Formula:
Dividing two numbers by the same amount of change will not change the size of quotient.
Remember when changing, and never discard 0.
Extended data:
Complete works of mathematical formulas and laws in junior high school;
1. The condition of the simplest radical:
The simplest radical three conditions,
Don't include a denominator in the symbol.
Power finger (number) and root finger (number) should be mutually prime,
The index finger is slightly smaller than the index finger.
2. Coordinate characteristics of special points:
Coordinate plane points (x, y), transverse to the front and longitudinal to the back;
(+,+), (-,+), (-,-) and (+,-), the four quadrants are divided into front and back;
Y is 0 on the x axis, and x is 0 on the y axis.
3. The bisector of the quadrant angle:
The bisector of the quadrant angle,
Coordinate features have characteristics,
One, three horizontal and three vertical are equal,
Second, the four horizontal and four vertical directions are just the opposite.
46 straight line parallel to the axis:
A straight line parallel to the axis,
The coordinates of the points are specific,
The straight line is parallel to the X axis, and the ordinate is equal and unequal;
The straight line is parallel to the Y axis, and the abscissa of the point remains unchanged.
5. The coordinates of the symmetry point:
Remember the coordinates of the symmetry point,
Don't confuse opposing positions,
The x axis is symmetrical and the y axis is opposite.
Y axis symmetry, with a negative sign in front of X;
Symmetry of origin is the easiest to remember,
Horizontal and vertical coordinates change sign.
6. The range of independent variables:
The denominator of the fraction is not zero,
Even times cannot be negative;
The zeroth radix is not zero,
Algebraic and homogeneous roots can do it.
7. Motion law of function image: If the primary analytic function is written as y = k (x+0)+b, and the analytic formula of quadratic function is written as y = a (x+h) 2+k, the following formula can be used.
Translate left and right in brackets,
Finally, translate up and down,
Zuo Zheng's correct responsibility must be borne in mind.
Up and down can't be wrong.
8. The properties of image formula and linear function;
The linear function is a straight line, and the image passes through three quadrants;
The proportional function is simpler, and the straight line passes through the origin;
These two coefficients, k and b, play a great role.
K is the included angle of slope, and b intersects the y axis.
K is right oblique, X increases or decreases and Y increases or decreases;
K is negative to the lower left, and the change law is just the opposite;
The greater the absolute value of k, the farther the straight line is from the horizontal axis.
9. The properties of image formula and quadratic function;
Quadratic parabola, image symmetry is the key;
Openings, vertices and intersections that determine the appearance of the image;
The opening and size are broken by a, and the c axis and the y axis intersect.
The symbol of B is special, and the symbol is associated with A;
First find the vertex position, and use the y axis as the reference line.
The difference between left and right is 0, remember that there is no confusion in your heart;
Vertex coordinates are the most important and appear in the general formula.
The horizontal scale is the axis of symmetry, and the maximum value of the vertical scale function is shown in.
If the position of the symmetry axis is found, the sign is reversed,
Generally, vertices, intersections and different expressions can be interchanged.
10. Image and property formula of inverse proportional function;
Inverse proportional function has its own characteristics, and hyperbola is far from each other.
K is positive, and the graph is within one or three boundaries.
K is negative, and the graph is within the boundary of 24 (image);
The graph is reduced in the first and third functions, and the two branches are reduced respectively.
In the second and fourth graphs, the two branches are opposite, and the two branches are increased respectively;
The longer the line is, the closer it is to the axis and it will never touch the axis.
1 1. Remember the definition of trigonometric function skillfully: The trigonometric functions learned in junior high school include sine, cosine, tangent and cotangent, which are actually the ratio of the sides of a right triangle. You can use/separate these two words and then use the following one.
12. Definition of a sentence:
An unwise cook taught his apprentice to kill fish and said, "I'm going straight to the fish (neighbor)."
Positive: sine or tangent, right: opposite positive; Remainder: cosine or cosine, adjacent: adjacent edges indicate that the remainder is adjacent; Tangents are right-angled edges.
13. Increase and decrease of trigonometric function: positive increase and residual decrease.
14. Special trigonometric function value memory:
First of all, remember that the denominators of sine and cosine values of 30 degrees, 45 degrees and 60 degrees are all 2, and the denominators of tangent and cotangent are all 3. The molecular formula "123,3213927" is enough.
15. Determination of parallelogram:
To prove a parallelogram, two conditions are needed.
