Mathematics concept of grade one in junior high school

Real number:

Rational numbers and irrational numbers are collectively called real numbers.

Rational number:

Integers and fractions are collectively called rational numbers.

Irrational number:

Irrational numbers refer to infinite cyclic decimals.

Natural number:

The numbers 0, 1, 2, 3, 4 ~ (including 0) representing objects are all called natural numbers.

Number axis:

The straight line that defines the point, the positive direction and the unit length is called the number axis.

Countdown:

Two numbers with different symbols are opposite.

Countdown:

Two numbers whose product is 1 are reciprocal.

Absolute value:

The distance between the point representing the number A and the point on the number axis is called the absolute value of A, the absolute value of a positive number is itself, the absolute value of a negative number is its inverse, and the absolute value of 0 is 0.

Mathematical theorem formula

Rational number arithmetic

(1) addition rule: add two numbers with the same symbol, take the same symbol, and add the absolute values; Add two numbers with different signs, take the sign of the addend with larger absolute value, subtract the smaller absolute value from the larger absolute value, and add two numbers with opposite numbers to get 0.

(2) Law of subtraction: subtracting a number is equal to adding the reciprocal of this number.

(3) Multiplication rule: two numbers are multiplied, the same sign is positive and the different sign is negative, and the multiplication takes the absolute value; Multiply any number by 0 to get 0.

(4) Division rule: dividing by a number is equal to multiplying the reciprocal of this number; Divide two numbers, the same sign is positive and the different sign is negative, and divide by the absolute value; Divide 0 by any number that is not equal to 0 to get 0.

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Respondent: HTQDG- Qian Zongsi 9-2 1 2 1:49.

1. What numbers does an integer include? What is a natural number? What is a rational number?

A: Integers include positive integers, zero and negative integers. Positive integers are also called natural numbers. Positive integer, zero, negative integer, positive fraction and negative fraction are collectively called rational numbers.

2. What is the number axis? How to express the numbers on the number axis?

A: The number axis is a straight line with direction, origin and specified length unit. Rational numbers can always find their corresponding points on the number axis. The arrow indicating the direction is at the right end of the straight line. The upper or right side of the number axis is positive, the left or lower side of the origin is negative, and the origin is zero.

3. What is the reciprocal? What is absolute value? How to judge the size of rational number?

A: Two numbers with the same distance from the origin are called opposites. The antonym of zero is zero. The distance from the number A represented on the number axis to the origin is called the absolute value of the number A, the absolute value of a positive number is itself, the absolute value of a negative number is its inverse, and the absolute value of zero is itself. Positive number is greater than zero, zero is greater than negative number, positive number is greater than negative number, and the absolute values of two negative numbers are larger but smaller.

4. What is the rational number addition rule?

Answer: two numbers with the same sign are added, the sign of sum is the same as that of addend, and their absolute values are added; Two numbers with different absolute values are added, and the sign of the sum is the sign of the addend with the larger absolute value, and the larger absolute value is subtracted from the smaller absolute value; The sum of mutually opposite numbers is zero; When any number is added to zero, the sum is this number.

5. What is the subtraction rule of rational numbers?

A: Subtracting a number equals adding the opposite number.

6. What is the commutative law of addition? What is the distribution law of addition?

Answer: when two numbers are added, the sum remains the same when the positions are exchanged. This is the exchange law of addition; When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and their values are unchanged. This is the associative law of addition.

7. What is the multiplication rule of rational numbers?

Answer: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied; Multiply any number by zero and the product is zero.

8. What is reciprocal?

A: Multiply two numbers. If the product is equal to 1, then these two numbers are reciprocal.

9. What is the commutative law of multiplication? What is the associative law of multiplication? What is the distribution law of multiplication?

Answer: Two numbers are complementary, and the positional products of exchange factors are equal, such as ab=ba, which is called multiplication exchange law; When three numbers are multiplied, the first two or the last two numbers are multiplied first, and the products are equal, such as: (ab)c=a(bc), which is called the multiplicative associative law; Multiplying a number by the sum of two numbers is equivalent to multiplying this number by these two numbers respectively, and the products add up, for example, a(b+c)=ab+ac, which is called the distribution law of multiplication.

10, what is the change rule of the symbol of each item when brackets are added and removed?

