[Mathematics from the beginning] No. 220 quarter with a computer to the college Entrance Examination (12)

plot summary:
[Machine Xiao Wei] in [engineer Ah Wei] escorted into the [nine turn elixir] of the turn of the practice. Imagine a scenario:
If you were allowed to take an Internet-connected computer to the college entrance exam, would you give up choosing a hand-held calculator and a draft book?
？ Ah Wei decided and Xiao Wei to try to use the computer to calculate high questions will be how the feeling.

drama start:

Star Calendar May 24, 2016 17:11:11, the Milky Way Galaxy Earles the Chinese Empire Jiangnan Line province.
[Engineer Ah Wei] is working with [machine Xiao Wei] to do 2011 years of Jiangsu Province Mathematics college entrance exam questions].

The 2011 paper, more difficult than the previous year's slightly smaller, but Ah Wei feel also reached the difficulty of the 5.5 ring.

The characteristic of this time is that the derivative of this piece of investigation accounted for half.

<span style= "FONT-SIZE:18PX;" > ' Title 2 ', ' g (x) = F\ ' (x) = 1/((2x+1) *ln5) > 0 ', ' = = 2x+1>0 ', ' + x>-1/2 ' </span>

<span style= "FONT-SIZE:18PX;" > #题8def tmp8 ():    solve = Stringalgsolve ();    f1 = [' 2x '];    F2 =[' 4x^[-1];    F1 = Alg.strformat (F1);    F2 = Alg.strformat (F2);        Print (' Step 1: ', F1);    Print (' Step 1: ', F2);    G1 = Alg.strcombine (Alg.stradd (Alg.strpow_n (F1, 2), Alg.strpow_n (F2, 2)));    Print (' Step 2: ', G1);</span>

<span style= "FONT-SIZE:18PX;" > #题11def tmp11 ():    solve = Stringalgsolve ();    f1 = [' 2 ', ' -2a ', ' A ', ' 1 ', ' a ', ' 2a '];    F1 = Solve.format (F1);    F1 = Solve.coefarray (F1, ' a ');    F1 = Solve.solvepoly (F1);    F1 = eval (f1[0]);    Print (F1);  #-1.5</span>

<span style= "FONT-SIZE:18PX;" > ' title ', ' S = 240x-8x^[2] ', ' V = 4 |2^[0.5]x^[2] (30-x) ' </span>

<span style= "FONT-SIZE:18PX;"    > #题18def tmp18 (): Solve = Stringalgsolve (); Equation = alg.    Equation ();    #椭圆长短轴 A, B = 2, 1.414;    M = [-A, 0];    N = [0,-b];    #直线PA PA = [[' x_[p] ', ' kx_[p] '], [' x_[a] ', ' kx_[a] '];    AC = [[' X_[a] ', ' kx_[a] '], [' x_[p] ', ' 0 '];    # mid = Np.array ([0.5]) * (Np.array (M) +np.array (N)); Print (mid);    #[-1.    -0.707] k = mid[1]/mid[0];    Print (k);    #y = 2x with the intersection of the ellipse f1 = [' (x^[2)] ', ' (1/2*4) x^[2] ', '-1 '];    F1 = Solve.format (F1);    x = Solve.coefarray (f1, ' X '); print (x);    #此步得到用x表示的y的各次方的系数阵列 x = solve.arrayeval (x);    print (x);    Roots = equation.quadratic (x);        print (roots);    #点P, A P = [roots[1], 2*roots[1]];    A = [Roots[0], 2*roots[0]]; Print (P, A);    [-1. -0.707]0.707[' (1/4) ^[2]+ (1/2*4) ^[2] ', ' 0 ', ' (-1) '][4.0625, 0, -1][-0.4961389383568338, 0.4961389383568338][ 0.4961389383568338, 0.9922778767136676] [ -0.4961389383568338, -0.9922778767136676]</span>

<span style= "FONT-SIZE:18PX;" > #题21Bdef tmp21b ():    A = [[[]], [2,1]];    B = [[1], [2]];    A_ = NP.LINALG.INV (A);    Print (A_);    A = Np.dot (A_, Np.dot (A_, B));    Print (a);    #验算    B = Np.dot (Np.dot (A, a), a);    Print (b);>>> [[ -1.  1.] [2.-1.] [[-1.] [2.]][[1.] [2.]]</span>

Originally Ah Wei want to let [machine small Wei] exhibition of skill, suddenly found that the avatar of small Wei didn't cultivate home,

So let's make a list of what Xiao Wei can do now, lest he should rejoice in his emptiness.

< Span style= "FONT-SIZE:18PX;" >if (1) {var text = new DrawText ();//left-justified by default from 20px, alignment is 300, right-aligned 580 var XL =, XM = +, XR = 580;var y = 50;text.bold ([' [' [Machine Wei] Avatar list '], XM, y, 0, ' black ', ' V ', ' M '), y + = 50;text.normal ([' 1. Fixed value calculation: The participating operations are given values, there is no unknown. ', ' 2. Numerical calculation: An iterative or recursive method is used to make a series of operation attempts to approximate the results. ', ' 3. Stroke drawing: Strokes the various functions and draws the image. '],xl, y, 0, ' blue ', +, ' L '); y+= 80;text.italic ([' above three] is the collective avatar of the Machine family, no longer repeat. '], XL, y, 0, ' #000088 ', +, ' L '); y+= 30;text.bold ([' 4. Geometric operations: When there is no unknown in the coordinates of a point, it can be used as a geometry operation. ', ' 5. Algebraic operations: For all algebraic expressions, polynomial operations can be performed to derive the polynomial as a result. ', ' 6. For non-exponential, logarithmic, triangular polynomial, you can change the expression of one of the parameters. ', ' 7. All parameters in the expression in step (5|6) are given a value, and the value or root can be computed. '],xl, y, 0, ' red ', +, ' L '); y+=100;text.italic ([' So we can get simple polynomial after simple polynomial operation, and can find its value or root ', ' The number of arguments is unlimited ', ' fractional ' or other non-simple polynomial algebraic formula, can participate in the evaluation or derive an algebraic result ', ' but cannot be further deformed or decomposed into simple polynomial groups. '], XL, y, 0, ' #000088 ', +, ' L ');//timestamp y+=80;text.bold ([' May 25, 2016 '], XR, y, 0, ' #880088 ', +, ' R ');} </span> 

The end of this section, to know how to funeral, please see tell.

[Mathematics from the beginning] No. 220 quarter with a computer to the college Entrance Examination (12)