1, geometric formula:

Triangle area formula: \[S=\frac{ 1}{2}bh\], right triangle pythagorean theorem: \ [A 2+B 2 = C 2 \], arbitrary triangle cosine theorem: \ [C 2 = A 2+B 2].

The perimeter formula of a circle: \[C=2\pir\], the area formula of a circle: \ [S = \ PIR 2 \], the area formula of an ellipse: \[S=\piab\], the area formula of a parallelogram: \[S=bh\], and the area formula of a trapezoid: \.

2. Algebra and function formulas:

The distance formula between two points is \ [d = \ sqrt {(x _ 2-x _1) 2+(y _ 2-y _1) 2} \], and the root formula of quadratic equation is \ [x = \ frac {-b \

Quadratic square difference formula: \ [a 2+2ab+b 2 = (a+b) 2 \], quadratic square sum formula: \ [a 2-2ab+b 2 = (a-b) 2 \], cosine sum and difference formula: \ [\]

Logarithm and exponent formula: \ [a {\ log _ {a} n} = n \], and fractional operation formula: \ (\ frac {a} {b}+\ frac {c} {d} = \ frac {ad+BC} {BD} \).

3, probability and statistical formula:

Arrangement formula: \ (p _ n m = \ frac {n! }{(n-m)！ } \), combined formula: \ (c _ n m = \ frac {n! }{m！ (n-m)！ Multiplication principle: If an experiment has \(m\) steps and \(i\) steps have \(n_i\) possible results, then the whole experiment has \(n _ 1 \ timesn2 \ ... \ timesn.

Addition principle: If there are \(m\) incompatible events in an experiment and the probability of \(i\) events is \(P(A_i)\, then the probability of the whole experiment is \ (p (a _ 1 \ cup _ 2 \ cup. ...

Multiplication formula: \ [p (a \ capb) = p (b) p (a | b) = p (a) p (b | a) \], full probability formula: \ [p (a) = p (a | b _ 1) p (b

4, derivative and integral formula:

Basic derivation formula: the derivative of constant function is 0, that of \ (x n \) is \ (NX {n-1} \), that of (sinx \) is \(\cos x\), and that of \(\cosx\) is.

The indefinite integral of the basic integral formula \ (a x \) is \ (\ frac {a x} {\ lna}+c \), while the indefinite integral of \(\sinx\) is \(-\cosx +C\), \(\cosx\).

Improper integral formula: the integral of \(|x|\) in interval \([-a, a]\) is 0, and \([a, +\infty)\) in interval \ (\ frac {1} {x 2} \).

Double integral formula: \ (\ iint _ df (x, y) dxdy = \ iint _ {d'} f (x (u, v), y (u, v)) | j (u, v) | dudv \), triple integral formula: \ (\ ii)

5, matrix and determinant formula:

Matrix multiplication formula: if the dimension of matrix \(A\) is \(m\timesn\) and the dimension of matrix \(B\) is \(n\timesp\), then the dimension of matrix \(AB\) is \(m\timesp\).

Determinant property: the transposition of determinant is equal to itself, and the signs of two rows of determinant are exchanged. The result of two equal determinant lines is 0, and the result of two proportional determinant lines is 0.

6, series and series formula:

Arithmetic progression \(n\) term and formula: \ [s _ n = \ frac {n} {2} (a _1+a _ n) \], geometric progression \(n\) term and formula: if \ (r \ neq65438). R\), convergence of power series \ (\ sum _ {n = 0} {\ infty} a _ NX n \); When \(|x| >R\), power series divergence; When \(|x|=R\), the convergence needs to be further determined.

7. Analytic geometric formula:

Distance formula from point to straight line: the distance from point \(P(x_0, y_0)\) to straight line \(Ax+By+C=0\) is \ [d = \ frac {| ax _ 0+by _ 0+c |} {\ sqrt {a 2}

8, solid geometry formula:

Spatial linear equation: general equation: \ [\ frac {x-x _ 0} {m} = \ frac {y-y _ 0} {n} = \ frac {z-z _ 0} {p} \] Symmetric equation: \ [\ frac {x-}

Arc length formula of space curve: the arc length formula of general curve \(C\) is \ [l = \ int _ {a} {b} \ sqrt {(dx) 2+(dy) 2+(dz) 2} \], and the area formula of space surface is \. ] Curvature formula of space surface: the curvature formula of general surface \(S\) is \ [k = \ frac {| f' _ x \ timesf' _ y |} {(1+(f' _ x) 2+(f' _ y)).

9, trigonometric identity:

Sine theorem: \ (\ frac {a} {\ sina} = \ frac {b} {\ sinb} = \ frac {c} {\ sinc} \), cosine theorem: \ (c 2 = a 2+b 2-2ab \)

Sum and difference angle formulas: \ (\ sin (a \ PMB) = \ Sina \ COSB \ PM \ COSA \ SINB \), \ (\ COS (a \ PMB) = \ COSA \ COSB \ MP \ SINB \), and

Triple angle formula: \ (\ SIN3A = 3 \ SINA-4 \ SIN3A \), \ (\ COS3A = 4 \ COS3A-3 \ COSA \), \ (\ TAN3A = \ FRAC {3 \ Tana-\ Tan.

10, mathematical analysis formula:

Mean value theorem: If the function \(f(x)\) is continuous in the interval \([a, b]\) and derivable in \((a, b)\), then there exists \(c \ in (a, b)\), which makes \ [\ frac].

Cauchy mean value theorem: If the function \(f(x), g(x)\) is continuous on the interval \([a, b]\), then it is derivable on \((a, b)\) and it exists.