Answer: If the factor outside the bracket is positive when the bracket is removed (added), the symbols of the items in the formula after the bracket is removed (added) are the same as those of the corresponding items in the formula in the original bracket; The factor outside parentheses is negative. After deleting (adding) brackets, the symbol of each item in the formula is opposite to that of the corresponding item in the original brackets.

1 1, what is a rational number division algorithm?

Answer: the division algorithm of two rational numbers can be expressed in two ways: one is to divide by a number that is not equal to zero, which is equal to multiplying the reciprocal of this number; Second, divide two numbers, the same sign is positive, and the different sign is negative, divided by the absolute value. Divide zero by any number that is not zero, and the business is zero.

12, what is the power of rational numbers? Power? Cardinality? Index?

A: The operation of multiplying the same factor is called power, the result of power is called power, the number of the same factor is called exponent, and this factor is called base. Write it down.

13, what is the law of rational number power operation?

A: The odd power of a negative number is negative, and the even power of a negative number is positive. Any positive power is positive. Any positive integer power of zero is zero.

14, when rational numbers are mixed, what is the rule of operation order?

Answer: In the mixed operation of rational numbers, the operation is divided into three levels, with addition and subtraction as the first level operation, multiplication and division as the second level operation and multiplication as the third level operation. At the same operation level, proceed from left to right in turn; Not a mixed operation at the same level, first calculate the power, then multiply and divide, and then add and subtract; If there are brackets in the operation, do the operation in brackets first, and then proceed in the order of brackets, brackets and braces.

What is scientific notation?

A: A number is represented by a× 10n, which is called scientific notation. Here a must be an integer with only one digit. N must be a positive integer. It is pronounced as a times 10 to the n power (or a times 10 to the n power).

16, what is it? How did you get the approximate figure? What is the accuracy of approximate figures?

A: A divisor is a number that is close to the exact number, but different from the exact number. In current textbooks, approximate values are obtained by rounding. The closeness between the approximate value and the exact value is called accuracy.

17, what is a significant number?

A: A number from the first non-zero number on the left to the last number is called the effective number of this number. If there are several significant numbers, it is said that this number has several significant numbers. For example, 0.0 1350 has four significant figures.

What is an equation? What is an equation?

A: The formula of equality is called equality. Equations with unknowns are called equations.

19, what is the essence of the equation? What is empathy?

A: The equation has two properties, 1. Adding (or subtracting) the same number (or formula) on both sides of the equation will still make the results equal. 2. Both sides of the equation are multiplied by the same number, or divided by the same non-zero number, and the results are still equal. After changing the sign, moving an item on one side of the equation to the other side is called moving the item.

20. What is the solution of the equation?

A: The value of the unknown quantity that can make both sides of the equation equal is called the solution of the equation (or the bitter root of the equation).

2 1, what is a linear equation? How to solve the one-dimensional linear equation?

A: An equation containing an unknown quantity with the degree of 1 is called a linear equation. The steps to solve a linear equation with one variable are: removing the denominator; Remove the brackets; Moving items (generally moving items with unknown numbers to the left and constant items to the right); Merge similar projects; Both sides of the equation are divided by unknown coefficients.

22. How to solve application problems?

A: The first step is to set an unknown number; The second step is to analyze the meaning of the question, find out the equivalence relationship and list the equations; Step 3, solve the listed equations; The fourth step, checking calculation; Step five, write the answer.

23. What are the basic elements of geometric figures? What are points, lines, surfaces and bodies?

A: The basic element in geometry is a point. Among geometric figures, figures with only position but no length, width and thickness are called points. For example, where two straight lines intersect is a point. Geometrical figures formed by moving points are called lines. A figure formed by moving lines is called a face. The figure formed by the moving surface is called volume.

24. What is the essence of a straight line?

A: There is a straight line after two o'clock, and there is only one straight line. (Two points are in a straight line)

25. What is a line segment? The endpoint of the line segment? Midpoint? What are the attributes of line segments? What is the distance between two points?

Answer: The part between two points on a straight line is called a line segment, these two points are called the end points of the line segment, and the point with the same distance between the two ends is called the midpoint of the line segment. The essence of a line segment is that between two points, the line segment is the shortest. The length of a line segment connecting two points is called the distance of the line segment.

26. What is a ray?

A: A straight line is cut by a point, and the rest is called a ray. In other words, a straight line with one end and an infinite extension at the other end is called a ray.

27. What is a horn? What is the unit for measuring angles? The bisector of the angle?

A: A figure composed of two rays with a common endpoint is called an angle. The units of angles are degrees, minutes and seconds, and the advancing rate from seconds to minutes and from minutes to degrees is 60. The ray that divides an angle into two equal parts is called the bisector of the angle.

