I want junior high school algebra formula.

Square difference: (a+b) (a-b) = A2-B2; Complete square: (a b) 2 = a 2 2ab+b 2.

x^2+(p+q)x+pq=(x+p)(x+q)； The volume of a cone is 1/3 of a cylinder with equal base and equal height.

Quadratic radical: √ a * √ b = √ (ab); A√C B√C=(A B)√C。

(A+N)/(B+N)= C； Then N=(A-BC)/(C- 1).

Regular sphere volume: 4/3 pie R cube (or 1/6 pie D cube); Surface area: 4 pa square.

Helen Qin Jiushao, triangle area formula: let three sides be A, B, C and the area be S; Half of the perimeter p is (A+B+C)/2.

S=√[P(P-A)(P-B)(P-C)]。 Degree: (MX+N) 2 = P, then MX+N = √ P.

The formula of unary quadratic equation: ax 2+bx+c = 0; Then x = {√ [(b 2-4ac)/2a]}-B. There is also a factorization method.

Root sum coefficient: for example, X 2+6x- 16 = 0, the solution is X 1=2, x2 =-8; X 1+X2=-6 (reciprocal of the coefficient of the first term), X 1*X2=- 16 (constant term).

Golden section: divide a line segment into two sections, so that the ratio of the longer section to the total length and the ratio of the shorter section to the longer section are equal.

(√5- 1)/2≈0.6 18. The first line segment of the five-pointed star has three proportions for the golden section.

Binary linear equation: 1, substitution transformation. 2. If the coefficients are the same or opposite, add or subtract.

For each fixed value of x, y has a unique fixed value corresponding to it. Then x is an independent variable and y is a function of X.

If Y=B when X=A, then b is called the function value when the value of the independent variable is a.

Y=KX, which is a proportional function. [K is a constant (proportional coefficient)]; Y=KX+B and y = kx have a translation relationship.

(b is unit length, > 0 translates upward,

When K>0, the straight line Y=KX+B rises from left to right and increases with the increase of X; & lt0, which decreases with the increase of x 。

Parsed image coordinates: (3,5), (-4,9). Let y = kx+B.

3K+B = 5； -4K+B=-9。 The solution is K=2 and B=- 1. So the analytical formula is Y=2X- 1.

A has 200 tons and B has 300 tons. The charges for sending C and D from A are 20 and 25 yuan/ton respectively.

B The charges for sending to C and D are 15 and 24 yuan/ton respectively. C needs 240 tons and D needs 260 tons. How to deliver the goods at the lowest cost?

Let the total cost be y yuan; A gives C, which is X tons. Then:

A to d, 200-x; B to c, 240-x; B to D, 60+X. Note: B→D, 260-(200-X) = 60+X. Unit: ton.

y = 20X+25(200-X)+ 15(240-X)+24(60+X)； Y=4X+ 10040(0 is not greater than x and not greater than 200).

Found that A sent 0 tons to C and 200 tons to D; B sends 240 tons to C and 60 tons to D; Minimum total cost 10040 yuan.

Y=K/X is an inverse proportional function, and the image is a hyperbola; When K>0 is located in the first and third quadrants respectively, Y decreases with the increase of X. 。

When k < 0, the two branches of hyperbola are located in the second quadrant and the fourth quadrant respectively. In each quadrant, the value of y increases with the increase of the value of x. 。

The inverse proportional function image passes through a (2 2,6). Q 1: In which quadrants? How does y change with the increase of x?

Question 2: Are points B (3 3,4), C(-2 and 1/2, -4 and 4/5) and D (2 2,5) on the image of this function?

Answer 1: let Y=K/X, substitute A (2 2,6), 6=K/2, K= 12. The expression is y =12/X.

Because of K>0, this function image is in the first and third quadrants, and Y decreases with the increase of X. 。

Answer 2: Substituting the coordinates of B, C and D into Y= 12/X, we can see that the coordinates of B and C satisfy the functional relationship, but D does not.

The ladder leans against the vertical wall, with a chord of 3 meters and a strand of 2.5 meters. If the ladder slides down the wall by 0.5m, the hook will increase by 0.5m?

A: 3 2-2 2 = 5; 3^2-2.5^2=2.75; √ 5-√ 2.75 √ 2.236-1.658 √ 0.578. The ticking increased by about 0.578 meters.

Weighted average means the importance of data. In many cases, arithmetic mean should not be used. ...

A company plans to recruit an English translator, and has tested two candidates, A and B, with the following results:

A: Listen to 85, say 83, read 78 and write 75; B: Listen to 73, say 80, read 85 and write 82.

Question 1: Recruit a person with strong oral English, and the scores of listening, speaking, reading and writing are 3: 3: 2: 2 respectively. Who should be admitted?

Question 2: Recruit a translator with strong translation skills, and his listening, speaking, reading and writing scores are 2: 2: 3: 3 respectively. Who should be admitted?

Question1:a (85 * 3+83 * 3+78 * 2+75 * 2)/(3+3+2+2); B is about the same. Finally, compare the weighted average of A and B. 。

Question 2: Similar question 1. a(85 * 2+83 * 2+78 * 3+75 * 3)/(2+2+3+3)。

If the number of data is even, the average of the middle two data is called the median of this data; If you are surprised, take the middle one.

In a set of data, the most common data is the pattern of this set of data.

The difference between the maximum data and the minimum data in a set of data is called the range of this set of data. Variance is often used to measure the volatility of a set of data.

The calculation of variance of a set of data: the square of (the average value of each data), the sum of variance of all data divided by the number of groups n.

[(X 1-X both) 2+(x2-x both) 2+(x3-x both) 2 ...]/n; In addition, the sum of the differences can be divided by the number n of groups.

Divide a figure into two sides along the central axis. If both sides are congruent, then this graph is axisymmetric.

A graph rotates 180 degrees around a certain point and coincides with the graph on the other side, so it is point symmetry (also called central symmetry) about these two graphs.

A line segment connecting any two points on a circle is called a "chord"; The chord passing through the center of the circle is called the diameter. Two points on a circle can create an arc.

Any two points on an arc are line segments centered on the center of the circle, and the included angle with the center of the circle is the central angle.

Any point on the arc is a line segment of any two points on the arc, and the included angle with the circumference is the circumferential angle.

In the same or equal circle:

1, the degree of the fillet is equal to half the degree of the arc it faces; The degree of the central angle is equal to the degree of the arc it faces.

Therefore, the degree of the circumferential angle is equal to half the degree of the central angle of the same arc or the same arc.

2. All circumferential angles in the same arc or equal arc are equal to each other; All central angles are equal to each other.

3. The circumference angle (or diameter) of a semicircle is a right angle; On the contrary, the chord it subtends is the diameter.

4. Diagonal complementation of a quadrilateral inscribed in a circle: any external angle is equal to its internal angle.

The positional relationship between a straight line and a circle: 1. A straight line is out of the circle and has no common point, so it is said to be out of the circle.

2. A straight line passes through two points on the arc. They have two things in common. This straight line is called the secant of a circle. Cut each other?

3. A straight line intersects a point on the arc, and they have only one common point (tangent point). This straight line is called the tangent of the circle.

4. Make a tangent at a point outside the circle, and the distance from the point to the tangent point is called the tangent length of the point to the circle.

Two tangents of a circle can be drawn from a point outside the circle, and their tangents are equal in length. The connecting line between this point and the center of the circle bisects the included angle of the two tangents.

Example △ABC draws an inscribed circle: draw bisectors of ∠B and ∠C respectively to make them intersect; The intersection point is the center of a triangle and the center of a circle.

Circle relationship: 1. If two circles have nothing in common, it is "separation".

(1) If a circle is inside another circle but has nothing in common, then they are "inclusive".

(2) If a circle is not in another circle and has no common points, then they are "disjoint".

2.( 1) If a circle is inside another circle and has a common point, then they are "inscribed".

(2) A circle is not in another circle, but it has one thing in common, so they are circumscribed.

3. Two circles have two things in common, so they "intersect".

The center of a regular polygon inscribed in a circle is the center (concentric) and the radius is the same; The central angle of each side of a regular polygon is its central angle;

The distance from the center of a regular polygon to one side is called its apogee.

Example: There is a pavilion whose foundation is a regular hexagon with a radius of 4M. Find the perimeter and area of the foundation.

Answer 1: It is known that the central angle is 360/6 = 60, and the circumscribed circle can be drawn as positive △.

So the length of each side is equal to its radius: number of sides * length of each side = perimeter = 6 * 4 = 24 (m);

Answer 2: perimeter * apothem /2= area of hexagonal foundation. Check to find apothem:

√[4^2-(4/2)^2]=√ 12=√3*√4=2√3; 24*2√3/2≈4 1.6(M^2)

Arc length calculation: the degree of central angle * pi * radius/180, that is, L=N pie R/ 180.

