I hope I can help you, please adopt it in time. Thank you!
Mathematics is a science about how to think. Reciting mathematical formulas is a shortcut to solving problems, and children's thinking will become faster. So as to memorize knowledge points more deeply, reduce children's learning burden and learn easily.
The following teacher Xiaoyou summarizes the 26 knowledge points that junior high school mathematics must master as follows, hoping to help you.
1 addition of rational numbers
The addition of the same number is one-sided; Use different symbols to add "big" and subtract "small".
The symbol follows the big one; Absolute values are equal, "zero" is just right.
2 Merge similar projects
Don't forget the rules for merging similar projects.
Just sum the coefficients, and the letters and indexes remain the same.
3 Rules for deleting and adding brackets
The key to removing brackets and adding brackets is to look at symbols.
The plus sign precedes the brackets, and the symbols are the same when the brackets are removed and added.
There is a minus sign in front of the brackets, which will change when the brackets are deleted and added.
4 One-dimensional linear equation
If the unknown is known to be separated, the separation method is moving,
The addition and subtraction shift terms should be changed, and the multiplication and division shift terms should be reversed.
5 square difference formula
There are two terms in the square difference formula, remember to keep the signs opposite.
The first tail multiplied by the first tail should not be confused with the complete formula.
6 complete square formula
There are three terms for a perfect square. The first and last symbols are fellow villagers.
The first square, the tail square, the first time and the second time in the center;
The first and last brackets are square, and the symbol of the last item follows the center.
7 factorization
One mention (common factor), two sets (formulas), three groups,
It is not unreasonable to look at several items carefully, and only the square difference is used for two items.
Keywords trident multiplication, clever array, not sloppy,
Look at these four items carefully. If there are three squares (terms),
Just use one three to group, or two two to group,
Five or six projects, two, three and three test groups,
If all the above fails, take a closer look at the items to be deleted and added.
8 single operation
Add, subtract, multiply, divide, multiply (open), three-level operation is clear,
The coefficient is calculated at the same level, and the exponential operation is degraded.
9 General steps to solve linear inequality in one variable
Remove denominator and brackets, and change symbols when moving items.
Similar terms are merged and then coefficients are removed.
Don't forget to change the direction of inequality when both sides are divided by (divided by) negative numbers.
Solution set of 10 linear inequality
Take the big one, take the small one,
Small and large, medium,
The big and the small are nowhere to be found.
Solution set of quadratic inequality and absolute inequality;
Big (fish) takes both sides (eats),
Small (fish) is in the middle of (eating).
1 1 fractional hybrid algorithm
Keywords fractional four operations, sequential multiplication, division, addition and subtraction,
For multiplication and division at the same level, the division sign must be changed (multiplied);
Keywords multiplication simplification, factorization priority,
The numerator and denominator meet and then operate;
The addition and subtraction of denominator should be consistent, and denominator integration is the key;
It is not difficult to find the simplest common denominator.
The sign must be changed in two places, and the result is the simplest.
Steps for Solving Fractional Equation of 12
Multiply the simplest common denominator and write it clearly in algebraic expressions.
After you get the solution, you must test the root.
Keep the original (root) and add (root), don't be vague.
The condition of the simplest root of 13
The simplest radical three conditions, the denominator is not included in the sign,
Power exponent (root exponent) should be coprime, and power exponent is a little smaller than root exponent.
Coordinate characteristics of 14 special point
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.
The bisector of the quadrant angle:
Quadrant bisector has its own characteristics.
The first and third vertical directions are equal, but the second and fourth vertical directions are opposite.
A straight line parallel to the axis:
A straight line parallel to the axis, the coordinates of 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.
15 coordinates of symmetry point
Remember the coordinates of the symmetry point, and don't confuse the positions of the opposites.
X-axis symmetry is opposite to Y-axis symmetry; X-axis symmetry is opposite to X-axis symmetry;
It is best to remember that the symmetry of the origin, the abscissa and the ordinate are all changing.
The value range of 16 independent variable
Fraction denominator is not zero, and it must be negative under even roots;
The base of the zeroth power is not zero, and both algebraic expressions and odd roots will do.
Motion law of 17 function image
If the analytic formula of a linear function is written as y = k (x+0)+b, and the analytic formula of a quadratic function is written as y = a (x+h) 2+k, the following formula can be used:
Translate left and right in brackets, and finally translate up and down,
Zuo Zheng's right and wrong should be kept in mind, he can't be wrong.
18 image formula and properties of 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.
Images and property formulas of 19 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;
Firstly, find the vertex position and take 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 coordinate is the most important, which appears 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.
Image formula and properties 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.
2 1 special trigonometric function value storage
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. Increase and decrease of trigonometric function: positive increase and residual decrease.
Twenty-two numbers were cleverly memorized.
= 1.4 14 (only),
= 1.73 1 (discussed by three people together),
=2.236 (the mountain road I measured),
=2.449 (food is wine),
=2.645 (second rate is me),
=2.828 (two dads and two dads),
=3. 16 (yam, 62).
23 Determination of parallelogram
To prove a parallelogram, two conditions are needed.
Two sides of the card are equal, or two 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".
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.
25 Add auxiliary line songs
Auxiliary line, how to add it? Finding the pattern is the key.
If there is an angular (horizontal) dividing line in the question, it can be vertical on both sides;
The perpendicular bisector of the line segment leads to the two ends of the connecting line;
The midpoints of the two sides of the triangle are connected to form a midline;
A triangle has a midline, and the midline is doubled.
26 yuan's Proof Song
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.
Circumference, 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.