28. What are right angles, right angles, rounded corners, complementary angles and complementary angles? What are the properties of complementary angle and complementary angle?

A: An angle of 90 is called a right angle, an angle of180 is called a right angle, and an angle of 360 is called a fillet. If the sum of two angles is equal to 90, then we call them complementary angles. The essence of complementary angles is that complementary angles of equal angles are equal. If the sum of two angles is equal to 180, then the two angles are said to be complementary. The essence of complementary angles is that complementary angles of equal angles are equal.

29. What angle can two straight lines intersect to form? What is their relationship?

A: The intersection of two straight lines can form adjacent complementary angles and relative vertex angles according to the positional relationship. There is a common side and the other side is two corners along a long line, which are called complementary corners adjacent to each other. There is a common vertex, and the other two sides are two angles along the long line, which are called antipodal angles. The vertex angles are equal.

30. What do you mean two straight lines are vertical? What is a vertical line? What do you mean by hanging your feet?

A: Two straight lines intersect at 90 degrees, which means they are perpendicular to each other. One of them is called the perpendicular of the other, and their intersection point is called the vertical foot.

3 1, what is the nature of the vertical line? What is the distance from a point to a straight line?

Answer: The essence of vertical line is that there is only one straight line perpendicular to the known straight line. The distance from a point to a straight line refers to the length from a point outside the straight line to the vertical section of the straight line. The vertical line segment is the shortest among the line segments connecting all points on the straight line and a point outside the straight line.

32. What are parallel lines? What is the axiom about parallel lines?

A: On a plane, if two straight lines never intersect, we call them parallel to each other. The axiom of parallel lines is: 1, crossing a point outside the straight line, there is only one straight line parallel to this straight line; 2. If two straight lines are parallel to the third straight line, then the two straight lines are also parallel.

33. What angle can two straight lines be cut by a straight line?

Answer: It can form isosceles angle, ipsilateral internal angle and internal dislocation angle.

34. Please describe the judgment theorem for judging that two straight lines are parallel?

A: 1. Two straight lines are cut by a third straight line. If congruent angles are equal, then two straight lines are parallel; 2. Two straight lines are cut by a third straight line. If they are complementary to the lateral inner angle, then the two straight lines are parallel; 3. Two straight lines are cut by the third straight line. If the internal dislocation angles are equal, two straight lines are parallel.

35. What are the properties of parallel lines?

Answer: 1, two parallel straight lines are cut by the third straight line, and the same angle is equal; 2. Two parallel straight lines are cut by a third straight line, which are complementary to the inner angle of the side surface; 3. Two parallel straight lines are cut by the third straight line, and the internal dislocation angles are equal.

36. What is the distance between parallel lines?

Answer: If a straight line is perpendicular to two parallel lines, the length of the line segment cut by the two parallel lines is called the distance between the two parallel lines.

37. What is a proposition? What are the two parts of the proposition? What is the general form?

A: The sentence that judges a thing is called a proposition. A proposition consists of two parts: the theme and the conclusion. Generally, it is written in the form of "If ……, then …".

38. What is the translation of graphics? What are the characteristics of translated graphics?

A: If you move the whole graph in a certain direction, you will get a new graph with the same size and shape as the original graph. This method is called translation transformation of graphics. Translation for short. The characteristic of translation graphics is that any point in the new graphics can always find its corresponding point in the old graphics, and the line segments connecting all the corresponding points are parallel to each other.

39, how to establish a plane rectangular coordinate system? What is the horizontal axis? Vertical axis? Born?

Answer: Draw two mutually perpendicular number axes on a plane, so that the origins of the two number axes coincide, thus establishing a plane rectangular coordinate system. In the plane rectangular coordinate system, the horizontal axis is called the horizontal axis or the X axis, and the vertical axis is called the vertical axis or the Y axis. The intersection of two number axes is called the origin.

40, how to use a point in the plane rectangular coordinate system to represent an ordered number?

A: A point P on the horizontal plane is perpendicular to the X-axis (horizontal axis), and the vertical foot is M and the vertical foot is N. If the value of M on the X-axis is A and the value of N is B, then P represents an ordered number pair (A, B), which is called the coordinate of the point P and is recorded as P (?

4 1, what is a quadrant? What are the characteristics of the coordinate values of each quadrant?

