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# Критерии

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```ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
1
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ
Ɍɪɟɛɨɜɚɥɨɫɶ ɧɚɩɢɫɚɬɶ ɩɪɨɝɪɚɦɦɭ, ɩɪɢ
ɜɵɩɨɥɧɟɧɢɢ ɤɨɬɨɪɨɣ ɫ ɤɥɚɜɢɚɬɭɪɵ
ɫɱɢɬɵɜɚɸɬɫɹ ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɤɢ ɧɚ
ɩɥɨɫɤɨɫɬɢ (x, y – ɞɟɣɫɬɜɢɬɟɥɶɧɵɟ
ɱɢɫɥɚ) ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ
ɷɬɨɣ ɬɨɱɤɢ ɡɚɞɚɧɧɨɣ ɡɚɤɪɚɲɟɧɧɨɣ
ɨɛɥɚɫɬɢ (ɜɤɥɸɱɚɹ ɝɪɚɧɢɰɵ). ɉɪɨɝɪɚɦɦɢɫɬ ɬɨɪɨɩɢɥɫɹ ɢ ɧɚɩɢɫɚɥ ɩɪɨɝɪɚɦɦɭ
ɧɟɩɪɚɜɢɥɶɧɨ.
C1
Ȼɟɣɫɢɤ
INPUT x, y
IF y>=x*x-2 THEN
IF y<=4-x*x THEN
IF x>=0 THEN
PRINT "ɩɪɢɧɚɞɥɟɠɢɬ"
ELSE
PRINT "ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ"
END IF
END IF
END IF
END
ɉɚɫɤɚɥɶ
var x,y: real;
begin
if y>=x*x-2 then
if y<=4-x*x then
if x>=0 then
write('ɩɪɢɧɚɞɥɟɠɢɬ')
else
write('ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ')
end.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
#include <stdio.h>
void main(){
float x,y;
scanf("%f %f",&x,&y);
if (y>=x*x-2)
if (y<=4-x*x)
if (x>=0)
printf("ɩɪɢɧɚɞɥɟɠɢɬ");
else
printf("ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ");
}
ɋɢ
ɚɥɝ
ɧɚɱ
ɜɟɳ x,y
ɜɜɨɞ x,y
ɟɫɥɢ y>=x*x-2 ɬɨ
ɟɫɥɢ y<=4-x*x ɬɨ
ɟɫɥɢ x>=0 ɬɨ
Ⱥɥɝɨɪɢɬɦɢɱɟɫɤɢɣ
ɜɵɜɨɞ 'ɩɪɢɧɚɞɥɟɠɢɬ'
ɹɡɵɤ
ɢɧɚɱɟ
ɜɵɜɨɞ 'ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ'
ɜɫɟ
ɜɫɟ
ɜɫɟ
ɤɨɧ
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɵɩɨɥɧɢɬɟ ɫɥɟɞɭɸɳɟɟ.
1. ɉɟɪɟɪɢɫɭɣɬɟ ɢ ɡɚɩɨɥɧɢɬɟ ɬɚɛɥɢɰɭ, ɤɨɬɨɪɚɹ ɩɨɤɚɡɵɜɚɟɬ, ɤɚɤ ɪɚɛɨɬɚɟɬ
ɩɪɨɝɪɚɦɦɚ ɩɪɢ ɚɪɝɭɦɟɧɬɚɯ, ɩɪɢɧɚɞɥɟɠɚɳɢɯ ɪɚɡɥɢɱɧɵɦ ɨɛɥɚɫɬɹɦ (A, B, C, D,
E, F, G, H). Ɍɨɱɤɢ, ɥɟɠɚɳɢɟ ɧɚ ɝɪɚɧɢɰɚɯ ɨɛɥɚɫɬɟɣ, ɨɬɞɟɥɶɧɨ ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɬɶ.
Ƚɪɚɧɢɰɚɦɢ ɨɛɥɚɫɬɟɣ A ɢ H ɹɜɥɹɸɬɫɹ ɩɚɪɚɛɨɥɵ ɢ ɨɫɶ Oy.
Ɉɛɥɚɫɬɶ
Ɉɛɥɚɫɬɶ
ɍɫɥɨɜɢɟ 1 ɍɫɥɨɜɢɟ 2 ɍɫɥɨɜɢɟ 3 ɉɪɨɝɪɚɦɦɚ ɨɛɪɚɛɚɬɵɜɚɟɬɫɹ
(y>=x*x-2) (y<=4-x*x)
(x>=0)
ɜɵɜɟɞɟɬ
ɜɟɪɧɨ
A
B
C
D
E
F
G
H
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
2
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
3
ȼ ɫɬɨɥɛɰɚɯ ɭɫɥɨɜɢɣ ɭɤɚɠɢɬɟ "ɞɚ", ɟɫɥɢ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɢɬɫɹ, "ɧɟɬ", ɟɫɥɢ
ɭɫɥɨɜɢɟ ɧɟ ɜɵɩɨɥɧɢɬɫɹ, "—" (ɩɪɨɱɟɪɤ), ɟɫɥɢ ɭɫɥɨɜɢɟ ɧɟ ɛɭɞɟɬ ɩɪɨɜɟɪɹɬɶɫɹ,
"ɧɟ ɢɡɜ.", ɟɫɥɢ ɩɪɨɝɪɚɦɦɚ ɜɟɞɟɬ ɫɟɛɹ ɩɨ-ɪɚɡɧɨɦɭ ɞɥɹ ɪɚɡɧɵɯ ɡɧɚɱɟɧɢɣ,
ɩɪɢɧɚɞɥɟɠɚɳɢɯ ɞɚɧɧɨɣ ɨɛɥɚɫɬɢ. ȼ ɫɬɨɥɛɰɟ "ɉɪɨɝɪɚɦɦɚ ɜɵɜɟɞɟɬ" ɭɤɚɠɢɬɟ,
ɱɬɨ ɩɪɨɝɪɚɦɦɚ ɜɵɜɟɞɟɬ ɧɚ ɷɤɪɚɧ. ȿɫɥɢ ɩɪɨɝɪɚɦɦɚ ɧɢɱɟɝɨ ɧɟ ɜɵɜɨɞɢɬ,
ɧɚɩɢɲɢɬɟ "—" (ɩɪɨɱɟɪɤ). ȿɫɥɢ ɞɥɹ ɪɚɡɧɵɯ ɡɧɚɱɟɧɢɣ, ɩɪɢɧɚɞɥɟɠɚɳɢɯ
ɨɛɥɚɫɬɢ, ɛɭɞɭɬ ɜɵɜɟɞɟɧɵ ɪɚɡɧɵɟ ɬɟɤɫɬɵ, ɧɚɩɢɲɢɬɟ "ɧɟ ɢɡɜ". ȼ ɩɨɫɥɟɞɧɟɦ
ɫɬɨɥɛɰɟ ɭɤɚɠɢɬɟ "ɞɚ" ɢɥɢ "ɧɟɬ".
2. ɍɤɚɠɢɬɟ, ɤɚɤ ɧɭɠɧɨ ɞɨɪɚɛɨɬɚɬɶ ɩɪɨɝɪɚɦɦɭ, ɱɬɨɛɵ ɧɟ ɛɵɥɨ ɫɥɭɱɚɟɜ ɟɟ
ɧɟɩɪɚɜɢɥɶɧɨɣ ɪɚɛɨɬɵ. (ɗɬɨ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɧɟɫɤɨɥɶɤɢɦɢ ɫɩɨɫɨɛɚɦɢ,
ɞɨɫɬɚɬɨɱɧɨ ɭɤɚɡɚɬɶ ɥɸɛɨɣ ɫɩɨɫɨɛ ɞɨɪɚɛɨɬɤɢ ɢɫɯɨɞɧɨɣ ɩɪɨɝɪɚɦɦɵ.)
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
ɗɥɟɦɟɧɬɵ ɨɬɜɟɬɚ:
1. ɉɪɚɜɢɥɶɧɨ ɡɚɩɨɥɧɟɧɧɚɹ ɬɚɛɥɢɰɚ:
Ɉɛɥɚɫɬɶ
ɍɫɥɨɜɢɟ 1
(y>=x*x-2)
ɍɫɥɨɜɢɟ 2
(y<=4-x*x)
ɍɫɥɨɜɢɟ 3
(x>=0)
ɉɪɨɝɪɚɦɦɚ
ɜɵɜɟɞɟɬ
A
B
C
Ⱦɚ
ɇɟɬ
Ⱦɚ
ɇɟɬ
—
Ⱦɚ
—
—
ɇɟɬ
D
Ⱦɚ
Ⱦɚ
ɇɟɬ
E
F
G
H
Ⱦɚ
Ⱦɚ
ɇɟɬ
ɇɟɬ
Ⱦɚ
Ⱦɚ
—
—
Ⱦɚ
Ⱦɚ
—
—
—
—
ɧɟ
ɩɪɢɧɚɞɥɟɠɢɬ
ɧɟ
ɩɪɢɧɚɞɥɟɠɢɬ
ɩɪɢɧɚɞɥɟɠɢɬ
ɩɪɢɧɚɞɥɟɠɢɬ
—
—
Ɉɛɥɚɫɬɶ
ɨɛɪɚɛɚɬɵɜɚɟɬɫɹ
ɜɟɪɧɨ
ɇɟɬ
ɇɟɬ
ɇɟɬ
Ⱦɚ
Ⱦɚ
Ⱦɚ
ɇɟɬ
ɇɟɬ
2. ȼɨɡɦɨɠɧɚɹ ɞɨɪɚɛɨɬɤɚ (ɩɪɢɦɟɪ ɧɚ ɉɚɫɤɚɥɟ):
if (y<=4-x*x) and ((x<=0) and (y>=0) or (x>0) and (y>=x*x-2))
then write('ɩɪɢɧɚɞɥɟɠɢɬ')
else write('ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ')
ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɞɨɪɚɛɨɬɤɢ.
Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ! ȼ ɡɚɞɚɱɟ ɬɪɟɛɨɜɚɥɨɫɶ ɜɵɩɨɥɧɢɬɶ ɬɪɢ ɞɟɣɫɬɜɢɹ: ɭɤɚɡɚɬɶ ɞɥɹ
ɤɚɠɞɨɣ ɨɛɥɚɫɬɢ, ɤɚɤ ɛɭɞɟɬ ɪɚɛɨɬɚɬɶ ɩɪɨɝɪɚɦɦɚ, ɱɬɨ ɨɧɚ ɜɵɜɟɞɟɬ ɧɚ ɷɤɪɚɧ ɢ ɩɪɚɜɢɥɶɧɨ
ɥɢ ɷɬɨ (ɜ ɜɢɞɟ ɬɚɛɥɢɰɵ), ɢ ɢɫɩɪɚɜɢɬɶ ɞɜɟ ɨɲɢɛɤɢ.
Ȼɚɥɥɵ ɡɚ ɞɚɧɧɨɟ ɡɚɞɚɧɢɟ ɧɚɱɢɫɥɹɸɬɫɹ ɤɚɤ ɫɭɦɦɚ ɛɚɥɥɨɜ ɡɚ ɜɟɪɧɨɟ ɜɵɩɨɥɧɟɧɢɟ ɤɚɠɞɨɝɨ
ɞɟɣɫɬɜɢɹ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
4
1. ȼɟɪɧɨɟ ɡɚɩɨɥɧɟɧɢɟ ɩɪɟɞɥɨɠɟɧɧɨɣ ɬɚɛɥɢɰɵ.
2. ɂɫɩɪɚɜɥɟɧɢɟ ɧɟɩɪɚɜɢɥɶɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɭɫɥɨɜɧɨɝɨ ɨɩɟɪɚɬɨɪɚ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ
ɩɪɢ ɧɟɜɵɩɨɥɧɟɧɢɢ ɩɟɪɜɨɝɨ ɢɥɢ ɜɬɨɪɨɝɨ ɭɫɥɨɜɢɹ ɩɪɨɝɪɚɦɦɚ ɧɟ ɜɵɞɚɜɚɥɚ ɧɢɱɟɝɨ
(ɨɬɫɭɬɫɬɜɭɸɬ ɫɥɭɱɚɢ ELSE). ɂɫɩɪɚɜɥɟɧɢɟɦ ɷɬɨɣ ɨɲɢɛɤɢ ɦɨɠɟɬ ɛɵɬɶ ɥɢɛɨ ɞɨɛɚɜɥɟɧɢɟ
ɫɥɭɱɚɹ ELSE ɤ ɤɚɠɞɨɦɭ ɭɫɥɨɜɢɸ IF, ɥɢɛɨ ɨɛɴɟɞɢɧɟɧɢɟ ɜɫɟɯ ɭɫɥɨɜɢɣ IF ɜ ɨɞɧɨ ɩɪɢ
ɩɨɦɨɳɢ ɤɨɧɴɸɧɤɰɢɢ.
ȼ ɫɥɨɠɧɵɯ ɫɥɭɱɚɹɯ ɷɬɨ ɞɟɣɫɬɜɢɟ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɩɪɨɝɪɚɦɦɚ ɜɵɞɚɟɬ ɨɞɧɨ
ɢɡ ɞɜɭɯ ɫɨɨɛɳɟɧɢɣ «ɩɪɢɧɚɞɥɟɠɢɬ» ɢɥɢ «ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ» ɞɥɹ ɥɸɛɵɯ ɱɢɫɟɥ x ɢ y, ɩɪɢ
ɷɬɨɦ ɩɪɨɝɪɚɦɦɚ ɧɟ ɫɬɚɥɚ ɪɚɛɨɬɚɬɶ ɯɭɠɟ, ɱɟɦ ɪɚɧɶɲɟ, ɬɨ ɟɫɬɶ ɞɥɹ ɜɫɟɯ ɬɨɱɟɤ, ɞɥɹ
ɤɨɬɨɪɵɯ ɩɪɨɝɪɚɦɦɚ ɪɚɧɟɟ ɜɵɞɚɜɚɥɚ ɜɟɪɧɵɣ ɨɬɜɟɬ, ɞɨɪɚɛɨɬɚɧɧɚɹ ɩɪɨɝɪɚɦɦɚ ɬɚɤɠɟ
ɞɨɥɠɧɚ ɜɵɞɚɜɚɬɶ ɜɟɪɧɵɣ ɨɬɜɟɬ.
3. ɂɫɩɪɚɜɥɟɧɢɟ ɧɟɜɟɪɧɨ ɨɩɪɟɞɟɥɟɧɧɵɯ ɝɪɚɧɢɰ ɡɚɤɪɚɲɟɧɧɨɣ ɨɛɥɚɫɬɢ. ɉɪɢɜɟɞɟɧɧɵɟ ɜ
ɩɪɨɝɪɚɦɦɟ ɬɪɢ ɨɝɪɚɧɢɱɟɧɢɹ ɧɟ ɩɨɡɜɨɥɹɸɬ ɨɬɞɟɥɢɬɶ ɨɛɥɚɫɬɶ C ɨɬ ɨɛɥɚɫɬɢ D ɢ ɧɟ
ɨɩɢɫɵɜɚɸɬ ɡɚɤɪɚɲɟɧɧɭɸ ɨɛɥɚɫɬɶ B. ɂɫɩɪɚɜɥɟɧɢɟɦ ɷɬɨɣ ɨɲɢɛɤɢ ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɛɢɟɧɢɟ
ɨɛɥɚɫɬɢ ɧɚ ɞɜɟ ɱɚɫɬɢ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɞɢɡɴɸɧɤɰɢɢ ɥɢɛɨ ɨɬɛɪɚɫɵɜɚɧɢɟ ɨɬ ɛɨɥɶɲɟɣ
ɨɛɥɚɫɬɢ ɟɟ ɱɚɫɬɢ.
ȼ ɫɥɨɠɧɵɯ ɫɥɭɱɚɹɯ ɷɬɨ ɞɟɣɫɬɜɢɟ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɜɟɪɧɨ ɨɩɪɟɞɟɥɟɧɚ
ɡɚɤɪɚɲɟɧɧɚɹ ɨɛɥɚɫɬɶ, ɬɨ ɟɫɬɶ ɩɪɨɝɪɚɦɦɚ ɜɵɜɨɞɢɬ ɫɨɨɛɳɟɧɢɟ «ɩɪɢɧɚɞɥɟɠɢɬ» ɞɥɹ ɜɫɟɯ
ɬɨɱɟɤ ɡɚɤɪɚɲɟɧɧɨɣ ɨɛɥɚɫɬɢ ɢ ɬɨɥɶɤɨ ɞɥɹ ɧɢɯ, ɞɥɹ ɬɨɱɟɤ ɜɧɟ ɡɚɤɪɚɲɟɧɧɨɣ ɨɛɥɚɫɬɢ
ɩɪɨɝɪɚɦɦɚ ɜɵɜɨɞɢɬ «ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ» ɢɥɢ ɧɟ ɜɵɜɨɞɢɬ ɧɢɱɟɝɨ.
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɟɧɵ ɨɛɚ ɩɭɧɤɬɚ ɡɚɞɚɧɢɹ. ȼɟɪɧɨ ɡɚɩɨɥɧɟɧɚ ɬɚɛɥɢɰɚ,
ɢɫɩɪɚɜɥɟɧɵ ɞɜɟ ɨɲɢɛɤɢ. ɉɪɨɝɪɚɦɦɚ ɞɥɹ ɜɫɟɯ ɩɚɪ ɱɢɫɟɥ x, y ɜɟɪɧɨ
ɨɩɪɟɞɟɥɹɟɬ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɬɨɱɤɢ ɡɚɤɪɚɲɟɧɧɨɣ ɨɛɥɚɫɬɢ. ȼ ɪɚɛɨɬɟ (ɜɨ
3
ɮɪɚɝɦɟɧɬɚɯ ɩɪɨɝɪɚɦɦ) ɞɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬɞɟɥɶɧɵɯ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ
ɨɲɢɛɨɤ, ɧɟ ɢɫɤɚɠɚɸɳɢɯ ɡɚɦɵɫɥɚ ɚɜɬɨɪɚ ɪɟɲɟɧɢɹ.
1. ɉɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɟɧɵ ɞɜɚ ɞɟɣɫɬɜɢɹ ɢɡ ɬɪɟɯ (ɢɫɩɪɚɜɥɟɧɵ ɨɛɟ ɨɲɢɛɤɢ, ɧɨ
ɜ ɩɟɪɜɨɦ ɩɭɧɤɬɟ ɡɚɞɚɧɢɹ ɧɟ ɩɪɢɜɟɞɟɧɚ ɬɚɛɥɢɰɚ (ɥɢɛɨ ɬɚɛɥɢɰɚ ɫɨɞɟɪɠɢɬ
ɨɲɢɛɤɢ ɜ ɞɜɭɯ ɢ ɛɨɥɟɟ ɫɬɪɨɤɚɯ), ɥɢɛɨ ɩɪɢɜɟɞɟɧɚ ɬɚɛɥɢɰɚ (ɤɨɬɨɪɚɹ ɫɨɞɟɪɠɢɬ
ɨɲɢɛɤɢ ɧɟ ɛɨɥɟɟ ɱɟɦ ɜ ɨɞɧɨɣ ɫɬɪɨɤɟ), ɧɨ ɢɫɩɪɚɜɥɟɧɚ ɬɨɥɶɤɨ ɨɞɧɚ ɨɲɢɛɤɚ
ɩɪɨɝɪɚɦɦɵ).