The opposite sides of the card are equal, or the opposite sides of the card are parallel.
You can also use a set of opposite sides, and they must be equal and parallel.
Diagonal, a treasure, can't run away even if it is divided equally.
It is also useful to have equal diagonals, and you can achieve "two diagonal groups".
16. Auxiliary line of trapezoidal problem;
Move the trapezoid diagonal, and the two waists will form a line;
Move one waist in parallel, with both waists in the "△" position;
Extend the waist intersection a little, there are parallel lines in the "△";
Make two trapezoidal high lines, and the rectangle will be displayed in front of your eyes;
Know the center line of the waist, don't forget to make the center line.
17. Add auxiliary songs:
Auxiliary line, how to add it?
Finding the pattern is the key. If there is an angle (horizontal) dividing line in the question, it can be vertical on both sides.
The middle perpendicular of the line segment leads to the connecting line at both ends, and the midpoint connecting the two sides of the triangle forms the middle line;
A triangle has a midline, and the midline is doubled.
18. Proof curve of circle:
It is not difficult to prove that the radius and diameter are often connected;
Chords can be used as the center distance of chords to vertically divide chords;
The diameter is the largest chord of a circle, and the straight fillet stands on the top.
If it bisects the chord vertically, the vertical diameter and shooting will affect the ear;
And the angle related to the circle. Don't forget that they are related by blood.
Perimeter, center of the circle, tangent angle, carefully find the relationship to connect the lines;
The angles of the circles of the same arc are equal, so it is most commonly used in proving problems.
If there is a tangent angle in the circle, it is easy to find the arc;
A circle has an inscribed quadrilateral with complementary diagonals.
The outer angle is equal to the inner diagonal, and the quadrilateral is inscribed with a circle;
Right angle opposite or * * * chord, try to add auxiliary circle;
If we turn the problem around, we can solve four problems;
It is proved that the tangent and vertical radius of the circle pass through the outer end,
There is a * * * point between the straight line and the circle, which proves that the vertical radius is connected.
If the straight line and the circle are not given points, it is necessary to prove that the radius is vertical;
A quadrilateral has an inscribed circle, and the sum of the opposite sides is a condition;
It's very important to know the location if you meet circle after circle.
The tangents of two circles are common tangents, and the intersections of two circles are common chords.
19. Proportional line segment in the circle:
In the case of equal product, change the equal ratio, and find the similarity horizontally and vertically;
Not similar, don't be angry, equal line and equal ratio instead,
Keywords encounter equal ratio, variational equal product, reference projection and circular power,
Parallel lines, scale, and find connecting lines at both ends.
20. Regular polygon magic:
To bisect a circle, the value of n must be greater than three.
Connect all the points in turn and connect a regular N polygon in front of your eyes.
Tangent line consists of dividing points, and the tangent line intersects with n points.
When n intersections are vertices, a circumscribed regular N polygon appears.
Regular n polygons are beautiful, with inscribed circles and circumscribed circles.
Both inscribed circle and circumscribed circle are unique, and the two circles are concentric circles.
Its graphic axis is symmetrical, and n axes of symmetry all pass through the center of the circle.
If the value of n is even, central symmetry is convenient.
Vertex and radius are the key points in the calculation of regular N-polygon.
The radius, apome and radius of inscribed circle and circumscribed circle change respectively,
Divided into 2n integers of a right triangle, the calculation is simple.
2 1. Functional learning:
The proportional function is a straight line, and the image must pass through the origin.
The symbol of k is the key, which determines the quadrant of the straight line.
Negative k goes through two or four limits, x increases and y decreases,
The up-and-down translation k is a constant, and the linear is obtained by derivation.
Add b up and subtract b down, and the image passes three limits.
Two points determine a line, and the selection coefficient is the key.
22. The hyperbola of inverse proportional function can be determined by only one point.
Positive k falls within one or three limits, x increases and y decreases,
At any point on the image, the rectangular area remains unchanged.
The symmetry axis is the angular bisector, and the order of x and y can be interchanged.
23. Quadratic function parabola requires three points to select.
Judging the positive and negative opening of a, the size of c, y axis,
The sign of △ is the simplest, and the number of intersections on the X axis,
On the left side of the same sign axis of A and B, the parabola translation A remains unchanged.
Vertex guides the image to turn, which can be changed in three forms.
Matching method plays the most important role.