正剧开始:
星历2016年05月20日 17:13:35, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起做着2006年的江苏省数学高考题]。
这一年,江苏重新使用了全国卷,并且这张试卷的难度也比较高,可以说,
也是打了考生一个措手不及。因为前两年试题太简单了,各学校又忘了
2003年的滑铁卢之痛了。
不过这次题目的难度前移到客观题部分了,也就说你就算蒙也能蒙点分回来,
后面的大题少了一个,选择题让了两题给填空,大致也就这样了。
总的来说,主观题难度在五环以下,而选择题、填空题却有非常难的。
其实就拿分的容易度来说,这张卷子比03年卷好拿分多了。
但这里还是给它评以5.5环的难度吧,其实阿伟觉得给5环难度更合适。
//题1
if (1) {
var r = 20;
config.setSector(1,1,1,1);
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,180);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 2, spaceY = 2;
var xS = -10, xE = 10;
var yS = -20, yE = 20;
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
var transform = new Transform();
//存放函数图像上的点
var a = [], b = [], c = [], d = [];
//需要显示的函数说明
//希腊字母表(存此用于Ctrl C/V
//ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
//αβγδεζηθικλμνξοπρστυφχψω
var f1 = 'y = sinx - 1', f2 = 'y = sinx', f3 = '', f4 = '';
var y1 = y2 = 0;
//(1-(x+2)^2)^0.5
for (var x = xS; x <= xE; x+=0.2) {
y1 = Math.sin(x)-1;
y2 = Math.sin(x);
a.push([x, y1]);
b.push([x, y2]);
}
//存放临时数组
var tmp = [];
//显示变换
if (a.length > 0) {
a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);
//函数1
tmp = [].concat(a);
shape.pointDraw(tmp, 'red');
tmp = [].concat(a);
shape.multiLineDraw(tmp, 'pink');
plot.setFillStyle('red');
plot.fillText(f1, 100, -90, 200);
}
//显示变换
if (b.length > 0) {
b = transform.scale(transform.translate(b, 0, 0), scaleX/spaceX, scaleY/spaceY);
//函数1
tmp = [].concat(b);
shape.pointDraw(tmp, 'blue');
tmp = [].concat(b);
shape.multiLineDraw(tmp, '#2288FF');
plot.setFillStyle('blue');
plot.fillText(f2, 100, -120, 200);
}
}
//题2
if (1) {
var r = 20;
config.setSector(1,1,1,1);
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,180);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 0.8, spaceY = 0.8;
var xS = -10, xE = 10;
var yS = -20, yE = 20;
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
var transform = new Transform();
//存放函数图像上的点
var a = [], b = [], c = [], d = [];
//需要显示的函数说明
//希腊字母表(存此用于Ctrl C/V
//ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
//αβγδεζηθικλμνξοπρστυφχψω
var f1 = '(x-1)^[2]+(y+1.732)^[2] = 1';
a = shape.nEdge(0, 0, 1, 36);
//存放临时数组
var tmp = [];
//显示变换
if (a.length > 0) {
a = transform.scale(transform.translate(a, 1, -1.732), scaleX/spaceX, scaleY/spaceY);
//函数1
tmp = [].concat(a);
shape.pointDraw(tmp, 'red');
tmp = [].concat(a);
shape.multiLineDraw(tmp, 'pink');
plot.setFillStyle('red');
plot.fillText(f1, 100, -90, 200);
}
}
//题3
if (1) {
var mathText = new MathText();
//希腊字母表(存此用于Ctrl C/V
//ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
//αβγδεζηθικλμνξοπρστυφχψω
var s = [
'x^[2] + y^[2] + 100 + 121 + 81 = (2 + 10*10) * 5',
'x^[2] + y^[2] + 302 = 510',
'x + y = 50-30 = 20',