ɉɪɢ ɧɚɩɢɫɚɧɢɢ ɨɩɟɪɚɰɢɣ ɫɪɚɜɧɟɧɢɹ ɞɨɩɭɫɤɚɟɬɫɹ ɨɞɧɨ ɧɟɩɪɚɜɢɥɶɧɨɟ
2
ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɫɬɪɨɝɢɯ/ɧɟɫɬɪɨɝɢɯ ɧɟɪɚɜɟɧɫɬɜ (ɫɱɢɬɚɟɬɫɹ ɧɟɫɭɳɟɫɬɜɟɧɧɨɣ
ɨɲɢɛɤɨɣ, ɩɨɝɪɟɲɧɨɫɬɶɸ ɡɚɩɢɫɢ). ɇɚɩɪɢɦɟɪ, ɜɦɟɫɬɨ «y>=0» ɢɫɩɨɥɶɡɭɟɬɫɹ
«y>0».
2. ɂɥɢ ɜɵɩɨɥɧɟɧɵ ɜɫɟ ɬɪɢ ɞɟɣɫɬɜɢɹ, ɧɨ ɩɪɢ ɷɬɨɦ ɜ ɥɨɝɢɱɟɫɤɨɦ ɜɵɪɚɠɟɧɢɢ
ɧɟɜɟɪɧɨ ɭɱɬɟɧɵ ɩɪɢɨɪɢɬɟɬɵ ɥɨɝɢɱɟɫɤɢɯ ɨɩɟɪɚɰɢɣ (ɧɟ ɪɚɫɫɬɚɜɥɟɧɵ ɢɥɢ
ɧɟɩɪɚɜɢɥɶɧɨ ɪɚɫɫɬɚɜɥɟɧɵ ɫɤɨɛɤɢ ɜ ɜɵɪɚɠɟɧɢɹɯ).
ɉɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɟɧɨ ɬɨɥɶɤɨ ɨɞɧɨ ɞɟɣɫɬɜɢɟ ɢɡ ɬɪɟɯ, ɬɨ ɟɫɬɶ, ɥɢɛɨ ɬɨɥɶɤɨ
ɩɪɢɜɟɞɟɧɚ ɬɚɛɥɢɰɚ, ɤɨɬɨɪɚɹ ɫɨɞɟɪɠɢɬ ɨɲɢɛɤɢ ɜ ɧɟ ɛɨɥɟɟ ɱɟɦ ɨɞɧɨɣ ɫɬɪɨɤɟ,
ɥɢɛɨ ɬɚɛɥɢɰɚ ɧɟ ɩɪɢɜɟɞɟɧɚ (ɢɥɢ ɩɪɢɜɟɞɟɧɚ ɢ ɫɨɞɟɪɠɢɬ ɨɲɢɛɤɢ ɛɨɥɟɟ ɱɟɦ ɜ
ɨɞɧɨɣ ɫɬɪɨɤɟ), ɧɨ ɢɫɩɪɚɜɥɟɧɚ ɪɨɜɧɨ ɨɞɧɚ ɨɲɢɛɤɚ ɩɪɨɝɪɚɦɦɵ. ɉɪɢ
1
ɨɰɟɧɢɜɚɧɢɢ ɷɬɨɝɨ ɡɚɞɚɧɢɹ ɧɚ 1 ɛɚɥɥ ɞɨɩɭɫɤɚɟɬɫɹ ɧɟ ɭɱɢɬɵɜɚɬɶ ɤɨɪɪɟɤɬɧɨɫɬɶ
ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦ ɧɚ ɬɨɱɤɚɯ ɝɪɚɧɢɰ ɨɛɥɚɫɬɟɣ (ɜɦɟɫɬɨ ɧɟɫɬɪɨɝɢɯ ɧɟɪɚɜɟɧɫɬɜ ɜ
ɪɟɲɟɧɢɢ ɛɵɥɢ ɢɫɩɨɥɶɡɨɜɚɧɵ ɫɬɪɨɝɢɟ ɧɟɪɚɜɟɧɫɬɜɚ ɢɥɢ ɧɚɨɛɨɪɨɬ)..
ȼɫɟ ɩɭɧɤɬɵ ɡɚɞɚɧɢɹ ɜɵɩɨɥɧɟɧɵ ɧɟɜɟɪɧɨ (ɬɚɛɥɢɰɚ ɚɧɚɥɢɡɚ ɩɪɚɜɢɥɶɧɨɫɬɢ
ɚɥɝɨɪɢɬɦɚ ɧɟ ɩɪɢɜɟɞɟɧɚ, ɥɢɛɨ ɫɨɞɟɪɠɢɬ ɨɲɢɛɤɢ ɜ ɞɜɭɯ ɢ ɛɨɥɟɟ ɫɬɪɨɤɚɯ,
0
ɩɪɨɝɪɚɦɦɚ ɧɟ ɩɪɢɜɟɞɟɧɚ, ɥɢɛɨ ɧɢ ɨɞɧɚ ɢɡ ɞɜɭɯ ɨɲɢɛɨɤ ɧɟ ɢɫɩɪɚɜɥɟɧɚ).
3
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
C2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
Ⱦɚɧ ɦɚɫɫɢɜ, ɫɨɞɟɪɠɚɳɢɣ 70 ɰɟɥɵɯ ɱɢɫɟɥ. Ɉɩɢɲɢɬɟ ɧɚ ɨɞɧɨɦ ɢɡ ɹɡɵɤɨɜ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɚɥɝɨɪɢɬɦ, ɩɨɡɜɨɥɹɸɳɢɣ ɧɚɣɬɢ ɢ ɜɵɜɟɫɬɢ ɧɚɢɦɟɧɶɲɟɟ
ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɟɱɟɬɧɨɟ ɱɢɫɥɨ, ɫɨɞɟɪɠɚɳɟɟɫɹ ɜ ɦɚɫɫɢɜɟ. Ƚɚɪɚɧɬɢɪɭɟɬɫɹ, ɱɬɨ
ɜ ɦɚɫɫɢɜɟ ɟɫɬɶ ɯɨɬɹ ɛɵ ɨɞɧɨ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɟɱɟɬɧɨɟ ɱɢɫɥɨ.
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɨɛɴɹɜɥɟɧɵ ɬɚɤ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɢɠɟ. Ɂɚɩɪɟɳɚɟɬɫɹ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɟɪɟɦɟɧɧɵɟ, ɧɟ ɨɩɢɫɚɧɧɵɟ ɧɢɠɟ, ɧɨ ɪɚɡɪɟɲɚɟɬɫɹ ɧɟ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɱɚɫɬɶ ɢɡ ɧɢɯ.
ɉɚɫɤɚɥɶ
const
N=70;
var
a: array [1..N] of integer;
i, j, m: integer;
begin
for i:=1 to N do
…
end.
ɚɥɝ
ɧɚɱ
ɰɟɥ N=70
ɰɟɥɬɚɛ a[1:N]
ɰɟɥ i, j, m
Ⱥɥɝɨɪɢɬɦɢɱɟɫɤɢɣ
ɧɰ ɞɥɹ i ɨɬ 1 ɞɨ N
ɹɡɵɤ
ɜɜɨɞ a[i]
ɤɰ
…
ɤɨɧ
Ȼɟɣɫɢɤ
N=70
DIM A(N) AS INTEGER
DIM I, J, M AS INTEGER
FOR I = 1 TO N
INPUT A(I)
NEXT I
…
END
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
5
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ɋɂ
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
6
#include <stdio.h>
#define N 70
void main(){
int a[N];
int i, j, m;
for (i=0; i<N; i++)
scanf("%d", &a[i]);
…
}
ȼ ɤɚɱɟɫɬɜɟ ɨɬɜɟɬɚ ȼɚɦ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɜɟɫɬɢ ɮɪɚɝɦɟɧɬ ɩɪɨɝɪɚɦɦɵ, ɤɨɬɨɪɵɣ
ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɧɚ ɦɟɫɬɟ ɦɧɨɝɨɬɨɱɢɹ. ȼɵ ɦɨɠɟɬɟ ɡɚɩɢɫɚɬɶ ɪɟɲɟɧɢɟ ɬɚɤɠɟ
ɧɚ ɞɪɭɝɨɦ ɹɡɵɤɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ (ɭɤɚɠɢɬɟ ɧɚɡɜɚɧɢɟ ɢ ɢɫɩɨɥɶɡɭɟɦɭɸ
ɜɟɪɫɢɸ ɹɡɵɤɚ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɧɚɩɪɢɦɟɪ, Free Pascal 2.4) ɢɥɢ ɜ ɜɢɞɟ
ɛɥɨɤ-ɫɯɟɦɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɵ ɞɨɥɠɧɵ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɟ ɠɟ ɫɚɦɵɟ ɢɫɯɨɞɧɵɟ
ɞɚɧɧɵɟ ɢ ɩɟɪɟɦɟɧɧɵɟ, ɤɚɤɢɟ ɛɵɥɢ ɩɪɟɞɥɨɠɟɧɵ ɜ ɭɫɥɨɜɢɢ.