Sector area: s = n * pie * R/360 square; Or S=LR/2. The line segment from the vertex of the cone to the circumference of the bottom surface is called generatrix L.

Cone surface area: the square of πR+π rl; Where bus L = √ (h 2+r 2).

Preliminary probability: Events that may or may not occur are called "random events". What will happen is an inevitable event.

The frequency M/N of event A will be stable near a constant p, which is called the probability P (a) = p 。

P(A)=p, and its value is not less than 0 and not more than 1. Note: small "P".

Generally speaking, if there are n possible results in an experiment, and they are equally likely to appear,

Event A contains m kinds of results, so the probability of event A is p (a) = m/n. 。

For example: two dice with uniform texture are thrown at the same time, and the probability of the following events is calculated: (1) The points of the two dice are the same;

(2) The sum of two chromatid points is 9; (3) The number of points of at least one dice is 2.

Analysis: (1) Two dice have 6*6=36 results, so the probability of the same number of points is 6/36= 1/6.

(2) The point sum of two chromatids has four results: 3+6, 4+5, 5+4, 6+3, so the probability is 4/36= 1/9.

(3) One, two, two, two and six results; 2 1, 23, 24 ... five results; So the probability is 1 1/36.

Buffon throwing the needle: draw a group of parallel lines with a distance of d on the plane and connect a section with a length of L (L

On this plane, find the probability that this needle intersects any parallel line. P=2L/ paid.

The relationship between the diagonal d of a polygon and the number of sides n: D=N(N-3)/2.

At present, the annual output of a product in a factory is 20 pieces, and it is planned to increase the output in the next two years.

If the output of this product is increased by x times every year over the previous year, the output of this product will be.

Output y will be determined according to the planned value of X. Write the expression of the relationship between Y and X, that is, Y = 20 (1+X) 2.

The form y = ax 2+bx+c (where a, b and c are constants and A≠0) is called a quadratic function.

X is the independent variable, and A, C and C are quadratic coefficient, linear coefficient and constant term respectively.

The image of quadratic function y = ax 2+bx+c is called parabola y = ax 2+bx+C.

The y axis is the symmetry axis of parabola y = x 2, and the intersection point (0,0) is called the vertex (lowest point) of parabola y = x 2.

Every parabola has an axis of symmetry, and the intersection point is called the vertex (highest point or lowest point) of the parabola.

The symmetry axis of parabola y = ax 2 is the Y axis, and the vertex is the origin. When a >; 0, the opening of the parabola is upward,

The vertex is the lowest point of a parabola. The larger a is, the smaller the opening of parabola is. When A<0, the opening of parabola is downward,

The vertex is the highest point of a parabola. The bigger a is, the bigger the opening of parabola is.

Translate the parabola y = x 2 upward by 1 unit to get y = x2+1; Translate one unit down to get y = x 2-1.

Translate the parabola y =- 1/2x 2 to the left by 1 unit to get y =-1/2 (x+1) 2; X- 1 right.

Translate the parabola Y =- 1/2x 2 downward to the left by 1 unit to obtain y =-1/2 (x+1) 2-1.

Example 1: build a circular fountain, install a water pipe vertically in the center of the fountain, and install a nozzle at the top of the water pipe.

So that the ejected parabolic water column reaches the highest at the horizontal distance from the center of the pool 1M,

The height is 3M, and the water column is 3M away from the center of the pond. How long should the water pipe be?

Solution: point (1, 3) is the vertex of parabola, that is, y = a (x-1) 2+3; Note: 0 is not greater than x is not greater than 3.

0 = A (3- 1) 2+3 can be obtained from this parabola passing through (3,0), and A =-3/4.

Therefore, y =-3/4 (x-1) 2+3; When X=0, Y=2.25, that is, the length of water pipe should be 2.25m..

Example 2: enclose a rectangular field with a fence with a total length of 60M, and the rectangular area s varies with the length l of one side of the rectangle;

When l is what, the area s of the site is the largest?

Analysis: Write the relationship between S and L first, and then find the L value that maximizes S. 。

The circumference is 60M, with L on one side and 60/2-L on the other.

That is, S=L(30-L) or s = 30l-l 2.

Because the vertex y = ax 2+bx+c of the parabola is the lowest (high) point, when X=-B/(2A)

The minimum (maximum) value of this function is (4ab-b 2)/4a.

Therefore, when l =-b/(2a) =-30/[2 * (1)] =15, the maximum value of s is (4ac-b 2)/4a.

= (-30 2)/[4 * (- 1)] = 225. That is to say, when L is 15M, the site area is the largest (S=225).