用 Wolfram 语言来做2017年高考数学试题之新课标Ⅲ理科卷

In[1]:= Solve[{x^2+y^2==1,y==x},{x,y},Reals]//LengthOut[1]={1, 2, 4}
Out[1]=2

In[1]:= Reduce[{(1+I)z==2I,Abs[z]==m},m,{z}]
Out[1]=m==√2

In[1]:=Cases[Expand[(x+y)〖(2x-y)〗^5]/.Plus→List,a_*x^3 y^3][[1]]
Out[1]=40x^3 y^3

In[1]:=n=Input[];t=1;M=100;s=0;
While[t≤n,s=s+M;M=-M/10;t=t+1]
s//N
当n=2时，s=90；当n=3时，s=91；当n=4时，s=90.9；当n=5时，s=90.91.

In[1]:= 1*(1-（1/2)）^2)*π
Out[1]= 3π/4

In[1]:= MinValue[{3x-4y,x-y≥0,x+y-2≤0,y≥0},{x,y}]
Out[1]=-1

In[1]:= f[x_] = Piecewise[{{x + 1, x <= 0}, {2^x, x > 0}}];
Reduce[f[x] + f[x - 1/2] > 1, x, Reals] // FullSimplify // Reduce
Out[1]= x>-1/4

In[1]:=  AB = {Cos[t], Sin[t], 1};
t = t /. Solve[{VectorAngle[AB, {1, 0, 0}] == Pi/3, 0 <= t <= Pi/2}, 
     t, Reals][[1, 1]];
VectorAngle[AB, {0, 1, 0}] // FullSimplify
Out[1]= π/3

In[2]:= Clear[t];
MinValue[{VectorAngle[AB,{1,0,0}],0≤t≤Pi/2},t,Reals]
Out[2]= π/4

In[1]:= MaxValue[{(x-1)/(Log[x]),0<x<1},x,Reals]
Out[1]=1

In[2]:= MinValue[{(x-1)/(Log[x]),x>1},x,Reals]
Out[2]=1

In[3]:= f[n_] = Product[1. + 1/2^i, {i, n}]; Table[f[10^i], {i, 1, 7}]
Out[3]={2.3819,2.38423,2.38423,2.38423,2.38423,2.38423,2.38423}

In[1]:= f[x_]=Abs[x+1]-Abs[x-2];Reduce[f[x]≥1,x,Reals]
Out[1]= x≥1

In[2]:= Reduce[Exists[x,f[x]≥x^2-x+m],m,Reals]
Out[2]= m≤5/4