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
ȼ ɡɚɞɚɱɟ ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɦɢɧɢɦɚɥɶɧɵɣ ɫɪɟɞɢ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ
ɡɚɞɚɧɧɨɦɭ ɜ ɭɫɥɨɜɢɢ ɨɝɪɚɧɢɱɟɧɢɸ. ɉɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɬɚɧɞɚɪɬɧɨɣ ɡɚɞɚɱɟɣ ɩɨɢɫɤɚ
ɦɢɧɢɦɚɥɶɧɨɝɨ ɫɪɟɞɢ ɜɫɟɯ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ ɞɨɩɨɥɧɢɬɟɥɶɧɚɹ ɫɥɨɠɧɨɫɬɶ ɞɚɧɧɨɣ ɡɚɞɚɱɢ
ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɧɟɥɶɡɹ ɛɪɚɬɶ ɜ ɤɚɱɟɫɬɜɟ ɩɟɪɜɨɝɨ ɡɧɚɱɟɧɢɹ ɦɢɧɢɦɭɦɚ ɩɟɪɜɵɣ
ɷɥɟɦɟɧɬ ɦɚɫɫɢɜɚ, ɬɚɤ ɤɚɤ ɷɬɨɬ ɷɥɟɦɟɧɬ ɦɨɠɟɬ ɧɟ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɡɚɞɚɧɧɵɦ
ɨɝɪɚɧɢɱɟɧɢɹɦ. ɇɟɥɶɡɹ ɬɚɤɠɟ ɩɪɢɧɹɬɶ ɜ ɤɚɱɟɫɬɜɟ ɩɟɪɜɨɝɨ ɡɧɚɱɟɧɢɹ ɛɨɥɶɲɨɟ ɱɢɫɥɨ,
ɡɚɜɟɞɨɦɨ ɩɪɟɜɨɫɯɨɞɹɳɟɟ ɜɫɟ ɜɨɡɦɨɠɧɵɟ ɡɧɚɱɟɧɢɹ ɞɚɧɧɵɯ, ɬɚɤ ɤɚɤ ɜ ɭɫɥɨɜɢɢ ɧɟ ɭɤɚɡɚɧ
ɞɢɚɩɚɡɨɧ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ.
ɇɢɠɟ
ɩɪɟɞɫɬɚɜɥɟɧɵ
ɧɟɫɤɨɥɶɤɨ
ɜɨɡɦɨɠɧɵɯ
ɫɩɨɫɨɛɨɜ
ɪɟɲɟɧɢɹ
ɡɚɞɚɱɢ,
ɩɪɨɢɥɥɸɫɬɪɢɪɨɜɚɧɧɵɟ ɮɪɚɝɦɟɧɬɚɦɢ ɩɪɨɝɪɚɦɦ ɧɚ ɪɚɡɧɵɯ ɹɡɵɤɚɯ. ɋɩɨɫɨɛɵ ɪɟɲɟɧɢɹ ɧɟ
ɩɪɢɜɹɡɚɧɵ ɤ ɹɡɵɤɚɦ: ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɫɩɨɫɨɛɨɜ ɦɨɠɟɬ ɛɵɬɶ ɪɟɚɥɢɡɨɜɚɧ ɧɚ ɥɸɛɨɦ
ɞɨɩɭɫɬɢɦɨɦ ɹɡɵɤɟ.
ɋɩɨɫɨɛ 1.
ȼ ɤɚɱɟɫɬɜɟ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɦɢɧɢɦɭɦɚ ɩɪɢɧɢɦɚɟɬɫɹ ɡɧɚɱɟɧɢɟ, ɡɚɜɟɞɨɦɨ ɧɟ
ɩɨɞɯɨɞɹɳɟɟ ɩɨɞ ɡɚɞɚɧɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ, ɧɚɩɪɢɦɟɪ, 0.
ɉɪɢɦɟɪ ɩɪɨɝɪɚɦɦɵ ɧɚ ɹɡɵɤɟ ɉɚɫɤɚɥɶ
m:=0;
for i:=1 to N do begin
if (a[i]>0) and (a[i] mod 2=1) and ((m=0) or (a[i]<m))
then m := a[i];
end;
writeln(m);
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
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ɋɩɨɫɨɛ 2.
ȼɦɟɫɬɨ ɩɪɨɜɟɪɤɢ ɫɩɟɰɢɚɥɶɧɨɝɨ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɬɞɟɥɶɧɚɹ
ɩɟɪɟɦɟɧɧɚɹ, ɩɨɤɚɡɵɜɚɸɳɚɹ, ɛɵɥ ɥɢ ɭɠɟ ɧɚɣɞɟɧ ɯɨɬɹ ɛɵ ɨɞɢɧ ɩɨɞɯɨɞɹɳɢɣ ɩɨɞ
ɨɝɪɚɧɢɱɟɧɢɹ ɷɥɟɦɟɧɬ. Ⱦɥɹ ɷɬɨɣ ɩɟɪɟɦɟɧɧɨɣ ɫɥɟɞɨɜɚɥɨ ɛɵ ɢɫɩɨɥɶɡɨɜɚɬɶ ɥɨɝɢɱɟɫɤɢɣ
ɬɢɩ, ɧɨ ɜ ɭɫɥɨɜɢɢ ɪɚɡɪɟɲɟɧɵ ɬɨɥɶɤɨ ɰɟɥɵɟ ɩɟɪɟɦɟɧɧɵɟ, ɩɨɷɬɨɦɭ ɥɨɝɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ
ɦɨɞɟɥɢɪɭɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɰɟɥɨɝɨ.
ɉɪɢɦɟɪ ɩɪɨɝɪɚɦɦɵ ɧɚ Ȼɟɣɫɢɤɟ
M = 0: J = 0
FOR I = 1 TO N
IF A(I)>0 AND A(i) MOD 2 = 1 AND (J = 0 OR A(I) < M) THEN
M = A(I)
J = 1
END IF
NEXT I
PRINT M
ɋɩɨɫɨɛ 3.
ɋɧɚɱɚɥɚ ɜ ɦɚɫɫɢɜɟ ɢɳɟɬɫɹ ɩɟɪɜɵɣ ɷɥɟɦɟɧɬ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɨɝɪɚɧɢɱɟɧɢɹɦ. Ɂɚɬɟɦ ɜ
ɨɫɬɚɜɲɟɣɫɹ ɱɚɫɬɢ ɦɚɫɫɢɜɚ ɢɳɟɬɫɹ ɩɨɞɯɨɞɹɳɢɣ ɧɚɢɦɟɧɶɲɢɣ ɷɥɟɦɟɧɬ. ɗɬɨɬ ɫɩɨɫɨɛ
ɩɪɢɜɨɞɢɬ ɤ ɛɨɥɟɟ ɞɥɢɧɧɨɣ (ɬɪɟɛɭɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɜɚ ɰɢɤɥɚ), ɧɨ ɧɟ ɦɟɧɟɟ
ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɟ.
ɉɪɢɦɟɪ ɩɪɨɝɪɚɦɦɵ ɧɚ ɚɥɝɨɪɢɬɦɢɱɟɫɤɨɦ ɹɡɵɤɟ
i:=1
ɧɰ ɩɨɤɚ ɧɟ (a[i]>0 ɢ mod(a[i],2)=1)
i := i+1
ɤɰ
m := a[i]
ɧɰ ɞɥɹ i ɨɬ i+1 ɞɨ N
ɟɫɥɢ a[i]>0 ɢ mod(a[i],2)=1 ɢ a[i]<m
ɬɨ m:=a[i]
ɜɫɟ
ɤɰ
ɜɵɜɨɞ m
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
8
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɟɞɥɨɠɟɧ ɩɪɚɜɢɥɶɧɵɣ ɚɥɝɨɪɢɬɦ, ɜɵɞɚɸɳɢɣ ɜɟɪɧɨɟ ɡɧɚɱɟɧɢɟ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɡɚɩɢɫɶ ɚɥɝɨɪɢɬɦɚ ɧɚ ɞɪɭɝɨɦ ɹɡɵɤɟ, ɢɫɩɨɥɶɡɭɸɳɚɹ ɚɧɚɥɨɝɢɱɧɵɟ
ɩɟɪɟɦɟɧɧɵɟ. ȼ ɫɥɭɱɚɟ, ɟɫɥɢ ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɨɬɥɢɱɧɵɣ ɨɬ
ɩɪɢɜɟɞɟɧɧɵɯ ɜ ɭɫɥɨɜɢɢ, ɢɫɩɨɥɶɡɭɟɬ ɬɢɩɢɡɢɪɨɜɚɧɧɵɟ ɩɟɪɟɦɟɧɧɵɟ, ɨɩɢɫɚɧɢɹ
ɩɟɪɟɦɟɧɧɵɯ ɞɨɥɠɧɵ ɛɵɬɶ ɚɧɚɥɨɝɢɱɧɵ ɨɩɢɫɚɧɢɹɦ ɩɟɪɟɦɟɧɧɵɯ ɧɚ
2
ɟɫɬɟɫɬɜɟɧɧɨɦ ɹɡɵɤɟ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɧɟɬɢɩɢɡɢɪɨɜɚɧɧɵɯ ɢɥɢ ɧɟɨɛɴɹɜɥɟɧɧɵɯ
ɩɟɪɟɦɟɧɧɵɯ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ, ɟɫɥɢ ɷɬɨ ɞɨɩɭɫɤɚɟɬɫɹ ɹɡɵɤɨɦ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. ɉɪɢ ɷɬɨɦ ɤɨɥɢɱɟɫɬɜɨ ɩɟɪɟɦɟɧɧɵɯ ɢ ɢɯ ɢɞɟɧɬɢɮɢɤɚɬɨɪɵ
ɞɨɥɠɧɵ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ. ȼ ɚɥɝɨɪɢɬɦɟ, ɡɚɩɢɫɚɧɧɨɦ ɧɚ ɹɡɵɤɟ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɞɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬɞɟɥɶɧɵɯ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ
ɨɲɢɛɨɤ, ɧɟ ɢɫɤɚɠɚɸɳɢɯ ɡɚɦɵɫɥɚ ɚɜɬɨɪɚ ɩɪɨɝɪɚɦɦɵ
ȼ ɥɸɛɨɦ ɜɚɪɢɚɧɬɟ ɪɟɲɟɧɢɹ ɦɨɠɟɬ ɩɪɢɫɭɬɫɬɜɨɜɚɬɶ ɧɟ ɛɨɥɟɟ ɨɞɧɨɣ ɨɲɢɛɤɢ ɢɡ
ɱɢɫɥɚ ɫɥɟɞɭɸɳɢɯ:
1) ɇɟ ɢɧɢɰɢɚɥɢɡɢɪɭɟɬɫɹ ɢɥɢ ɧɟɜɟɪɧɨ ɢɧɢɰɢɚɥɢɡɢɪɭɟɬɫɹ ɩɟɪɟɦɟɧɧɚɹ m. ȼ
ɱɚɫɬɧɨɫɬɢ, ɧɟɥɶɡɹ ɢɧɢɰɢɚɥɢɡɢɪɨɜɚɬɶ ɷɬɭ ɩɟɪɟɦɟɧɧɭɸ ɩɟɪɜɵɦ ɷɥɟɦɟɧɬɨɦ
ɦɚɫɫɢɜɚ. ɇɟɥɶɡɹ ɬɚɤɠɟ ɢɧɢɰɢɚɥɢɡɢɪɨɜɚɬɶ ɟɟ ɤɚɤɢɦ-ɬɨ ɨɱɟɧɶ ɛɨɥɶɲɢɦ
ɡɧɚɱɟɧɢɟɦ (ɧɚɩɪɢɦɟɪ, maxInt ɜ ɉɚɫɤɚɥɟ)
2) ɇɟɜɟɪɧɨ ɩɪɨɜɟɪɹɟɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨɫɬɶ ɢ ɧɟɱɟɬɧɨɫɬɶ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ
3) ȼ ɫɥɨɠɧɨɦ ɥɨɝɢɱɟɫɤɨɦ ɭɫɥɨɜɢɢ ɩɪɨɫɬɵɟ ɩɪɨɜɟɪɤɢ ɜɟɪɧɵ, ɧɨ ɭɫɥɨɜɢɟ ɜ
ɰɟɥɨɦ ɩɨɫɬɪɨɟɧɨ ɧɟɜɟɪɧɨ (ɧɚɩɪɢɦɟɪ, ɩɟɪɟɩɭɬɚɧɵ ɨɩɟɪɚɰɢɢ ɂ ɢ ɂɅɂ,
1
ɧɟɜɟɪɧɨ ɪɚɫɫɬɚɜɥɟɧɵ ɫɤɨɛɤɢ ɜ ɥɨɝɢɱɟɫɤɨɦ ɜɵɪɚɠɟɧɢɢ).