'|x-y| = (208-(400-208))^[0.5] = 4'
];
var x =40, y=40;
var r1 = 40;
var len = s.length;
for (var i = 0; i < len; i++) {
if (s[i] == '') {
if (x < 100) {
x += 300;
y-=r1*3;
}
else {
x = 20;
y += r1;
}
}
else {
mathText.print(s[i], x, y, '@');
y+=r1;
}
}
}
//题4
if (1) {
var r = 20;
config.setSector(1,1,1,1);
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,180);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 90, spaceY = 1;
var xS = -720, xE = 720;
var yS = -10, yE = 10;
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
var transform = new Transform();
//存放函数图像上的点
var a = [], b = [], c = [], d = [];
//需要显示的函数说明
//希腊字母表(存此用于Ctrl C/V
//ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
//αβγδεζηθικλμνξοπρστυφχψω
var f1 = 'y = 2sin(x/3+pi/6)', f2 = 'y = 2sinx', f3 = '', f4 = '';
var y1 = y2 = 0;
//(1-(x+2)^2)^0.5
for (var x = xS; x <= xE; x+=10) {
y1 = 2*Math.sin(x/3/180*Math.PI+1/6*Math.PI);
y2 = 2*Math.sin(x/180*Math.PI)
a.push([x, y1]);
b.push([x, y2]);
}
//存放临时数组
var tmp = [];
//显示变换
if (a.length > 0) {
a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);
//函数1
tmp = [].concat(a);
shape.pointDraw(tmp, 'red');
tmp = [].concat(a);
shape.multiLineDraw(tmp, 'pink');
plot.setFillStyle('red');
plot.fillText(f1, 100, -90, 200);
}
//显示变换
if (b.length > 0) {
b = transform.scale(transform.translate(b, 0, 0), scaleX/spaceX, scaleY/spaceY);
//函数1
tmp = [].concat(b);
shape.pointDraw(tmp, 'blue');
tmp = [].concat(b);
shape.multiLineDraw(tmp, '#2288FF');
plot.setFillStyle('blue');
plot.fillText(f2, 100, -120, 200);
}
}
#题5
def tmp5():
a = alg.strformat(['x^[0.5]', '(1/3)*x^[-1]']);
a = alg.strpow_n(a, 10);
a = alg.strcombine(a);
print(a);
>>>
['(1)*x^[5.0]', '(3.33333)*x^[3.5]', '(4.999995)*x^[2.0]', '(4.44444)*x^[0.5]',
'(2.59266)*x^[-1.0]', '(1.03698)*x^[-2.5]', '(0.28812)*x^[-4.0]', '(0.05484)*x^[-5.5]',
'(0.00684)*x^[-7.0]', '(0.00051)*x^[-8.5]', '(1.7e-05)*x^[-10]']
#题6
def tmp6():
P = ['x', 'y'];
abs_MN = 4;
abs_MP_2 = ['x^[2]', '4x', '4', 'y^[2]']; #'((x+2)^[2]+y^[2])^[0.5]';
MN = ['4x', '-8'] #'(4, 0)*(x-2, y) = 4x-8
abs_MP_2 = alg.strformat(abs_MP_2);
MN = alg.strformat(MN);
MN_2 = alg.strpow_n(MN, 2);
MN_2 = alg.strcombine(MN_2);
MN_2 = alg.minus(MN_2);
abs_MP_2 = alg.strdot(abs_MP_2, ['16']);
result = alg.stradd(abs_MP_2 , MN_2);
result = alg.strcombine(result);
print(result);
#这个多项式 = 0
>>>
['(0)', '(128)*x^[1]', '(0)', '(16)*y^[2]']
#题8
def tmp8():
num = [1, 2, 3];
answer = 'ABCD';
for i in range(3):
a = num[(i)%3];
b = num[(i+1)%3];
c = num[(i+2)%3];
if (abs(a-b) <= abs(a-c)+abs(b-c)):
print('A');
if (a**2+1/(a**2) >= a + 1/a):
print('B');
if (abs(a-b) + 1/(a-b) >= 2):
print('C');
if (math.sqrt(a+3) - math.sqrt(a+1) <= math.sqrt(a+2) - math.sqrt(a)):
