is called an algebraic expression.
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