4) ȼɦɟɫɬɨ ɡɧɚɱɟɧɢɹ ɷɥɟɦɟɧɬɚ ɩɪɨɜɟɪɹɟɬɫɹ ɟɝɨ ɢɧɞɟɤɫ.
5) Ɉɬɫɭɬɫɬɜɭɟɬ ɜɵɜɨɞ ɨɬɜɟɬɚ.
6)
ɂɫɩɨɥɶɡɭɟɬɫɹ ɩɟɪɟɦɟɧɧɚɹ, ɧɟ ɨɛɴɹɜɥɟɧɧɚɹ ɜ ɪɚɡɞɟɥɟ ɨɩɢɫɚɧɢɹ
ɩɟɪɟɦɟɧɧɵɯ.
7) ɇɟ ɭɤɚɡɚɧɨ ɢɥɢ ɧɟɜɟɪɧɨ ɭɤɚɡɚɧɨ ɭɫɥɨɜɢɟ ɡɚɜɟɪɲɟɧɢɹ ɰɢɤɥɚ.
8)
ȼ ɰɢɤɥɟ, ɝɞɟ ɧɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɢɡɦɟɧɹɟɦɚɹ ɩɟɪɟɦɟɧɧɚɹ
ɰɢɤɥɚ, ɢɧɞɟɤɫɧɚɹ ɩɟɪɟɦɟɧɧɚɹ ɜ ɬɟɥɟ ɰɢɤɥɚ ɹɜɧɨ ɧɟ ɦɟɧɹɟɬɫɹ ɢɥɢ ɦɟɧɹɟɬɫɹ
ɧɟɜɟɪɧɨ.
Ɉɲɢɛɨɤ, ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜ ɩ. 1–8, ɞɜɟ ɢɥɢ ɛɨɥɶɲɟ, ɢɥɢ ɚɥɝɨɪɢɬɦ
0
ɫɮɨɪɦɭɥɢɪɨɜɚɧ ɧɟɜɟɪɧɨ.
2
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
C3
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
9
Ⱦɜɚ ɢɝɪɨɤɚ, ɉɟɬɹ ɢ ȼɚɧɹ, ɢɝɪɚɸɬ ɜ ɫɥɟɞɭɸɳɭɸ ɢɝɪɭ. ɉɟɪɟɞ ɧɢɦɢ ɥɟɠɚɬ ɞɜɟ
ɤɭɱɤɢ ɤɚɦɧɟɣ, ɜ ɩɟɪɜɨɣ ɢɡ ɤɨɬɨɪɵɯ 4, ɚ ɜɨ ɜɬɨɪɨɣ – 3 ɤɚɦɧɹ. ɍ ɤɚɠɞɨɝɨ ɢɝɪɨɤɚ
ɧɟɨɝɪɚɧɢɱɟɧɧɨ ɦɧɨɝɨ ɤɚɦɧɟɣ. ɂɝɪɨɤɢ ɯɨɞɹɬ ɩɨ ɨɱɟɪɟɞɢ, ɩɟɪɜɵɣ ɯɨɞ ɞɟɥɚɟɬ
ɉɟɬɹ. ɏɨɞ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɢɝɪɨɤ ɢɥɢ ɭɬɪɚɢɜɚɟɬ ɱɢɫɥɨ ɤɚɦɧɟɣ ɜ ɤɚɤɨɣ-ɬɨ
ɤɭɱɟ, ɢɥɢ ɞɨɛɚɜɥɹɟɬ 1 ɤɚɦɟɧɶ ɜ ɤɚɤɭɸ-ɬɨ ɤɭɱɭ. ɂɝɪɚ ɡɚɜɟɪɲɚɟɬɫɹ ɜ ɬɨɬ ɦɨɦɟɧɬ,
ɤɨɝɞɚ ɨɛɳɟɟ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ ɜ ɞɜɭɯ ɤɭɱɚɯ ɫɬɚɧɨɜɢɬɫɹ ɧɟ ɦɟɧɟɟ 20.
ȿɫɥɢ ɜ ɦɨɦɟɧɬ ɡɚɜɟɪɲɟɧɢɹ ɢɝɪɵ ɨɛɳɟɟ ɱɢɫɥɨ ɤɚɦɧɟɣ ɜ ɞɜɭɯ ɤɭɱɚɯ ɧɟ ɦɟɧɟɟ
35, ɬɨ ɜɵɢɝɪɚɥ ȼɚɧɹ, ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ – ɉɟɬɹ. Ʉɬɨ ɜɵɢɝɪɵɜɚɟɬ ɩɪɢ
ɛɟɡɨɲɢɛɨɱɧɨɣ ɢɝɪɟ ɨɛɨɢɯ ɢɝɪɨɤɨɜ? ɍɤɚɠɢɬɟ, ɫɬɪɚɬɟɝɢɸ ɜɵɢɝɪɵɜɚɸɳɟɝɨ
ɢɝɪɨɤɚ – ɤɚɤɨɣ ɯɨɞ ɨɧ ɞɨɥɠɟɧ ɫɞɟɥɚɬɶ ɜ ɤɚɠɞɨɣ ɢɡ ɩɨɡɢɰɢɣ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ
ɟɦɭ ɜɫɬɪɟɬɢɬɶɫɹ ɩɪɢ ɩɪɚɜɢɥɶɧɨɣ ɢɝɪɟ. Ⱦɨɤɚɠɢɬɟ, ɱɬɨ ɨɩɢɫɚɧɧɚɹ ɫɬɪɚɬɟɝɢɹ –
ɜɵɢɝɪɵɲɧɚɹ.
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
ȼɵɢɝɪɵɜɚɟɬ ɉɟɬɹ. ȿɝɨ ɜɨɡɦɨɠɧɚɹ ɫɬɪɚɬɟɝɢɹ ɩɨɤɚɡɚɧɚ ɜ ɬɚɛɥɢɰɟ, ɤɨɬɨɪɚɹ ɢɡɨɛɪɚɠɚɟɬ
ɧɟɩɨɥɧɨɟ ɞɟɪɟɜɨ ɢɝɪɵ.
1-ɣ ɯɨɞ
2-ɣ ɯɨɞ
2-ɣ ɯɨɞ
3-ɣ ɯɨɞ
ɂ.ɩ. 1-ɣ ɯɨɞ
ɉɟɬɢ
ȼɚɧɢ
ɉɟɬɢ
ȼɚɧɢ
ɉɟɬɢ
(12, 12); 24
(4, 12); 16
ȼɉ
(4, 3); 7 (4, 4); 8
(5, 6); 11 (5, 18); 23
ȼɉ
(4, 5); 9
(5, 5); 10
(5, 15); 20
ȼɉ
ȼ ɤɚɠɞɨɣ ɤɥɟɬɤɟ ɢɡɨɛɪɚɠɟɧɚ ɩɨɡɢɰɢɹ, ɜɨɡɧɢɤɚɸɳɚɹ ɩɨɫɥɟ ɨɱɟɪɟɞɧɨɝɨ ɯɨɞɚ. ȼ ɫɤɨɛɤɚɯ
ɭɤɚɡɚɧɨ, ɫɤɨɥɶɤɨ ɤɚɦɧɟɣ ɜ ɤɚɠɞɨɣ ɤɭɱɟ. ɉɨɫɥɟ ɫɤɨɛɤɢ (ɞɥɹ ɧɚɝɥɹɞɧɨɫɬɢ) ɭɤɚɡɚɧɨ
ɫɭɦɦɚɪɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ ɜ ɞɜɭɯ ɤɭɱɚɯ. Ⱦɥɹ ɉɟɬɢ ɭɤɚɡɚɧ ɩɪɚɜɢɥɶɧɵɣ ɯɨɞ ɜɨ ɜɫɟɯ
ɜɨɡɧɢɤɚɸɳɢɯ ɩɨɡɢɰɢɹɯ. Ⱦɥɹ ȼɚɧɢ – ɜɫɟ ɟɝɨ ɜɨɡɦɨɠɧɵɟ ɯɨɞɵ (ɱɬɨɛɵ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ ɭ
ɉɟɬɢ ɧɚ ɥɸɛɨɣ ɢɡ ɧɢɯ ɟɫɬɶ ɜɵɢɝɪɵɜɚɸɳɢɣ ɨɬɜɟɬ). Ʉɚɤ ɜɢɞɧɨ ɢɡ ɬɚɛɥɢɰɵ, ɩɪɢ ɥɸɛɵɯ
ɨɬɜɟɬɚɯ ȼɚɧɢ ɢɝɪɚ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɩɨɛɟɞɨɣ ɉɟɬɢ.