print('D');
print('----');
>>>
A
B
D
----
A
B
D
----
A
B
C
D
----
#题10
def tmp10():
#下面是错误的解答,但是知道哪些思考是错的也重要
#只要所有线路的开头和结尾的序号都不一样,就可以全部连通
#总连接数
total = (alg.arrangement(6, 6))**2;
print(total);
#目标连接数
#源
t_0 = 6*5;
t_1 = 5*4;
t_2 = 4*3;
t_3 = 3*2;
t_4 = 2*1;
choice = t_0*t_1*t_2*t_3*t_4;
print(choice/total); #1/6
#现在分成三组,左边先任意分,不用管
#右边要保证任意一组都不能两个头和左边完全一样,
#至少要有一个不一样
#0个位置相同
p_0 = alg.arrangement(5, 5);
#6个位置只有一个相同
p_1 = 6 * alg.arrangement(4, 4);
#6个位置有两个相同,但不能在一组
p_2 = alg.combination(3, 2)*alg.arrangement(3, 3);
#有3个相同
p_3 = alg.arrangement(2, 2);
res = (p_0+p_1+p_2+p_3)
total = alg.arrangement(6, 6);
print(res);
print(res/total);
#正确答案是8/15,让人吐血的题
#题12
def tmp12():
BC = 12;
A = 60;
B = 45;
tri_ABC = geo.solveTriangle([BC, '?', '?', A, B, '?']);
AC = tri_ABC[1];
print(AC);
>>>
9.797958971132712
#题13
def tmp13():
total = alg.arrangement(9, 9);
red = alg.arrangement(2,2);
yellow = alg.arrangement(3, 3);
white = alg.arrangement(4, 4);
total /= (red*yellow*white);
print(total);
>>>
1260.0
#题14
def tmp14():
a = 70/180*math.pi;
b = 10/180*math.pi;
c = 40/180*math.pi;
result = math.tan(a)*math.cos(b)+1.732*math.sin(b)*math.tan(a)-2*math.cos(c);
print(result);
这个题有定义域的问题。
//题17
if (1) {
var r = 20;
config.setSector(1,1,1,1);
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,180);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 1, spaceY = 5;
var xS = -10, xE = 10;
var yS = -20, yE = 20;
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
var transform = new Transform();
//存放函数图像上的点
var a = [], b = [], c = [], d = [];
//需要显示的函数说明
//希腊字母表(存此用于Ctrl C/V
//ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
//αβγδεζηθικλμνξοπρστυφχψω
var f1 = 'y = log_2(x+1/x+6)-3 <= 0', f2 = '', f3 = '', f4 = '';
var y1 = y2 = 0;
//(1-(x+2)^2)^0.5
for (var x = xS; x <= xE; x+=0.2) {
y1 = Math.log(x+1/x+6)/Math.log(2) - 3;
a.push([x, y1]);
}
//存放临时数组
var tmp = [];
//显示变换
if (a.length > 0) {
a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);
//函数1
tmp = [].concat(a);
shape.pointDraw(tmp, 'red');
tmp = [].concat(a);
shape.multiLineDraw(tmp, 'pink');
plot.setFillStyle('red');
plot.fillText(f1, 100, -90, 200);
}
//显示变换
if (b.length > 0) {
b = transform.scale(transform.translate(b, 0, 0), scaleX/spaceX, scaleY/spaceY);
//函数1
tmp = [].concat(b);
shape.pointDraw(tmp, 'blue');
tmp = [].concat(b);
shape.multiLineDraw(tmp, '#2288FF');
plot.setFillStyle('blue');
plot.fillText(f2, 100, -120, 200);
}
}
#题19
def tmp19():
AB = AC = BC = 3;
AE = CP = CF = 1;
AF = BE = BP = 2;
A = B = C = 60;
A1E = AE;
#设ED 是过E垂直于BP
DE = 3*1.732/2*2/3;
#解三角形A1DE
tri_A1DE = geo.solveTriangle([DE, A1E, '?', '?', '?', 90]);
#直线A1E与平面A1BP所成的角
angle = tri_A1DE[3];
print(angle);
>>>
59.999272219172646
本节到此结束,欲知后事如何,请看下回分解。