A: The plane rectangular coordinate system divides the plane into four parts, and each part is called a quadrant. The part enclosed by the positive direction of the X axis and the positive direction of the Y axis is called the first quadrant, and the counterclockwise direction is the second quadrant, the third quadrant and the fourth quadrant respectively. The x and y coordinates of the first quadrant are positive values; The second quadrant x is negative and y is positive; The third quadrant x and y are both negative values; The fourth quadrant x is positive and y is negative.

42. What is a triangle? What is the relationship between the sides of a triangle? What does the angle have to do with it?

A: The figure formed by the end-to-end connection of three line segments that are not on the same line is called a triangle. The sum of any two sides in a triangle is greater than the third side. The sum of the three internal angles of a triangle is equal to 180. The difference between any two sides of a triangle is less than the third side.

43. What are the bisectors of the triangle height, midline and angle?

A: The vertical line passing through the vertex of the triangle is the opposite side, and the opposite side intersects at one point (that is, the vertical foot). The line segment connecting the vertex and this point is called the height of this side of the triangle. A triangle has three sides, so it has three high lines.

The line segment connecting the vertex of a triangle and the midpoint of its opposite side is called the midline of this side of the triangle. A triangle has three sides, so it has three middle lines.

Make the bisector of an inner angle of a triangle, pass through the opposite side of this angle to a point, and the line segment connecting this point and the vertex of this inner angle is called the bisector of the triangle. A triangle has three angles, so it has three bisectors.

44. What is the outer corner of a triangle? What is the nature of the external angle?

Answer: The angle formed by one side of a triangle and the extension line of the other side is called the outer angle of the triangle. The outer angle is equal to the sum of two non-adjacent inner angles. It can be inferred that the outer angle of a triangle is larger than any inner angle that is not adjacent to it.

45. What is a polygon? How are polygons named? What is a regular polygon?

A: On the plane, a figure composed of some line segments end to end is called a polygon. Polygons are named according to the number of sides, a few sides are called polygons, and n sides are n polygons. If all sides of a polygon are equal and all internal angles are equal, then the polygon is called a regular polygon. Such as regular pentagons and regular hexagons.

46. What is a convex polygon? The interior angle of a polygon? Diagonal?

A: If a polygon is on one side of any extension line, it is called a convex polygon. Junior high school mathematics studies convex polygons. The included angle between two adjacent sides of a polygon is called the inner angle of the polygon. The connecting line between two nonadjacent vertices is the diagonal of a polygon.

47. What is the internal angle of a polygon? What is the outer corner?

Answer: The inner angle of a polygon is equal to (n-2) × 180. The sum of the outer angles of a polygon is 360 degrees.

48. What is a binary linear equation? What is a system of binary linear equations?

A: An equation with two unknowns of degree 1 is called a binary linear equation. The combination of two binary linear equations is called binary linear equations.

49, what is the solution of binary linear equation? What is the solution of binary linear equations?

Answer: the values of two unknowns that make both sides of a binary linear equation equal are called the solutions of a binary linear equation. In binary linear equations, the common solution of two equations is called the solution of binary linear equations.

50. What is elimination? What kinds of elimination methods are there to solve binary linear equations?

A: When solving binary linear equations, because there are two unknowns, we often eliminate one of them and turn binary linear equations into univariate linear equations. This method is called elimination. We use substitution elimination method and addition and subtraction elimination method.

5 1. How to solve binary linear equations by substitution elimination method?

Answer: 1. Select an equation from the binary linear equations, and use the algebraic expression of another unknown (such as Y) to represent an unknown (such as X) in this equation; 2. Substitute algebraic expression into another equation to make it a linear equation, and solve this equation to get an unknown solution; 3. Substitute the solution in 2 into an equation in the equation set, and solve this equation to get another unknown solution.

52. How to solve binary linear equations by adding, subtracting and eliminating?

Answer: 1. Transform the equation to make the coefficient of an unknown in the two equations equal or opposite (if the coefficient of an unknown in the original equation is equal or opposite, this step can be omitted); 2. Add and subtract the two sides of the equation (adding coefficient in the opposite direction and subtracting coefficient in the opposite direction), eliminate an unknown, solve this one-dimensional linear equation, and get the solution of this unknown; 3. Substitute the solution in 2 into an equation in the equation set, and solve this equation to get another unknown solution.

53. What is inequality? Solution of inequality? Solution set of inequality?

Answer: use > or