ɍ ɉɟɬɢ ɟɫɬɶ ɢ ɞɪɭɝɢɟ ɜɵɢɝɪɵɜɚɸɳɢɟ ɫɬɪɚɬɟɝɢɢ. ɗɤɡɚɦɟɧɭɟɦɨɦɭ ɞɨɫɬɚɬɨɱɧɨ ɨɩɢɫɚɬɶ
ɥɸɛɭɸ ɢɡ ɧɢɯ. ȿɫɥɢ ɜɵɛɪɚɧɚ ɫɬɪɚɬɟɝɢɹ, ɧɟ ɫɨɜɩɚɞɚɸɳɚɹ ɫ ɨɩɢɫɚɧɧɨɣ ɜɵɲɟ, ɩɪɢ
ɩɪɨɜɟɪɤɟ ɧɟɨɛɯɨɞɢɦɨ ɭɛɟɞɢɬɶɫɹ ɜ ɟɟ ɩɪɚɜɢɥɶɧɨɫɬɢ ɢ ɩɨɥɧɨɬɟ ɨɩɢɫɚɧɢɹ, ɩɪɢ ɷɬɨɦ ɜɫɟ
ɤɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɫɨɯɪɚɧɹɸɬɫɹ ɞɥɹ ɥɸɛɨɣ ɜɟɪɧɨɣ ɫɬɪɚɬɟɝɢɢ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
10
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧ ɜɵɢɝɪɵɜɚɸɳɢɣ ɢɝɪɨɤ. ɉɨɥɧɨɫɬɶɸ ɨɩɢɫɚɧɚ ɟɝɨ
ɫɬɪɚɬɟɝɢɹ. Ɉɛɴɹɫɧɟɧɨ (ɫ ɩɨɦɨɳɶɸ ɢɥɢ ɛɟɡ ɩɨɦɨɳɢ ɞɟɪɟɜɚ ɢɝɪɵ), ɱɬɨ ɩɪɢ
ɨɩɢɫɚɧɢɢ ɫɬɪɚɬɟɝɢɢ ɪɚɡɨɛɪɚɧɵ ɜɫɟ ɩɨɡɢɰɢɢ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɜɨɡɧɢɤɚɬɶ ɭ
ɜɵɢɝɪɵɜɚɸɳɟɝɨ ɢɝɪɨɤɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɢɝɪɵ ɟɝɨ ɩɪɨɬɢɜɧɢɤɚ. Ⱦɨɤɚɡɚɧɨ,
3
ɱɬɨ ɩɪɢɜɟɞɟɧɧɚɹ ɫɬɪɚɬɟɝɢɹ – ɜɵɢɝɪɵɲɧɚɹ. ɇɚɩɪɢɦɟɪ, ɟɫɥɢ ɫɬɪɚɬɟɝɢɹ
ɨɩɢɫɚɧɚ ɮɪɚɝɦɟɧɬɨɦ ɞɟɪɟɜɚ ɢɝɪɵ (ɫɦ. ɬɚɛɥɢɰɭ), ɬɨ ɭɤɚɡɚɧɨ, ɱɬɨ ɜɫɟ
ɡɚɤɥɸɱɢɬɟɥɶɧɵɟ ɩɨɡɢɰɢɢ – ɜɵɢɝɪɵɲɧɵɟ ɞɥɹ ɉɟɬɢ.
Ⱦɜɚ ɛɚɥɥɚ ɫɬɚɜɹɬɫɹ ɜ ɨɞɧɨɦ ɢɡ ɞɜɭɯ ɫɥɭɱɚɟɜ:
1.
ɉɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧ ɩɨɛɟɞɢɬɟɥɶ, ɩɪɚɜɢɥɶɧɨ ɩɨɫɬɪɨɟɧɨ ɞɟɪɟɜɨ ɢɝɪɵ.
Ɉɞɧɚɤɨ ɧɟ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɪɚɡɨɛɪɚɧɵ ɜɫɟ ɩɨɡɢɰɢɢ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɜɨɡɧɢɤɚɬɶ
2
ɭ ɜɵɢɝɪɵɜɚɸɳɟɝɨ ɢɝɪɨɤɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɢɝɪɵ ɟɝɨ ɩɪɨɬɢɜɧɢɤɚ.
2. ɉɪɚɜɢɥɶɧɨ ɩɨɫɬɪɨɟɧɨ ɞɟɪɟɜɨ ɢɝɪɵ, ɨɞɧɚɤɨ, ɧɟɜɟɪɧɨ ɭɤɚɡɚɧ ɩɨɛɟɞɢɬɟɥɶ
(ɜɨɡɦɨɠɧɨ, ɢɡ-ɡɚ ɨɩɢɫɤɢ)
ɉɪɚɜɢɥɶɧɨ ɪɚɡɨɛɪɚɧɵ ɩɟɪɜɵɟ ɯɨɞɵ ɢɝɪɨɤɨɜ, ɨɞɧɚɤɨ, ɞɚɥɶɧɟɣɲɢɣ ɚɧɚɥɢɡ
1
ɢɝɪɵ ɧɟɩɨɥɨɧ. ɉɪɚɜɢɥɶɧɨ ɧɚɩɢɫɚɧ ɨɬɜɟɬ, ɧɨ ɧɟɬ ɟɝɨ ɨɛɨɫɧɨɜɚɧɢɹ.
ɇɟ ɜɵɩɨɥɧɟɧɨ ɧɢ ɨɞɧɨ ɢɡ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜɵɲɟ ɭɫɥɨɜɢɣ
0
3
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
C4
ɇɚ ɩɥɨɫɤɨɫɬɢ ɞɚɧ ɧɚɛɨɪ ɬɨɱɟɤ ɫ ɰɟɥɨɱɢɫɥɟɧɧɵɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ. ɇɟɨɛɯɨɞɢɦɨ
ɧɚɣɬɢ ɬɪɟɭɝɨɥɶɧɢɤ ɧɚɢɛɨɥɶɲɟɣ ɩɥɨɳɚɞɢ ɫ ɜɟɪɲɢɧɚɦɢ ɜ ɷɬɢɯ ɬɨɱɤɚɯ, ɨɞɧɚ ɢɡ
ɫɬɨɪɨɧ ɤɨɬɨɪɨɝɨ ɥɟɠɢɬ ɧɚ ɨɫɢ Ox.
ɇɚɩɢɲɢɬɟ ɷɮɮɟɤɬɢɜɧɭɸ, ɜ ɬɨɦ ɱɢɫɥɟ ɩɨ ɩɚɦɹɬɢ, ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɛɭɞɟɬ
ɪɟɲɚɬɶ ɷɬɭ ɡɚɞɚɱɭ. Ɋɚɡɦɟɪ ɩɚɦɹɬɢ, ɤɨɬɨɪɭɸ ɢɫɩɨɥɶɡɭɟɬ ȼɚɲɚ ɩɪɨɝɪɚɦɦɚ, ɧɟ
ɞɨɥɠɟɧ ɡɚɜɢɫɟɬɶ ɨɬ ɞɥɢɧɵ ɩɟɪɟɞɚɧɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɱɢɫɟɥ.
ɉɟɪɟɞ ɬɟɤɫɬɨɦ ɩɪɨɝɪɚɦɦɵ ɤɪɚɬɤɨ ɨɩɢɲɢɬɟ ɢɫɩɨɥɶɡɭɟɦɵɣ ɜɚɦɢ ɚɥɝɨɪɢɬɦ
ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɢ ɭɤɚɠɢɬɟ ɢɫɩɨɥɶɡɭɟɦɵɣ ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɢ ɟɝɨ
ɜɟɪɫɢɸ.
Ɉɩɢɫɚɧɢɟ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ
ȼ ɩɟɪɜɨɣ ɫɬɪɨɤɟ ɜɜɨɞɢɬɫɹ ɨɞɧɨ ɰɟɥɨɟ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɱɢɫɥɨ – ɤɨɥɢɱɟɫɬɜɨ
ɬɨɱɟɤ N.
Ʉɚɠɞɚɹ ɢɡ ɫɥɟɞɭɸɳɢɯ N ɫɬɪɨɤ ɫɨɞɟɪɠɢɬ ɞɜɚ ɰɟɥɵɯ ɱɢɫɥɚ – ɫɧɚɱɚɥɚ
ɤɨɨɪɞɢɧɚɬɚ x, ɡɚɬɟɦ ɤɨɨɪɞɢɧɚɬɚ y ɨɱɟɪɟɞɧɨɣ ɬɨɱɤɢ.
