Real number operation 1 add
Add two numbers with the same sign, take the same sign, and add the absolute values; Add different symbols with different absolute values of two numbers, take the symbol with the larger absolute value, and subtract the symbol with the smaller absolute value from the larger absolute value; Two opposite numbers add up to 0; Add a number to 0 and you still get the number.
2. subtraction: subtracting a number is equal to adding the reciprocal of this number.
multiply
Multiply several non-zero real numbers, and the sign of the product is determined by the number of negative factors. When there are even negative factors, the product is positive. When there are odd negative factors, the product is negative. Multiply several numbers, one factor is 0 and the product is 0.
break up
Dividing by a number is equal to multiplying the reciprocal of this number. Divide two numbers, the same sign is positive, the different sign is negative, and the absolute value is divided by 0. Divide by any number that is not equal to 0 to get 0.
5. Multipliers and prescriptions
The meaning of (1)an is the product a of n, any power of positive number is positive, even power of negative number is positive, and odd power of negative number is negative.
(2) Positive numbers and 0 can be squared, but negative numbers cannot be squared; Positive numbers, negative numbers and 0 can all be turned on.
(3) Zero exponent and negative exponent.
Planar Cartesian coordinate system 1, ordered number pair: A number pair consisting of two numbers A and B in sequence is called an ordered number pair.
2. Plane rectangular coordinate system
Draw two mutually perpendicular number axes with overlapping origins on the plane to form a plane rectangular coordinate system. The horizontal axis is called the X axis or the horizontal axis, and it is customary to take the right as the positive direction; The vertical axis is called the Y axis or the vertical axis takes 2 as the positive direction; The intersection of the two coordinate axes is the origin of the plane rectangular coordinate system.
Any point on the plane can be represented by an ordered number pair.
After the rectangular coordinate system is established, the coordinate plane is divided into four parts, I, II, III and IV, which are called the first quadrant, the second quadrant, the third quadrant and the fourth quadrant respectively. The points on the coordinate axis do not belong to any quadrant.
3, using coordinates to represent the geographical location
The process of drawing the distribution plan of some places in the area using the plane rectangular coordinate system is as follows:
(1) Establish a coordinate system, select a suitable reference point as the origin, and determine the positive direction of the X axis and the Y axis;
⑵ Determine the appropriate scale according to specific problems and mark the unit length on the coordinate axis;
(3) Draw these points on the coordinate plane and write down the coordinates of each point and the name of each place.
4. Coordinate translation.
In the plane rectangular coordinate system, the corresponding point (x+a, y) (or (x-a, y)) can be obtained by translating the point (x, y) to the right (or to the left) by a unit length. The corresponding point (x, y+b) (or (x, y-b)) can be obtained by translating the point (x, y) up (or down) by b unit lengths.
In the plane rectangular coordinate system, if a positive number A is added (or subtracted) to the abscissa of each point of the graph, the corresponding new graph is to translate the original graph to the right (or left) by a unit length; If a positive number A is added (or subtracted) to the ordinate of each point, the corresponding new figure is to translate the original figure up (or down) by a unit length.
Collection and arrangement of data The step of describing data with histogram (that is, the step of making histogram)
1. Calculate the difference between the maximum and minimum values.
2. Determine the distance and number of groups.
Principle: When the number of data is less than 100, it is divided into 5~ 12 groups according to the number of data.
Group Distance: Divide all data into several groups, and the distance between two endpoints of each group (the range of values of data in the group).
3. Column frequency distribution table
Frequency: The number of data in each group is called frequency.
4. Draw the histogram of frequency distribution.
5. The area of the small rectangle indicates the frequency. The vertical axis is. When grouped at equal intervals, the frequency is usually expressed directly by the height of a small rectangle, that is, the vertical axis is "frequency".
6. Frequency distribution diagram. Draw the frequency distribution diagram according to the frequency distribution diagram: ① Take the midpoint on the upper side of each small rectangle and the point on the X axis that is half a group distance away from the leftmost and rightmost straight lines. 2 connection.
One-dimensional linear inequality (group) 1. Inequality: a formula connecting two algebraic expressions with inequality symbol >
2. The basic properties of inequality:
Add (or subtract) the same number or the same algebraic expression on both sides of inequality A, and the direction of inequality remains unchanged;
Both sides of inequality B multiply (or divide) the same positive number, and the direction of inequality remains unchanged;
Both sides of C inequality are multiplied by (or divided by) the same negative number, and the direction of inequality should be changed.
3. Solution set of inequality: the value of the unknown quantity that can make the inequality hold is called the solution of this inequality; The set of all solutions of an inequality is called the solution set of this inequality.
4. One-dimensional linear inequality: an inequality with only one unknown number, degree 1 and coefficient not equal to zero is called one-dimensional linear inequality; Its standard form is ax+b > 0 or ax+b < 0, (a≠0).
5. Represent by inequality, and solve the inequality group by number axis or formula (formula (simple inequality): the same big takes the big, the same small takes the small, the big (middle) small (middle) big takes the middle, the big (middle) size (middle) is small, and the solution is gone.