Ɉɩɢɫɚɧɢɟ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ
ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ – ɦɚɤɫɢɦɚɥɶɧɭɸ ɩɥɨɳɚɞɶ
ɬɪɟɭɝɨɥɶɧɢɤɚ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɝɨ ɭɫɥɨɜɢɹɦ ɡɚɞɚɱɢ. ȿɫɥɢ ɬɚɤɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ
ɧɟ ɫɭɳɟɫɬɜɭɟɬ, ɩɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɧɨɥɶ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
11
ɉɪɢɦɟɪ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ:
6
0 0
2 0
0 4
3 3
5 5
-6 -6
ɉɪɢɦɟɪ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ ɞɥɹ ɩɪɢɜɟɞɟɧɧɨɝɨ ɜɵɲɟ ɩɪɢɦɟɪɚ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ:
6
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
ɉɪɨɝɪɚɦɦɚ ɱɢɬɚɟɬ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ, ɧɟ ɡɚɩɨɦɢɧɚɹ ɜɫɟ ɬɨɱɤɢ ɜ ɦɚɫɫɢɜɟ. Ⱦɥɹ ɤɚɠɞɨɣ
ɬɨɱɤɢ ɩɪɨɜɟɪɹɟɬɫɹ ɟɟ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɨɫɢ Ox (ɭɫɥɨɜɢɟ y=0). ɋɪɟɞɢ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɧɚ
ɨɫɢ, ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɧɚɢɛɨɥɟɟ ɞɚɥɟɤɨ ɨɬɫɬɨɹɳɢɟ ɞɪɭɝ ɨɬ ɞɪɭɝɚ – ɨɧɢ ɞɚɞɭɬ
ɧɚɢɛɨɥɶɲɟɟ ɜɨɡɦɨɠɧɨɟ ɨɫɧɨɜɚɧɢɟ ɬɪɟɭɝɨɥɶɧɢɤɚ. ɗɬɨ ɛɭɞɭɬ ɬɨɱɤɢ ɫ ɧɚɢɦɟɧɶɲɢɦ ɢ
ɧɚɢɛɨɥɶɲɢɦ ɡɧɚɱɟɧɢɟɦ ɤɨɨɪɞɢɧɚɬɵ x. ɋɪɟɞɢ ɬɨɱɟɤ, ɧɟ ɥɟɠɚɳɢɯ ɧɚ ɨɫɢ, ɧɚɞɨ ɧɚɣɬɢ
ɬɨɱɤɭ, ɞɚɥɶɲɟ ɜɫɟɯ ɨɬɫɬɨɹɳɭɸ ɨɬ ɷɬɨɣ ɨɫɢ – ɨɧɚ ɞɚɫɬ ɧɚɢɛɨɥɶɲɟɟ ɜɨɡɦɨɠɧɨɟ ɡɧɚɱɟɧɢɟ
ɜɵɫɨɬɵ. ɗɬɨ ɛɭɞɟɬ ɬɨɱɤɚ ɫ ɧɚɢɛɨɥɶɲɢɦ ɩɨ ɦɨɞɭɥɸ ɡɧɚɱɟɧɢɟɦ ɤɨɨɪɞɢɧɚɬɵ y.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɡɚɞɚɱɚ ɫɜɨɞɢɬɫɹ ɤ ɧɚɯɨɠɞɟɧɢɸ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɢ ɦɢɧɢɦɚɥɶɧɨɝɨ x ɫɪɟɞɢ
ɬɨɱɟɤ, ɭ ɤɨɬɨɪɵɯ y=0, ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɩɨ ɦɨɞɭɥɸ y ɫɪɟɞɢ ɨɫɬɚɥɶɧɵɯ ɬɨɱɟɤ ɢ
ɧɚɯɨɠɞɟɧɢɸ ɩɥɨɳɚɞɢ ɬɪɟɭɝɨɥɶɧɢɤɚ ɧɚ ɨɫɧɨɜɟ ɷɬɢɯ ɞɚɧɧɵɯ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɉɪɢɦɟɪ ɩɪɚɜɢɥɶɧɨɣ ɢ ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ ɹɡɵɤɟ ɉɚɫɤɚɥɶ:
program c4;
var
n: integer;
x, y: integer;
xmin, xmax: integer;
xsearch: boolean;
ymax: integer;
i: integer;
s: real;
begin
xsearch := true;
xmin := 0; xmax := 0;
ymax := 0;
for i:=1 to n do begin
if y=0 then begin
if xsearch or (x<xmin) then xmin:=x;
if xsearch or (x>xmax) then xmax:=x;
xsearch:=false;
end
else if abs(y)>ymax then ymax:=abs(y);
end;
s := (xmax-xmin)*ymax/2;
writeln(s);
end.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
12
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɉɪɢɦɟɪ ɩɪɚɜɢɥɶɧɨɣ ɢ ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ Ⱥɥɝɨɪɢɬɦɢɱɟɫɤɨɦ ɹɡɵɤɟ:
ɚɥɝ c4
ɧɚɱ
ɰɟɥ n
ɰɟɥ x,y
ɰɟɥ xmin=0, xmax=0
ɥɨɝ xsearch=ɞɚ
ɰɟɥ ymax=0
ɰɟɥ i
ɜɟɳ s
ɜɜɨɞ n
ɧɰ ɞɥɹ i ɨɬ 1 ɞɨ n
ɜɜɨɞ x, y
ɟɫɥɢ y=0
ɬɨ
ɟɫɥɢ xsearch ɢɥɢ x<xmin ɬɨ xmin:=x ɜɫɟ
ɟɫɥɢ xsearch ɢɥɢ x>xmax ɬɨ xmax:=x ɜɫɟ
xsearch:=ɧɟɬ
ɢɧɚɱɟ
ɟɫɥɢ iabs(y)>ymax ɬɨ ymax:=iabs(y) ɜɫɟ
ɜɫɟ
ɤɰ
s:=(xmax-xmin)*ymax/2
ɜɵɜɨɞ s
ɤɨɧ
13
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
14
ɉɪɢɦɟɪ ɩɪɚɜɢɥɶɧɨɣ ɢ ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ ɹɡɵɤɟ Ȼɟɣɫɢɤ:
DIM n AS INTEGER
DIM x, y AS INTEGER
DIM xmin, xmax AS INTEGER
DIM xsearch AS INTEGER
DIM ymax AS INTEGER
DIM i AS INTEGER
DIM s AS DOUBLE
xsearch = 1
xmin = 0: xmax = 0
ymax = 0
INPUT n
FOR i = 1 TO n
INPUT x, y
IF y = 0 THEN
IF xsearch = 1 OR x < xmin THEN xmin = x
IF xsearch = 1 OR x > xmax THEN xmax = x
xsearch = 0
ELSEIF ABS(y) > ymax THEN ymax = ABS(y)
END IF
NEXT i
s = (xmax - xmin) * ymax / 2
PRINT s
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɨɝɪɚɦɦɚ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɞɥɹ ɥɸɛɵɯ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ ɩɪɨɢɡɜɨɥɶɧɨɝɨ
ɪɚɡɦɟɪɚ ɢ ɧɚɯɨɞɢɬ ɨɬɜɟɬ, ɧɟ ɫɨɯɪɚɧɹɹ ɜɯɨɞɧɵɟ ɞɚɧɧɵɟ ɜ ɦɚɫɫɢɜɟ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɜ ɬɟɤɫɬɟ ɩɪɨɝɪɚɦɦɵ ɨɞɧɨɣ ɫɢɧɬɚɤɫɢɱɟɫɤɨɣ ɨɲɢɛɤɢ:
ɩɪɨɩɭɳɟɧ ɢɥɢ ɧɟɜɟɪɧɨ ɭɤɚɡɚɧ ɡɧɚɤ ɩɭɧɤɬɭɚɰɢɢ, ɧɟɜɟɪɧɨ ɧɚɩɢɫɚɧɨ ɢɥɢ
4
ɩɪɨɩɭɳɟɧɨ ɡɚɪɟɡɟɪɜɢɪɨɜɚɧɧɨɟ ɫɥɨɜɨ ɹɡɵɤɚ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɧɟ ɨɩɢɫɚɧɚ
ɢɥɢ ɧɟɜɟɪɧɨ ɨɩɢɫɚɧɚ ɩɟɪɟɦɟɧɧɚɹ, ɩɪɢɦɟɧɹɟɬɫɹ ɨɩɟɪɚɰɢɹ, ɧɟɞɨɩɭɫɬɢɦɚɹ ɞɥɹ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɬɢɩɚ ɞɚɧɧɵɯ (ɟɫɥɢ ɨɞɧɚ ɢ ɬɚ ɠɟ ɨɲɢɛɤɚ ɜɫɬɪɟɱɚɟɬɫɹ
ɧɟɫɤɨɥɶɤɨ ɪɚɡ, ɬɨ ɷɬɨ ɫɱɢɬɚɟɬɫɹ ɡɚ ɨɞɧɭ ɨɲɢɛɤɭ).
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1-2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɉɪɨɝɪɚɦɦɚ ɪɚɛɨɬɚɟɬ ɜɟɪɧɨ, ɧɨ ɪɚɡɦɟɪ ɢɫɩɨɥɶɡɭɟɦɨɣ ɩɚɦɹɬɢ ɡɚɜɢɫɢɬ ɨɬ
ɤɨɥɢɱɟɫɬɜɚ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ. ɇɚɩɪɢɦɟɪ, ɜɯɨɞɧɵɟ ɞɚɧɧɵɟ (ɤɨɨɪɞɢɧɚɬɵ
ɬɨɱɟɤ) ɡɚɩɨɦɢɧɚɸɬɫɹ ɜ ɦɚɫɫɢɜɟ ɢɥɢ ɞɪɭɝɨɣ ɫɬɪɭɤɬɭɪɟ ɞɚɧɧɵɯ, ɪɚɡɦɟɪ
ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɨɥɢɱɟɫɬɜɭ ɬɨɱɟɤ. ɉɪɢ ɷɬɨɦ ɨɛɪɚɛɨɬɤɚ ɞɚɧɧɵɯ
ɩɪɨɢɫɯɨɞɢɬ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɷɮɮɟɤɬɢɜɧɨɝɨ ɚɥɝɨɪɢɬɦɚ, ɚɧɚɥɨɝɢɱɧɨɝɨ
ɩɪɢɜɟɞɟɧɧɵɦ ɜɵɲɟ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɨɞɧɚ ɢɡ ɫɥɟɞɭɸɳɢɯ ɨɲɢɛɨɤ:
1) ɉɨɢɫɤ ɦɢɧɢɦɭɦɚ ɢɥɢ ɦɚɤɫɢɦɭɦɚ ɧɟ ɭɱɢɬɵɜɚɟɬ, ɱɬɨ ɩɟɪɜɵɣ ɩɨɞɯɨɞɹɳɢɣ
ɷɥɟɦɟɧɬ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɧɚ ɥɸɛɨɦ ɦɟɫɬɟ ɜ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢɥɢ ɜɨɨɛɳɟ
ɨɬɫɭɬɫɬɜɨɜɚɬɶ.
2)
ɉɟɪɟɩɭɬɚɧɵ ɤɨɨɪɞɢɧɚɬɵ x ɢ y ɩɪɢ ɩɨɢɫɤɟ ɨɫɧɨɜɚɧɢɹ, ɢɳɭɬɫɹ
ɦɚɤɫɢɦɚɥɶɧɵɟ ɢ ɦɢɧɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ y ɩɪɢ x=0
3) ɉɟɪɟɩɭɬɚɧɵ ɤɨɨɪɞɢɧɚɬɵ x ɢ y ɩɪɢ ɩɨɢɫɤɟ ɜɵɫɨɬɵ, ɢɳɟɬɫɹ ɦɚɤɫɢɦɚɥɶɧɨɟ
ɡɧɚɱɟɧɢɟ x.
4) ɉɪɢ ɩɨɢɫɤɟ ɜɵɫɨɬɵ ɢɳɟɬɫɹ ɦɚɤɫɢɦɭɦ ɡɧɚɱɟɧɢɹ ɤɨɨɪɞɢɧɚɬɵ y, ɚ ɧɟ ɟɟ
ɦɨɞɭɥɹ.
5) ɉɪɢ ɩɨɢɫɤɟ ɜɵɫɨɬɵ ɡɚɩɨɦɢɧɚɟɬɫɹ ɧɟ ɦɨɞɭɥɶ, ɚ ɡɧɚɱɟɧɢɟ y, ɩɪɢ ɷɬɨɦ ɩɪɢ
ɜɵɱɢɫɥɟɧɢɢ ɩɥɨɳɚɞɢ ɦɨɞɭɥɶ ɬɨɠɟ ɧɟ ɛɟɪɟɬɫɹ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɨɠɟɬ
ɩɨɥɭɱɢɬɶɫɹ ɨɬɪɢɰɚɬɟɥɶɧɚɹ ɩɥɨɳɚɞɶ.
6)
ȼɫɟ ɜɟɪɲɢɧɵ ɨɩɪɟɞɟɥɟɧɵ ɩɪɚɜɢɥɶɧɨ, ɧɨ ɩɥɨɳɚɞɶ ɬɪɟɭɝɨɥɶɧɢɤɚ
ɨɩɪɟɞɟɥɟɧɚ ɧɟɜɟɪɧɨ, ɧɚɩɪɢɦɟɪ, ɢɫɩɨɥɶɡɨɜɚɧɚ ɧɟɜɟɪɧɚɹ ɮɨɪɦɭɥɚ.
7)
ɇɟ ɭɱɢɬɵɜɚɟɬɫɹ, ɱɬɨ ɜɵɱɢɫɥɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɩɥɨɳɚɞɢ ɦɨɠɟɬ ɛɵɬɶ
ɧɟɰɟɥɵɦ. ɇɚɩɪɢɦɟɪ, ɡɧɚɱɟɧɢɟ ɩɥɨɳɚɞɢ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɩɟɪɟɦɟɧɧɨɣ ɰɟɥɨɝɨ
ɬɢɩɚ, ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɩɥɨɳɚɞɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɩɟɪɚɰɢɹ ɰɟɥɨɱɢɫɥɟɧɧɨɝɨ
ɞɟɥɟɧɢɹ (div ɜ ɉɚɫɤɚɥɟ, ɞɟɥɟɧɢɟ ɰɟɥɵɯ ɜɟɥɢɱɢɧ ɛɟɡ ɩɪɢɜɟɞɟɧɢɹ ɬɢɩɨɜ ɜ ɋɢ),
ɩɪɢ ɮɨɪɦɚɬɧɨɦ ɜɵɜɨɞɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɮɨɪɦɚɬ ɰɟɥɨɝɨ ɱɢɫɥɚ ɢ ɞɪɭɝɢɟ
ɩɨɞɨɛɧɵɟ ɨɲɢɛɤɢ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɧɟɜɟɪɧɨɦɭ ɪɟɡɭɥɶɬɚɬɭ ɩɪɢ ɞɪɨɛɧɨɦ ɨɬɜɟɬɟ.
8)
ɇɟɜɟɪɧɨ ɨɛɪɚɛɚɬɵɜɚɟɬɫɹ ɫɢɬɭɚɰɢɹ, ɤɨɝɞɚ ɢɫɤɨɦɵɣ ɬɪɟɭɝɨɥɶɧɢɤ
ɨɬɫɭɬɫɬɜɭɟɬ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬ ɨɞɧɨɣ ɞɨ ɬɪɟɯ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ ɨɲɢɛɨɤ, ɨɩɢɫɚɧɧɵɯ
ɜɵɲɟ.
ɉɪɨɝɪɚɦɦɚ ɪɚɛɨɬɚɟɬ ɜ ɰɟɥɨɦ ɜɟɪɧɨ, ɷɮɮɟɤɬɢɜɧɨ ɢɥɢ ɧɟɬ. ȼɨɡɦɨɠɧɵ
ɩɟɪɟɛɨɪɧɵɟ ɪɟɲɟɧɢɹ, ɩɪɢ ɤɨɬɨɪɵɯ ɜɫɟ ɬɨɱɤɢ ɯɪɚɧɹɬɫɹ ɜ ɦɚɫɫɢɜɟ, ɢɡ ɧɢɯ
ɜɵɛɢɪɚɸɬɫɹ ɩɨɞɯɨɞɹɳɢɟ ɬɪɟɭɝɨɥɶɧɢɤɢ, ɜɵɱɢɫɥɹɟɬɫɹ ɢ ɫɪɚɜɧɢɜɚɟɬɫɹ ɢɯ
ɩɥɨɳɚɞɶ.
ȼ ɪɟɚɥɢɡɚɰɢɢ ɚɥɝɨɪɢɬɦɚ ɞɨɩɭɳɟɧɨ ɛɨɥɟɟ 1 ɨɲɢɛɤɢ ɢɡ ɱɢɫɥɚ ɩɟɪɟɱɢɫɥɟɧɧɵɯ
ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɭɧɤɬɟ ɢɥɢ ɞɨɩɭɳɟɧɵ ɞɪɭɝɢɟ ɨɲɢɛɤɢ, ɩɪɢɜɨɞɹɳɢɟ ɤ
ɧɟɜɟɪɧɨɣ ɪɚɛɨɬɟ ɩɪɨɝɪɚɦɦɵ ɜ ɨɬɞɟɥɶɧɵɯ ɫɥɭɱɚɹɯ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬ ɨɞɧɨɣ ɞɨ ɩɹɬɢ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ ɨɲɢɛɨɤ, ɨɩɢɫɚɧɧɵɯ
ɜɵɲɟ.
ɉɪɨɝɪɚɦɦɚ ɪɚɛɨɬɚɟɬ ɜ ɨɬɞɟɥɶɧɵɯ ɱɚɫɬɧɵɯ ɫɥɭɱɚɹɯ.
Ɉɞɢɧ ɛɚɥɥ ɬɚɤɠɟ ɫɬɚɜɢɬɫɹ, ɟɫɥɢ ɩɪɨɝɪɚɦɦɚ ɧɚɩɢɫɚɧɚ ɧɟɜɟɪɧɨ, ɧɨ ɢɡ
ɨɩɢɫɚɧɢɹ ɚɥɝɨɪɢɬɦɚ ɢ ɨɛɳɟɣ ɫɬɪɭɤɬɭɪɵ ɩɪɨɝɪɚɦɦɵ ɜɢɞɧɨ, ɱɬɨ
ɷɤɡɚɦɟɧɭɟɦɵɣ ɜ ɰɟɥɨɦ ɩɪɚɜɢɥɶɧɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɩɭɬɶ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ.
ɇɟ ɜɵɩɨɥɧɟɧɨ ɧɢ ɨɞɧɨ ɢɡ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜɵɲɟ ɭɫɥɨɜɢɣ
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
3
2
1
0
4
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
15
Информатика. 11 класс. Вариант 1
Видеоразбор на сайте www.statgrad.cde.ru
Информатика.11 класс. Вариант 2
Видеоразбор на сайте www.statgrad.cde.ru
Ответы к заданиям с выбором ответа
Ответы к заданиям с выбором ответа
№
задания
А1.
А2
А3.
А4.
А5.
А6.
А7.
Ответ
2
1
1
2
2
1
1
№
задания
А8.
А9.
А10.
А11.
А12.
А13
Ответ
2
1
2
2
2
2
№
задания
А1
А2
А3
А4
А5
А6
А7
Ответ
3
2
4
2
1
4
3
№
задания
А8
А9
А10
А11
А12
А13
Ответ
3
3
3
3
3
2
Ответы к заданиям с кратким ответом
Ответы к заданиям с кратким ответом
№
задания
В1.
В2
В3.
В4.
В5.
В6.
В7.
В8
Ответ
21221
50
7
24
11
60
9
75
№
задания
В9
В10
В11
В12
В13
В14
В15
Ответ
20
А48
ECFA
1500
60
16
11
© МИОО 2012 г. Публикация в Интернете или печатных изданиях без письменного согласия МИОО запрещена
№
задания
В1
В2
В3
В4
В5
В6
В7
В8
Ответ
11212
55
11
28
11
360
9
73
№
задания
В9
В10
В11
В12
В13
В14
В15
Ответ
16
А100
DEFA
3400
30
27
13
© МИОО 2012 г. Публикация в Интернете или печатных изданиях без письменного согласия МИОО запрещена
```
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