Ⱦɚɥɟɟ ɩɪɨɫɭɦɦɢɪɭɟɦ ɩɨɥɭɱɢɜɲɟɟɫɹ ɤɨɥɢɱɟɫɬɜɨ ɟɞɢɧɢɰ ɜ ɹɱɟɣɤɭ G3
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ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 1 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 2 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ 19 ȼ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɡɚɧɟɫɥɢ ɪɟɡɭɥɶɬɚɬɵ ɬɟɫɬɢɪɨɜɚɧɢɹ ɭɱɚɳɢɯɫɹ ɩɨ ɪɚɡɥɢɱɧɵɦ ɩɪɟɞɦɟɬɚɦ. ɇɚ ɪɢɫɭɧɤɟ ɩɪɢɜɟɞɟɧɵ ɩɟɪɜɵɟ ɫɬɪɨɤɢ ɩɨɥɭɱɢɜɲɟɣɫɹ ɬɚɛɥɢɰɵ. A 1 2 3 4 5 6 7 8 Ɏɚɦɢɥɢɹ Ⱥɛɚɩɨɥɶɧɢɤɨɜ Ⱥɛɪɚɦɨɜ Ⱥɜɞɨɧɢɧ Ⱥɜɟɪɶɹɧɨɜ Ⱥɜɟɬɢɫɹɧ Ⱥɜɪɚɦɟɧɤɨ Ⱥɜɯɚɱɟɜ B ɂɦɹ Ɋɨɦɚɧ Ʉɢɪɢɥɥ ɇɢɤɨɥɚɣ ɇɢɤɢɬɚ Ⱦɚɧɢɢɥ Ⱥɥɟɤɫɟɣ Ʉɨɧɫɬɚɧɬɢɧ C D Ʉɥɚɫɫ Ɇɚɬɟɦɚɬɢɤɚ 11 5 7 6 4 6 7 4 3 0 5 5 4 0 E Ɋɭɫɫɤɢɣ ɹɡɵɤ 2 5 0 1 1 5 4 F ɂɧɨɫɬɪɚɧɧɵɣ ɹɡɵɤ 2 1 0 1 4 3 2 ɋɤɨɩɢɪɭɟɦ ɮɨɪɦɭɥɭ ɜɨ ɜɫɟ ɹɱɟɣɤɢ ɞɢɚɩɚɡɨɧɚ H2:H1001. Ȼɥɚɝɨɞɚɪɹ ɢɫɩɨɥɶɡɨɜɚɧɢɸ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɫɫɵɥɨɤ ɜ ɫɬɨɥɛɰɟ H ɜ ɫɬɪɨɤɚɯ 2–1001 ɛɭɞɭɬ ɡɚɩɢɫɚɧɵ ɥɢɛɨ 1 ɥɢɛɨ 0. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɧɚɣɬɢ ɫɭɦɦɭ, ɜ ɹɱɟɣɤɭ G1 ɜɧɟɫɺɦ ɮɨɪɦɭɥɭ =ɋɍɆɆ(H2:H1001) =SUM(H2:H1001) Ⱦɥɹ ɨɬɜɟɬɚ ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ ɹɱɟɣɤɟ, ɧɚɩɪɢɦɟɪ ɜ I2, ɧɚɩɢɲɟɦ ɮɨɪɦɭɥɭ, ɤɨɬɨɪɚɹ ɛɭɞɟɬ ɨɰɟɧɢɜɚɬɶ ɢɦɟɟɬ ɥɢ ɭɱɟɧɢɤ 0 ɛɚɥɥɨɜ ɩɨ ɤɚɤɨɦɭ-ɧɢɛɭɞɶ ɢɡ ɩɪɟɞɦɟɬɨɜ =ȿɋɅɂ(ɂɅɂ(D2=0;E2=0;F2=0);1;0) =IF(OR(D2=0;E2=0;F2=0);1;0) Ⱦɚɥɟɟ ɩɪɨɫɭɦɦɢɪɭɟɦ ɩɨɥɭɱɢɜɲɟɟɫɹ ɤɨɥɢɱɟɫɬɜɨ ɟɞɢɧɢɰ ɜ ɹɱɟɣɤɭ G3 =ɋɍɆɆ(I2:I1001) =SUM(I2:I1001) ȼɵɪɚɡɢɦ ɩɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɩɪɨɰɟɧɬɚɯ ɨɬ ɨɛɳɟɝɨ ɱɢɫɥɚ ɭɱɚɫɬɧɢɤɨɜ ɬɟɫɬɢɪɨɜɚɧɢɹ. Ɋɟɡɭɥɶɬɚɬ ɡɚɩɢɲɟɦ ɜ ɹɱɟɣɤɭ G2: =G3/1000*100 ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ. ȿɫɥɢ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɩɪɚɜɢɥɶɧɨ ɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɹ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɮɚɣɥɵ, ɫɩɟɰɢɚɥɶɧɨ ɩɨɞɝɨɬɨɜɥɟɧɧɵɟ ɞɥɹ ɩɪɨɜɟɪɤɢ ɜɵɩɨɥɧɟɧɢɹ ɞɚɧɧɨɝɨ ɡɚɞɚɧɢɹ, ɬɨ ɞɨɥɠɧɵ ɩɨɥɭɱɢɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɨɬɜɟɬɵ: ɧɚ ɩɟɪɜɵɣ ɜɨɩɪɨɫ – 20; ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ – 42,1 ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ ɉɨɥɭɱɟɧɵ ɩɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɚ ɨɛɚ ɜɨɩɪɨɫɚ. ɋɩɨɫɨɛ ɩɨɥɭɱɟɧɢɹ ɨɬɜɟɬɚ ɦɨɠɟɬ ɧɟ ɫɨɜɩɚɞɚɬɶ ɫ ɩɪɢɜɟɞɺɧɧɵɦ ɜɵɲɟ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɜ ɞɪɭɝɢɟ ɹɱɟɣɤɢ (ɨɬɥɢɱɧɵɟ ɨɬ ɬɟɯ, ɤɨɬɨɪɵɟ ɭɤɚɡɚɧɵ ɜ ɡɚɞɚɧɢɢ) ɩɪɢ ɭɫɥɨɜɢɢ 2 ɩɪɚɜɢɥɶɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɨɬɜɟɬɨɜ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɫ ɛɨɥɶɲɟɣ ɬɨɱɧɨɫɬɶɸ 1 ɉɨɥɭɱɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɬɨɥɶɤɨ ɧɚ ɨɞɢɧ ɢɡ ɞɜɭɯ ɜɨɩɪɨɫɨɜ ɉɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɟ ɩɨɥɭɱɟɧɵ ɧɢ ɧɚ ɨɞɢɧ ɢɡ ɜɨɩɪɨɫɨɜ 0 2 Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ ȼ ɫɬɨɥɛɰɟ A ɭɤɚɡɚɧɚ ɮɚɦɢɥɢɹ, ɜ ɫɬɨɥɛɰɟ B – ɢɦɹ ɭɱɚɳɟɝɨɫɹ, C – ɤɥɚɫɫ; ɜ ɫɬɨɥɛɰɚɯ D, E, F – ɛɚɥɥɵ, ɩɨɥɭɱɟɧɧɵɟ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨ ɦɚɬɟɦɚɬɢɤɟ, ɪɭɫɫɤɨɦɭ ɹɡɵɤɭ ɢ ɢɧɨɫɬɪɚɧɧɨɦɭ ɹɡɵɤɭ. ɉɨ ɤɚɠɞɨɦɭ ɩɪɟɞɦɟɬɭ ɦɨɠɧɨ ɛɵɥɨ ɧɚɛɪɚɬɶ ɨɬ 1 ɞɨ 5 ɛɚɥɥɨɜ, 0 ɛɚɥɥɨɜ – ɭɱɚɳɢɣɫɹ ɧɟ ɫɞɚɜɚɥ ɷɤɡɚɦɟɧ. ȼɫɟɝɨ ɜ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɛɵɥɢ ɡɚɧɟɫɟɧɵ ɞɚɧɧɵɟ ɩɨ 1000 ɭɱɚɳɢɯɫɹ. ɉɨɪɹɞɨɤ ɡɚɩɢɫɟɣ ɜ ɬɚɛɥɢɰɟ ɩɪɨɢɡɜɨɥɶɧɵɣ. ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ. Ɉɬɤɪɨɣɬɟ ɮɚɣɥ ɫ ɞɚɧɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɚɛɥɢɰɟɣ (ɪɚɫɩɨɥɨɠɟɧɢɟ ɮɚɣɥɚ ȼɚɦ ɫɨɨɛɳɚɬ ɨɪɝɚɧɢɡɚɬɨɪɵ ɷɤɡɚɦɟɧɚ). ɇɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɷɬɨɣ ɬɚɛɥɢɰɟ, ɨɬɜɟɬɶɬɟ ɧɚ ɞɜɚ ɜɨɩɪɨɫɚ. 1. ɋɤɨɥɶɤɨ ɭɱɟɧɢɤɨɜ 10 ɢ 11 ɤɥɚɫɫɨɜ, ɫɞɚɥɢ ɷɤɡɚɦɟɧɵ ɩɨ ɪɭɫɫɤɨɦɭ ɢ ɢɧɨɫɬɪɚɧɧɨɦɭ ɹɡɵɤɭ ɧɚ ɨɰɟɧɤɭ 4 ɢ 5 ɛɚɥɥɨɜ. Ɉɬɜɟɬ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ G1. 2. Ʉɚɤɨɣ ɩɪɨɰɟɧɬ ɭɱɟɧɢɤɨɜ ɧɟ ɫɞɚɜɚɥɢ ɷɤɡɚɦɟɧ ɯɨɬɹ ɛɵ ɩɨ ɨɞɧɨɦɭ ɩɪɟɞɦɟɬɭ? Ɉɬɜɟɬ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɨɞɧɨɝɨ ɡɧɚɤɚ ɩɨɫɥɟ ɡɚɩɹɬɨɣ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ G2 ɬɚɛɥɢɰɵ. ɉɨɥɭɱɟɧɧɭɸ ɬɚɛɥɢɰɭ ɧɟɨɛɯɨɞɢɦɨ ɫɨɯɪɚɧɢɬɶ ɩɨɞ ɢɦɟɧɟɦ, ɭɤɚɡɚɧɧɵɦ ɨɪɝɚɧɢɡɚɬɨɪɚɦɢ ɷɤɡɚɦɟɧɚ. ɉɪɢɦɟɱɚɧɢɟ. ɉɪɢ ɪɟɲɟɧɢɢ ɞɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɥɸɛɵɯ ɜɨɡɦɨɠɧɨɫɬɟɣ ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. Ⱥɥɝɨɪɢɬɦɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɞɥɹ OpenOffice.org Calc ɢ Microsoft Excel ɫɨɜɩɚɞɚɸɬ. Ɏɨɪɦɭɥɵ ɧɚɩɢɫɚɧɵ ɞɥɹ ɨɛɟɢɯ ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. ȼ ɫɬɨɥɛɰɟ H ɞɥɹ ɤɚɠɞɨɝɨ ɭɱɚɳɟɝɨɫɹ ɡɚɩɢɲɟɦ 1, ɟɫɥɢ ɨɧ ɭɱɢɬɫɹ 10 ɢ 11 ɤɥɚɫɫɟ ɢ ɫɞɚɥ ɷɤɡɚɦɟɧɵ ɩɨ ɪɭɫɫɤɨɦɭ ɢ ɢɧɨɫɬɪɚɧɧɨɦɭ ɹɡɵɤɭ ɧɚ ɨɰɟɧɤɭ 4 ɢ 5 ɛɚɥɥɨɜ, ɚ 0 ɜ ɞɪɭɝɢɯ ɫɥɭɱɚɹɯ. ȼ ɹɱɟɣɤɭ H2 ɡɚɩɢɲɟɦ ɮɨɪɦɭɥɭ =ȿɋɅɂ(ɂ(C2>9;E2>3;F2>3);1;0) =IF(AND(C2>9;E2>3;F2>3);1;0) © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 3 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 4 ȼɵɛɟɪɢɬɟ ɬɨɥɶɤɨ ɈȾɇɈ ɢɡ ɩɪɟɞɥɨɠɟɧɧɵɯ ɡɚɞɚɧɢɣ: 20.1 ɢɥɢ 20.2. 20.1 ɂɫɩɨɥɧɢɬɟɥɶ Ɋɨɛɨɬ ɭɦɟɟɬ ɩɟɪɟɦɟɳɚɬɶɫɹ ɩɨ ɥɚɛɢɪɢɧɬɭ, ɧɚɱɟɪɱɟɧɧɨɦɭ ɧɚ ɩɥɨɫɤɨɫɬɢ, ɪɚɡɛɢɬɨɣ ɧɚ ɤɥɟɬɤɢ. ɇɢɠɟ ɩɪɢɜɟɞɟɧɨ ɨɩɢɫɚɧɢɟ Ɋɨɛɨɬɚ. ɍ Ɋɨɛɨɬɚ ɟɫɬɶ ɱɟɬɵɪɟ ɤɨɦɚɧɞɵ ɩɟɪɟɦɟɳɟɧɢɹ: ɜɜɟɪɯ ɜɧɢɡ ɜɥɟɜɨ ɜɩɪɚɜɨ ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɤɨɦɚɧɞ Ɋɨɛɨɬ ɩɟɪɟɦɟɳɚɟɬɫɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: ɜɜɟɪɯ Ĺ, ɜɧɢɡ Ļ, ɜɥɟɜɨ ĸ, ɜɩɪɚɜɨ ĺ. Ɇɟɠɞɭ ɫɨɫɟɞɧɢɦɢ (ɩɨ ɫɬɨɪɨɧɚɦ) ɤɥɟɬɤɚɦɢ ɦɨɠɟɬ ɫɬɨɹɬɶ ɫɬɟɧɚ, ɱɟɪɟɡ ɤɨɬɨɪɭɸ Ɋɨɛɨɬ ɩɪɨɣɬɢ ɧɟ ɦɨɠɟɬ. ȿɫɥɢ Ɋɨɛɨɬ ɩɨɥɭɱɢɬ ɤɨɦɚɧɞɭ ɩɟɪɟɞɜɢɠɟɧɢɹ ɱɟɪɟɡ ɫɬɟɧɭ, ɬɨ ɨɧ ɪɚɡɪɭɲɢɬɫɹ. ɑɟɬɵɪɟ ɤɨɦɚɧɞɵ ɩɪɨɜɟɪɹɸɬ ɢɫɬɢɧɧɨɫɬɶ ɭɫɥɨɜɢɹ ɨɬɫɭɬɫɬɜɢɹ ɫɬɟɧɵ ɭ ɤɚɠɞɨɣ ɫɬɨɪɨɧɵ ɬɨɣ ɤɥɟɬɤɢ, ɝɞɟ ɧɚɯɨɞɢɬɫɹ Ɋɨɛɨɬ: ɫɜɟɪɯɭ ɫɜɨɛɨɞɧɨ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɗɬɢ ɤɨɦɚɧɞɵ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɦɟɫɬɟ ɫ ɭɫɥɨɜɢɟɦ «eɫɥɢ», ɢɦɟɸɳɢɦ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: ɟɫɥɢ <ɭɫɥɨɜɢɟ> ɬɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ ɜɫɟ «ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ» – ɷɬɨ ɨɞɧɚ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɸɛɵɯ ɤɨɦɚɧɞ, ɜɵɩɨɥɧɹɟɦɵɯ Ɋɨɛɨɬɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɟɪɟɞɜɢɠɟɧɢɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɜɩɪɚɜɨ, ɟɫɥɢ ɫɩɪɚɜɚ ɧɟɬ ɫɬɟɧɤɢ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɚɤɨɣ ɚɥɝɨɪɢɬɦ: ɟɫɥɢ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɬɨ ɜɩɪɚɜɨ ɜɫɟ ȼ ɨɞɧɨɦ ɭɫɥɨɜɢɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɟɫɤɨɥɶɤɨ ɤɨɦɚɧɞ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɣ, ɩɪɢɦɟɧɹɹ ɥɨɝɢɱɟɫɤɢɟ ɫɜɹɡɤɢ ɢ, ɢɥɢ, ɧɟ, ɧɚɩɪɢɦɟɪ: ɟɫɥɢ (ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ) ɢ (ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ) ɬɨ ɜɩɪɚɜɨ ɜɫɟ Ⱦɥɹ ɩɨɜɬɨɪɟɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɤɨɦɚɧɞ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɰɢɤɥ «ɩɨɤɚ», ɢɦɟɸɳɢɣ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: ɧɰ ɩɨɤɚ < ɭɫɥɨɜɢɟ > ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ ɤɰ ɇɚɩɪɢɦɟɪ, ɞɥɹ ɞɜɢɠɟɧɢɹ ɜɩɪɚɜɨ, ɩɨɤɚ ɷɬɨ ɜɨɡɦɨɠɧɨ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɣ ɚɥɝɨɪɢɬɦ: ɧɰ ɩɨɤɚ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɜɩɪɚɜɨ ɤɰ Ɍɚɤɠɟ ɭ Ɋɨɛɨɬɚ ɟɫɬɶ ɤɨɦɚɧɞɚ ɡɚɤɪɚɫɢɬɶ, ɡɚɤɪɚɲɢɜɚɸɳɚɹ ɤɥɟɬɤɭ, ɜ ɤɨɬɨɪɨɣ Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɜ ɧɚɫɬɨɹɳɢɣ ɦɨɦɟɧɬ. ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ. ɇɚ ɛɟɫɤɨɧɟɱɧɨɦ ɩɨɥɟ ɢɦɟɟɬɫɹ ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɬɟɧɚ, ɞɥɢɧɚ ɫɬɟɧɵ ɧɟɢɡɜɟɫɬɧɚ. Ɉɬ ɜɟɪɯɧɟɝɨ ɤɨɧɰɚ ɫɬɟɧɵ ɜɩɪɚɜɨ ɨɬɯɨɞɢɬ ɝɨɪɢɡɨɧɬɚɥɶɧɚɹ ɫɬɟɧɚ ɬɚɤɠɟ ɧɟɢɡɜɟɫɬɧɨɣ ɞɥɢɧɵ, ɚ ɩɨɬɨɦ ɫɧɨɜɚ ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɬɟɧɚ ɧɟɢɡɜɟɫɬɧɨɣ ɞɥɢɧɵ. Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɜ ɤɥɟɬɤɟ, ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɫɩɪɚɜɚ ɨɬ ɧɢɠɧɟɝɨ ɤɪɚɹ ɩɟɪɜɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɟɧɵ. ɇɚ ɪɢɫɭɧɤɟ ɭɤɚɡɚɧ ɨɞɢɧ ɢɡ ɜɨɡɦɨɠɧɵɯ ɫɩɨɫɨɛɨɜ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɬɟɧ ɢ Ɋɨɛɨɬɚ (Ɋɨɛɨɬ ɨɛɨɡɧɚɱɟɧ ɛɭɤɜɨɣ «Ɋ») . ɇɚɩɢɲɢɬɟ ɞɥɹ Ɋɨɛɨɬɚ ɚɥɝɨɪɢɬɦ, ɡɚɤɪɚɲɢɜɚɸɳɢɣ ɜɫɟ ɤɥɟɬɤɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɥɟɜɟɟ ɥɟɜɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɟɧɵ ɢ ɩɪɚɜɟɟ ɩɪɚɜɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɟɧɵ. Ɋɨɛɨɬ ɞɨɥɠɟɧ ɡɚɤɪɚɫɢɬɶ ɬɨɥɶɤɨ ɤɥɟɬɤɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɞɚɧɧɨɦɭ ɭɫɥɨɜɢɸ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɪɢɜɟɞɺɧɧɨɝɨ ɜɵɲɟ ɪɢɫɭɧɤɚ Ɋɨɛɨɬ ɞɨɥɠɟɧ ɡɚɤɪɚɫɢɬɶ ɫɥɟɞɭɸɳɢɟ ɤɥɟɬɤɢ (ɫɦ. ɪɢɫɭɧɨɤ) . © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 5 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 6 Ʉɨɧɟɱɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ Ɋɨɛɨɬɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɵɦ. Ⱥɥɝɨɪɢɬɦ ɞɨɥɠɟɧ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɪɚɡɦɟɪɚ ɩɨɥɹ ɢ ɥɸɛɨɝɨ ɞɨɩɭɫɬɢɦɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɬɟɧ ɜɧɭɬɪɢ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɩɨɥɹ. ɉɪɢ ɢɫɩɨɥɧɟɧɢɢ ɚɥɝɨɪɢɬɦɚ Ɋɨɛɨɬ ɧɟ ɞɨɥɠɟɧ ɪɚɡɪɭɲɢɬɶɫɹ. 20.2 ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɺɬɧɨɟ ɱɢɫɥɨ. ɉɪɨɝɪɚɦɦɚ ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɰɟɥɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ ɜɜɟɞɺɧɧɵɯ ɱɢɫɟɥ ɧɟɢɡɜɟɫɬɧɨ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɱɢɫɟɥ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 – ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ) . Ƚɚɪɚɧɬɢɪɭɟɬɫɹ, ɱɬɨ ɯɨɬɹ ɛɵ ɨɞɧɨ ɱɺɬɧɨɟ ɱɢɫɥɨ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɟɫɬɶ. Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 1000. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɩɨ ɦɨɞɭɥɸ ɧɟ ɩɪɟɜɵɲɚɸɬ 30 000. ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɺɬɧɨɟ ɱɢɫɥɨ. ɉɪɢɦɟɪ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ: ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ 40 Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.1 ɢɫɩɨɥɶɡɨɜɚɬɶ Ɋɨɛɨɬ ɚɥɝ ɧɚɱ ɜɧɢɡ ɜɥɟɜɨ ɜɜɟɪɯ ɧɰ ɩɨɤɚ ɧɟ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɡɚɤɪɚɫɢɬɶ ɜɜɟɪɯ ɤɰ ɜɩɪɚɜɨ ɧɰ ɩɨɤɚ ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɜɩɪɚɜɨ ɤɰ ɜɧɢɡ ɧɰ ɩɨɤɚ ɧɟ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɡɚɤɪɚɫɢɬɶ ɜɧɢɡ ɤɰ ɤɨɧ ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ Ɂɚɩɢɫɚɧ ɩɪɚɜɢɥɶɧɵɣ ɚɥɝɨɪɢɬɦ, ɧɟ ɩɪɢɜɨɞɹɳɢɣ ɤ ɭɧɢɱɬɨɠɟɧɢɸ Ɋɨɛɨɬɚ, ɩɨɥɧɨɫɬɶɸ ɪɟɲɚɸɳɢɣ ɩɨɫɬɚɜɥɟɧɧɭɸ ɡɚɞɚɱɭ. Ⱦɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ 2 ɢɧɨɝɨ ɫɢɧɬɚɤɫɢɫɚ ɢɧɫɬɪɭɤɰɢɣ ɢɫɩɨɥɧɢɬɟɥɹ, ɛɨɥɟɟ ɩɪɢɜɵɱɧɨɝɨ ɭɱɚɳɢɦɫɹ. Ⱥɥɝɨɪɢɬɦ ɜ ɰɟɥɨɦ ɡɚɩɢɫɚɧ ɜɟɪɧɨ, ɧɨ ɦɨɠɟɬ ɫɨɞɟɪɠɚɬɶ ɨɞɧɭ ɨɲɢɛɤɭ. ɉɪɢɦɟɪɵ ɨɲɢɛɨɤ: 1) Ɋɨɛɨɬ ɡɚɤɪɚɲɢɜɚɟɬ ɨɞɧɭ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɢɲɧɢɯ ɤɥɟɬɨɤ; 1 2) Ɋɨɛɨɬ ɧɟ ɡɚɤɪɚɲɢɜɚɟɬ ɨɞɧɭ ɢɡ ɤɥɟɬɨɤ (ɧɚɩɪɢɦɟɪ, ɤɥɟɬɤɭ ɩɨɞ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɬɟɧɨɣ) Ɂɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɧɟɜɟɪɧɨ, ɢɥɢ ɜɨɡɦɨɠɧɵɯ ɨɲɢɛɨɤ 0 ɜ ɚɥɝɨɪɢɬɦɟ ɛɨɥɶɲɟ ɨɞɧɨɣ 2 Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.2 ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɺɬɧɨɟ ɱɢɫɥɨ. ɉɪɨɝɪɚɦɦɚ ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɰɟɥɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ ɜɜɟɞɺɧɧɵɯ ɱɢɫɟɥ ɧɟɢɡɜɟɫɬɧɨ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɱɢɫɟɥ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 – ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ). Ƚɚɪɚɧɬɢɪɭɟɬɫɹ, ɱɬɨ ɯɨɬɹ ɛɵ ɨɞɧɨ ɱɺɬɧɨɟ ɱɢɫɥɨ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɟɫɬɶ. Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 1000. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɩɨ ɦɨɞɭɥɸ ɧɟ ɩɪɟɜɵɲɚɸɬ 30 000. ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɺɬɧɨɟ ɱɢɫɥɨ. 40 45 11 -25 77 0 © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 7 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 8 ɧɚɱ ɰɟɥ ɚ,answer answer:=0; ɜɜɨɞ ɚ ɧɰ ɩɨɤɚ ɚ<>0 ɟɫɥɢ (mod (ɚ,2) = 0) ɢ (a > answer) ɬɨ answer:=a ɜɫɟ ɜɜɨɞ ɚ ɤɰ ɜɵɜɨɞ answer ɤɨɧ ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɜɚɪɢɚɧɬɵ ɪɟɲɟɧɢɹ. Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ ɬɟɫɬɵ: Ɍɚɛɥɢɰɚ ɬɟɫɬɢɪɨɜɚɧɢɹ ʋ ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ 1 1 2 2 0 2 4 4 5 2 3 0 3 2 2 1023 11111 2121 0 ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ ɉɪɟɞɥɨɠɟɧɨ ɜɟɪɧɨɟ ɪɟɲɟɧɢɟ. ɉɪɨɝɪɚɦɦɚ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɧɚ ɜɫɟɯ ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ ɬɟɫɬɚɯ. ɉɪɨɝɪɚɦɦɚ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɧɚ ɥɸɛɨɦ ɹɡɵɤɟ 2 ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɟɜɟɪɧɵɣ ɨɬɜɟɬ ɧɚ ɨɞɧɨɦ ɢɡ ɬɟɫɬɨɜ, ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ. ɇɚɩɪɢɦɟɪ, ɪɟɲɟɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɡɚɞɚɧɨ ɬɨɥɶɤɨ ɩɪɨɜɟɪɤɚ ɱɟɬɧɨɫɬɢ ɩɪɢ ɨɬɛɨɪɟ ɱɢɫɟɥ: mod (ɚ,2) = 0) 1 ɜɵɞɚɫɬ ɧɟɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɬɟɫɬɟ ʋ 2. ɂɅɂ Ɉɬɛɢɪɚɸɬɫɹ ɧɟɱɺɬɧɵɟ ɱɢɫɥɚ. ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɜɫɟɯ ɬɟɫɬɚɯ ɨɬɜɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɧɟɱɺɬɧɨɟ ɱɢɫɥɨ. ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɬɟɫɬɚɯ ɧɟɜɟɪɧɵɟ ɨɬɜɟɬɵ, ɨɬɥɢɱɧɵɟ ɨɬ ɨɩɢɫɚɧɧɵɯ ɜ 0 ɤɪɢɬɟɪɢɢ ɧɚ 1 ɛɚɥɥ. Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ 2 © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 1 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 2 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ =ȿɋɅɂ(ɂ(B2<10;C2>D2;C2>E2);1;0) =IF(AND (B2<10;C2>D2;C2>E2);1;0) ɋɤɨɩɢɪɭɟɦ ɮɨɪɦɭɥɭ ɜɨ ɜɫɟ ɹɱɟɣɤɢ ɞɢɚɩɚɡɨɧɚ F3:F368. Ȼɥɚɝɨɞɚɪɹ ɢɫɩɨɥɶɡɨɜɚɧɢɸ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɫɫɵɥɨɤ ɜ ɫɬɨɥɛɰɟ F ɜ ɫɬɪɨɤɚɯ 2 – 368 ɛɭɞɭɬ ɡɚɩɢɫɚɧɵ ɥɢɛɨ 1 ɥɢɛɨ 0. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɧɚɣɬɢ ɫɭɦɦɭ, ɜ ɹɱɟɣɤɭ G1 ɜɧɟɫɺɦ ɮɨɪɦɭɥɭ =ɋɍɆɆ(F2:F368) =SUM(F2:F368) Ⱦɥɹ ɨɬɜɟɬɚ ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ ɜ ɹɱɟɣɤɟ, ɧɚɩɪɢɦɟɪ ɜ H2, ɧɚɩɢɲɟɦ ɮɨɪɦɭɥɭ, ɤɨɬɨɪɚɹ ɛɭɞɟɬ ɨɰɟɧɢɜɚɬɶ ɩɨɥɭɱɢɥ ɥɢ ɭɱɟɧɢɤ 10 ɢɥɢ 11 ɤɥɚɫɫɚ ɫɪɟɞɧɢɣ ɛɚɥ ɛɨɥɶɲɟ 50 ɩɨ ɬɪɺɦ ɷɤɡɚɦɟɧɚɦ. =ȿɋɅɂ(ɂ(B2>9;ɋɊɁɇȺɑ(C2:E2)>50);1;0) =IF(AND(B2>9;AVERAGE(C2:E2)>50);1;0) Ⱦɚɥɟɟ ɩɪɨɫɭɦɦɢɪɭɟɦ ɩɨɥɭɱɢɜɲɟɟɫɹ ɤɨɥɢɱɟɫɬɜɨ ɟɞɢɧɢɰ ɜ ɹɱɟɣɤɭ G3 =ɋɍɆɆ(H2:H368) =SUM(H2:H368) ȼɵɪɚɡɢɦ ɩɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɩɪɨɰɟɧɬɚɯ ɨɬ ɨɛɳɟɝɨ ɱɢɫɥɚ ɭɱɚɫɬɧɢɤɨɜ ɬɟɫɬɢɪɨɜɚɧɢɹ. Ɋɟɡɭɥɶɬɚɬ ɡɚɩɢɲɟɦ ɜ ɹɱɟɣɤɭ G2: =G3/368*100 ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ. ȿɫɥɢ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɩɪɚɜɢɥɶɧɨ ɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɹ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɮɚɣɥɵ, ɫɩɟɰɢɚɥɶɧɨ ɩɨɞɝɨɬɨɜɥɟɧɧɵɟ ɞɥɹ ɩɪɨɜɟɪɤɢ ɜɵɩɨɥɧɟɧɢɹ ɞɚɧɧɨɝɨ ɡɚɞɚɧɢɹ, ɬɨ ɞɨɥɠɧɵ ɩɨɥɭɱɢɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɨɬɜɟɬɵ: ɧɚ ɩɟɪɜɵɣ ɜɨɩɪɨɫ – 75; ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ – 22,8. ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ ɉɨɥɭɱɟɧɵ ɩɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɚ ɨɛɚ ɜɨɩɪɨɫɚ. ɋɩɨɫɨɛ ɩɨɥɭɱɟɧɢɹ ɨɬɜɟɬɚ ɦɨɠɟɬ ɧɟ ɫɨɜɩɚɞɚɬɶ ɫ ɩɪɢɜɟɞɺɧɧɵɦ ɜɵɲɟ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɜ ɞɪɭɝɢɟ ɹɱɟɣɤɢ (ɨɬɥɢɱɧɵɟ ɨɬ ɬɟɯ, ɤɨɬɨɪɵɟ ɭɤɚɡɚɧɵ ɜ ɡɚɞɚɧɢɢ) ɩɪɢ ɭɫɥɨɜɢɢ 2 ɩɪɚɜɢɥɶɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɨɬɜɟɬɨɜ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɫ ɛɨɥɶɲɟɣ ɬɨɱɧɨɫɬɶɸ ɉɨɥɭɱɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɬɨɥɶɤɨ ɧɚ ɨɞɢɧ ɢɡ ɞɜɭɯ ɜɨɩɪɨɫɨɜ 1 0 ɉɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɟ ɩɨɥɭɱɟɧɵ ɧɢ ɧɚ ɨɞɢɧ ɢɡ ɜɨɩɪɨɫɨɜ 2 Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ 19 ȼ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɡɚɧɟɫɥɢ ɪɟɡɭɥɶɬɚɬɵ ɬɟɫɬɢɪɨɜɚɧɢɹ ɭɱɚɳɢɯɫɹ 8Ť11 ɤɥɚɫɫɨɜ ɩɨ ɪɚɡɥɢɱɧɵɦ ɩɪɟɞɦɟɬɚɦ. ɇɚ ɪɢɫɭɧɤɟ ɩɪɢɜɟɞɟɧɵ ɩɟɪɜɵɟ ɫɬɪɨɤɢ ɩɨɥɭɱɢɜɲɟɣɫɹ ɬɚɛɥɢɰɵ. 1 2 3 4 5 6 7 8 9 10 A Ɏɚɦɢɥɢɹ ɢɦɹ ɀɢɥɢɧɫɤɚɹ Ⱥɥɟɤɫɚɧɞɪɚ Ʉɨɦɚɯɢɧ Ⱥɥɟɤɫɚɧɞɪ ɒɢɬɨɜɚ Ɇɚɪɢɹ əɲɢɧ Ⱥɧɞɪɟɣ Ɏɨɦɢɧ Ⱦɟɧɢɫ ɒɚɣɤɨɜɚ Ⱥɧɧɚ ɋɬɟɩɚɧɨɜ ȼɥɚɞɢɫɥɚɜ Ʉɨɥɭɩɚɟɜɚ Ɍɚɬɶɹɧɚ Ɍɢɬɟɟɜɚ Ɇɚɪɢɹ B C Ʉɥɚɫɫ Ɋɭɫɫɤɢɣ ɹɡɵɤ 8 60 11 9 8 62 8 65 9 56 10 80 9 92 11 7 8 11 D Ɇɚɬɟɦɚɬɢɤɚ 57 61 37 94 66 96 43 62 76 E Ɏɢɡɤɭɥɶɬɭɪɚ 69 11 49 23 50 49 74 28 51 ȼ ɫɬɨɥɛɰɟ A ɭɤɚɡɚɧɵ ɮɚɦɢɥɢɹ ɢ ɢɦɹ, ɜ ɫɬɨɥɛɰɟ B – ɤɥɚɫɫ ɭɱɚɳɟɝɨɫɹ; ɜ ɫɬɨɥɛɰɚɯ C, D, E – ɛɚɥɥɵ, ɩɨɥɭɱɟɧɧɵɟ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨ ɪɭɫɫɤɨɦɭ ɹɡɵɤɭ, ɦɚɬɟɦɚɬɢɤɟ ɢ ɮɢɡɤɭɥɶɬɭɪɟ. ɉɨ ɤɚɠɞɨɦɭ ɩɪɟɞɦɟɬɭ ɦɨɠɧɨ ɛɵɥɨ ɧɚɛɪɚɬɶ ɨɬ 1 ɞɨ 100 ɛɚɥɥɨɜ. ȼɫɟɝɨ ɜ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɛɵɥɢ ɡɚɧɟɫɟɧɵ ɞɚɧɧɵɟ ɩɨ 367 ɭɱɚɳɢɦɫɹ. ɉɨɪɹɞɨɤ ɡɚɩɢɫɟɣ ɜ ɬɚɛɥɢɰɟ ɩɪɨɢɡɜɨɥɶɧɵɣ. ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ. Ɉɬɤɪɨɣɬɟ ɮɚɣɥ ɫ ɞɚɧɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɚɛɥɢɰɟɣ (ɪɚɫɩɨɥɨɠɟɧɢɟ ɮɚɣɥɚ ȼɚɦ ɫɨɨɛɳɚɬ ɨɪɝɚɧɢɡɚɬɨɪɵ ɷɤɡɚɦɟɧɚ). ɇɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɷɬɨɣ ɬɚɛɥɢɰɟ, ɨɬɜɟɬɶɬɟ ɧɚ ɞɜɚ ɜɨɩɪɨɫɚ. 1. ɋɤɨɥɶɤɨ ɭɱɟɧɢɤɨɜ ɢɡ 8 ɢ 9 ɤɥɚɫɫɨɜ ɩɨɥɭɱɢɥɢ ɨɰɟɧɤɭ ɩɨ ɪɭɫɫɤɨɦɭ ɹɡɵɤɭ ɛɨɥɶɲɟ, ɱɟɦ ɨɰɟɧɤɭ ɩɨ ɦɚɬɟɦɚɬɢɤɟ ɢ ɩɨ ɮɢɡɤɭɥɶɬɭɪɟ. Ɉɬɜɟɬ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ G1. 2. Ʉɚɤɨɣ ɩɪɨɰɟɧɬ ɭɱɟɧɢɤɨɜ 10 ɢ 11 ɤɥɚɫɫɨɜ ɩɨɥɭɱɢɥɢ ɫɪɟɞɧɢɣ ɛɚɥ ɛɨɥɶɲɟ 50 ɩɨ ɬɪɺɦ ɷɤɡɚɦɟɧɚɦ? Ɉɬɜɟɬ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɨɞɧɨɝɨ ɡɧɚɤɚ ɩɨɫɥɟ ɡɚɩɹɬɨɣ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ G2 ɬɚɛɥɢɰɵ. ɉɨɥɭɱɟɧɧɭɸ ɬɚɛɥɢɰɭ ɧɟɨɛɯɨɞɢɦɨ ɫɨɯɪɚɧɢɬɶ ɩɨɞ ɢɦɟɧɟɦ, ɭɤɚɡɚɧɧɵɦ ɨɪɝɚɧɢɡɚɬɨɪɚɦɢ ɷɤɡɚɦɟɧɚ. ɉɪɢɦɟɱɚɧɢɟ. ɉɪɢ ɪɟɲɟɧɢɢ ɞɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɥɸɛɵɯ ɜɨɡɦɨɠɧɨɫɬɟɣɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. Ⱥɥɝɨɪɢɬɦɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɞɥɹ OpenOffice.org Calc ɢ Microsoft Excel ɫɨɜɩɚɞɚɸɬ. Ɏɨɪɦɭɥɵ ɧɚɩɢɫɚɧɵ ɞɥɹ ɨɛɟɢɯ ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. ȼɬɨɪɨɣ ɜɚɪɢɚɧɬ – ɞɥɹ OpenOffice.org Calc. ȼ ɫɬɨɥɛɰɟ F ɞɥɹ ɤɚɠɞɨɝɨ ɭɱɚɳɟɝɨɫɹ ɡɚɩɢɲɟɦ 1, ɟɫɥɢ ɨɧ ɭɱɢɬɫɹ 8 ɢɥɢ 9 ɤɥɚɫɫɟ, ɢ ɩɨɥɭɱɢɥ ɨɰɟɧɤɭ ɩɨ ɪɭɫɫɤɨɦɭ ɹɡɵɤɭ ɛɨɥɶɲɟ, ɱɟɦ ɨɰɟɧɤɭ ɩɨ ɦɚɬɟɦɚɬɢɤɟ ɢ ɩɨ ɮɢɡɤɭɥɶɬɭɪɟ, ɢ 0 – ɜ ɨɛɪɚɬɧɨɦ ɫɥɭɱɚɟ. ȼ ɹɱɟɣɤɭ F2 ɡɚɩɢɲɟɦ ɮɨɪɦɭɥɭ © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 3 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 4 ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ ɉɨɥɭɱɟɧɵ ɩɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɚ ɨɛɚ ɜɨɩɪɨɫɚ. ɋɩɨɫɨɛ ɩɨɥɭɱɟɧɢɹ ɨɬɜɟɬɚ ɦɨɠɟɬ ɧɟ ɫɨɜɩɚɞɚɬɶ ɫ ɩɪɢɜɟɞɺɧɧɵɦ ɜɵɲɟ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɜ ɞɪɭɝɢɟ ɹɱɟɣɤɢ (ɨɬɥɢɱɧɵɟ ɨɬ ɬɟɯ, ɤɨɬɨɪɵɟ ɭɤɚɡɚɧɵ ɜ ɡɚɞɚɧɢɢ) ɩɪɢ ɭɫɥɨɜɢɢ 2 ɩɪɚɜɢɥɶɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɨɬɜɟɬɨɜ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɫ ɛɨɥɶɲɟɣ ɬɨɱɧɨɫɬɶɸ ɉɨɥɭɱɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɬɨɥɶɤɨ ɧɚ ɨɞɢɧ ɢɡ ɞɜɭɯ ɜɨɩɪɨɫɨɜ 1 ɉɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɟ ɩɨɥɭɱɟɧɵ ɧɢ ɧɚ ɨɞɢɧ ɢɡ ɜɨɩɪɨɫɨɜ 0 2 Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ ȼɵɛɟɪɢɬɟ ɬɨɥɶɤɨ ɈȾɇɈ ɢɡ ɩɪɟɞɥɨɠɟɧɧɵɯ ɡɚɞɚɧɢɣ: 20.1 ɢɥɢ 20.2. 20.1 ɂɫɩɨɥɧɢɬɟɥɶ Ɋɨɛɨɬ ɭɦɟɟɬ ɩɟɪɟɦɟɳɚɬɶɫɹ ɩɨ ɥɚɛɢɪɢɧɬɭ, ɧɚɱɟɪɱɟɧɧɨɦɭ ɧɚ ɩɥɨɫɤɨɫɬɢ, ɪɚɡɛɢɬɨɣ ɧɚ ɤɥɟɬɤɢ. ɇɢɠɟ ɩɪɢɜɟɞɟɧɨ ɨɩɢɫɚɧɢɟ Ɋɨɛɨɬɚ. ɍ Ɋɨɛɨɬɚ ɟɫɬɶ ɱɟɬɵɪɟ ɤɨɦɚɧɞɵ ɩɟɪɟɦɟɳɟɧɢɹ: ɜɜɟɪɯ ɜɧɢɡ ɜɥɟɜɨ ɜɩɪɚɜɨ ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɤɨɦɚɧɞ Ɋɨɛɨɬ ɩɟɪɟɦɟɳɚɟɬɫɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: ɜɜɟɪɯ Ĺ, ɜɧɢɡ Ļ, ɜɥɟɜɨ ĸ, ɜɩɪɚɜɨ ĺ. Ɇɟɠɞɭ ɫɨɫɟɞɧɢɦɢ (ɩɨ ɫɬɨɪɨɧɚɦ) ɤɥɟɬɤɚɦɢ ɦɨɠɟɬ ɫɬɨɹɬɶ ɫɬɟɧɚ, ɱɟɪɟɡ ɤɨɬɨɪɭɸ Ɋɨɛɨɬ ɩɪɨɣɬɢ ɧɟ ɦɨɠɟɬ. ȿɫɥɢ Ɋɨɛɨɬ ɩɨɥɭɱɢɬ ɤɨɦɚɧɞɭ ɩɟɪɟɞɜɢɠɟɧɢɹ ɱɟɪɟɡ ɫɬɟɧɭ, ɬɨ ɨɧ ɪɚɡɪɭɲɢɬɫɹ. ɑɟɬɵɪɟ ɤɨɦɚɧɞɵ ɩɪɨɜɟɪɹɸɬ ɢɫɬɢɧɧɨɫɬɶ ɭɫɥɨɜɢɹ ɨɬɫɭɬɫɬɜɢɹ ɫɬɟɧɵ ɭ ɤɚɠɞɨɣ ɫɬɨɪɨɧɵ ɬɨɣ ɤɥɟɬɤɢ, ɝɞɟ ɧɚɯɨɞɢɬɫɹ Ɋɨɛɨɬ: ɫɜɟɪɯɭ ɫɜɨɛɨɞɧɨ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɗɬɢ ɤɨɦɚɧɞɵ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɦɟɫɬɟ ɫ ɭɫɥɨɜɢɟɦ «eɫɥɢ», ɢɦɟɸɳɢɦ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: ɟɫɥɢ <ɭɫɥɨɜɢɟ> ɬɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ ɜɫɟ «ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ» – ɷɬɨ ɨɞɧɚ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɸɛɵɯ ɤɨɦɚɧɞ, ɜɵɩɨɥɧɹɟɦɵɯ Ɋɨɛɨɬɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɟɪɟɞɜɢɠɟɧɢɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɜɩɪɚɜɨ, ɟɫɥɢ ɫɩɪɚɜɚ ɧɟɬ ɫɬɟɧɤɢ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɚɤɨɣ ɚɥɝɨɪɢɬɦ: ɟɫɥɢ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɬɨ ɜɩɪɚɜɨ ɜɫɟ ȼ ɨɞɧɨɦ ɭɫɥɨɜɢɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɟɫɤɨɥɶɤɨ ɤɨɦɚɧɞ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɣ, ɩɪɢɦɟɧɹɹ ɥɨɝɢɱɟɫɤɢɟ ɫɜɹɡɤɢ ɢ, ɢɥɢ, ɧɟ, ɧɚɩɪɢɦɟɪ: ɟɫɥɢ (ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ) ɢ (ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ) ɬɨ ɜɩɪɚɜɨ ɜɫɟ Ⱦɥɹ ɩɨɜɬɨɪɟɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɤɨɦɚɧɞ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɰɢɤɥ «ɩɨɤɚ», ɢɦɟɸɳɢɣ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: ɧɰ ɩɨɤɚ < ɭɫɥɨɜɢɟ > ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ ɤɰ ɇɚɩɪɢɦɟɪ, ɞɥɹ ɞɜɢɠɟɧɢɹ ɜɩɪɚɜɨ, ɩɨɤɚ ɷɬɨ ɜɨɡɦɨɠɧɨ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɣ ɚɥɝɨɪɢɬɦ: ɧɰ ɩɨɤɚ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɜɩɪɚɜɨ ɤɰ Ɍɚɤɠɟ ɭ Ɋɨɛɨɬɚ ɟɫɬɶ ɤɨɦɚɧɞɚ ɡɚɤɪɚɫɢɬɶ, ɡɚɤɪɚɲɢɜɚɸɳɚɹ ɤɥɟɬɤɭ, ɜ ɤɨɬɨɪɨɣ Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɜ ɧɚɫɬɨɹɳɢɣ ɦɨɦɟɧɬ. © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 5 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 6 ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ. ɇɚ ɛɟɫɤɨɧɟɱɧɨɦ ɩɨɥɟ ɢɦɟɟɬɫɹ ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɬɟɧɚ, ɞɥɢɧɚ ɫɬɟɧɵ ɧɟɢɡɜɟɫɬɧɚ. Ɉɬ ɜɟɪɯɧɟɝɨ ɤɨɧɰɚ ɫɬɟɧɵ ɜɥɟɜɨ ɨɬɯɨɞɢɬ ɝɨɪɢɡɨɧɬɚɥɶɧɚɹ ɫɬɟɧɚ ɬɚɤɠɟ ɧɟɢɡɜɟɫɬɧɨɣ ɞɥɢɧɵ. Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɩɨɞ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɬɟɧɨɣ, ɜ ɤɥɟɬɤɟ, ɩɪɢɦɵɤɚɸɳɟɣ ɤ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɟɧɟ. ɇɚ ɪɢɫɭɧɤɟ ɭɤɚɡɚɧ ɨɞɢɧ ɢɡ ɜɨɡɦɨɠɧɵɯ ɫɩɨɫɨɛɨɜ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɬɟɧ ɢ Ɋɨɛɨɬɚ (Ɋɨɛɨɬ ɨɛɨɡɧɚɱɟɧ ɛɭɤɜɨɣ «Ɋ») . 20.2 ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɫɭɦɦɭ ɱɺɬɧɵɯ ɱɢɫɟɥ, ɤɪɚɬɧɵɯ 3. ɉɪɨɝɪɚɦɦɚ ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɰɟɥɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ ɜɜɟɞɺɧɧɵɯ ɱɢɫɟɥ ɧɟɢɡɜɟɫɬɧɨ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɱɢɫɟɥ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 – ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ) . Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 1000. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɩɨ ɦɨɞɭɥɸ ɧɟ ɩɪɟɜɵɲɚɸɬ 30 000. ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɫɭɦɦɭ ɱɺɬɧɵɯ ɱɢɫɟɥ, ɤɪɚɬɧɵɯ 3. ɉɪɢɦɟɪ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ: ȼɯɨɞɧɵɟ ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ ɞɚɧɧɵɟ 40 18 6 9 12 0 ɇɚɩɢɲɢɬɟ ɞɥɹ Ɋɨɛɨɬɚ ɚɥɝɨɪɢɬɦ, ɡɚɤɪɚɲɢɜɚɸɳɢɣ ɜɫɟ ɤɥɟɬɤɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɩɪɚɜɟɟ ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɭɱɚɫɬɤɚ ɫɬɟɧɵ ɢ ɧɚɞ ɝɨɪɢɡɨɧɬɚɥɶɧɵɦ ɭɱɚɫɬɤɨɦ ɫɬɟɧɵ. Ɋɨɛɨɬ ɞɨɥɠɟɧ ɡɚɤɪɚɫɢɬɶ ɬɨɥɶɤɨ ɤɥɟɬɤɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɞɚɧɧɨɦɭ ɭɫɥɨɜɢɸ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɪɢɜɟɞɺɧɧɨɝɨ ɜɵɲɟ ɪɢɫɭɧɤɚ Ɋɨɛɨɬ ɞɨɥɠɟɧ ɡɚɤɪɚɫɢɬɶ ɫɥɟɞɭɸɳɢɟ ɤɥɟɬɤɢ (ɫɦ. ɪɢɫɭɧɨɤ) . Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.1 ɢɫɩɨɥɶɡɨɜɚɬɶ Ɋɨɛɨɬ ɚɥɝ ɧɚɱ ɧɰ ɩɨɤɚ ɧɟ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɜɧɢɡ ɤɰ ɜɩɪɚɜɨ ɜɜɟɪɯ ɧɰ ɩɨɤɚ ɧɟ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɡɚɤɪɚɫɢɬɶ ɜɜɟɪɯ ɤɰ ɜɥɟɜɨ ɧɰ ɩɨɤɚ ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɡɚɤɪɚɫɢɬɶ ɜɥɟɜɨ ɤɰ ɤɨɧ Ʉɨɧɟɱɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ Ɋɨɛɨɬɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɵɦ. Ⱥɥɝɨɪɢɬɦ ɞɨɥɠɟɧ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɪɚɡɦɟɪɚ ɩɨɥɹ ɢ ɥɸɛɨɝɨ ɞɨɩɭɫɬɢɦɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɬɟɧ ɜɧɭɬɪɢ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɩɨɥɹ. ɉɪɢ ɢɫɩɨɥɧɟɧɢɢ ɚɥɝɨɪɢɬɦɚ Ɋɨɛɨɬ ɧɟ ɞɨɥɠɟɧ ɪɚɡɪɭɲɢɬɶɫɹ. © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 7 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 8 ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ Ɂɚɩɢɫɚɧ ɩɪɚɜɢɥɶɧɵɣ ɚɥɝɨɪɢɬɦ, ɧɟ ɩɪɢɜɨɞɹɳɢɣ ɤ ɭɧɢɱɬɨɠɟɧɢɸ Ɋɨɛɨɬɚ, ɩɨɥɧɨɫɬɶɸ ɪɟɲɚɸɳɢɣ ɩɨɫɬɚɜɥɟɧɧɭɸ ɡɚɞɚɱɭ. Ⱦɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ 2 ɢɧɨɝɨ ɫɢɧɬɚɤɫɢɫɚ ɢɧɫɬɪɭɤɰɢɣ ɢɫɩɨɥɧɢɬɟɥɹ, ɛɨɥɟɟ ɩɪɢɜɵɱɧɨɝɨ ɭɱɚɳɢɦɫɹ. Ⱥɥɝɨɪɢɬɦ ɜ ɰɟɥɨɦ ɡɚɩɢɫɚɧ ɜɟɪɧɨ, ɧɨ ɦɨɠɟɬ ɫɨɞɟɪɠɚɬɶ ɨɞɧɭ ɨɲɢɛɤɭ. ɉɪɢɦɟɪɵ ɨɲɢɛɨɤ: 1 1) Ɋɨɛɨɬ ɡɚɤɪɚɲɢɜɚɟɬ ɨɞɧɭ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɢɲɧɢɯ ɤɥɟɬɨɤ; 2) Ɋɨɛɨɬ ɧɟ ɡɚɤɪɚɲɢɜɚɟɬ ɨɞɧɭ ɢɡ ɤɥɟɬɨɤ Ɂɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɧɟɜɟɪɧɨ, ɢɥɢ ɜɨɡɦɨɠɧɵɯ ɨɲɢɛɨɤ ɜ ɚɥɝɨɪɢɬɦɟ ɛɨɥɶɲɟ 0 ɨɞɧɨɣ 2 Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.2 ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɫɭɦɦɭ ɱɺɬɧɵɯ ɱɢɫɟɥ, ɤɪɚɬɧɵɯ 3. ɉɪɨɝɪɚɦɦɚ ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɰɟɥɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ ɜɜɟɞɺɧɧɵɯ ɱɢɫɟɥ ɧɟɢɡɜɟɫɬɧɨ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɱɢɫɟɥ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 – ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ). Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 1000. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɩɨ ɦɨɞɭɥɸ ɧɟ ɩɪɟɜɵɲɚɸɬ 30 000. ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɫɭɦɦɭ ɱɺɬɧɵɯ ɱɢɫɟɥ, ɤɪɚɬɧɵɯ 3. ɧɚɱ ɰɟɥ ɚ,answer answer:=0; ɜɜɨɞ ɚ ɧɰ ɩɨɤɚ ɚ<>0 ɟɫɥɢ (mod (ɚ,2) = 0) ɢ (mod (ɚ,3) = 0) ɬɨ answer:=answer+a ɜɫɟ ɜɜɨɞ ɚ ɤɰ ɜɵɜɨɞ answer ɤɨɧ ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɜɚɪɢɚɧɬɵ ɪɟɲɟɧɢɹ. ɇɚɩɪɢɦɟɪ, ɜɦɟɫɬɨ ɭɫɥɨɜɢɹ (mod (ɚ,2) = 0) ɢ (mod (ɚ,3) = 0) ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɭɫɥɨɜɢɟ mod (a,6) = 0. Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ ɬɟɫɬɵ: Ɍɚɛɥɢɰɚ ɬɟɫɬɢɪɨɜɚɧɢɹ ʋ 1 7 8 25 27 9 0 18 12 0 10 24 10051 36 0 ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ 0 ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ 2 30 3 60 ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ ɉɪɟɞɥɨɠɟɧɨ ɜɟɪɧɨɟ ɪɟɲɟɧɢɟ. ɉɪɨɝɪɚɦɦɚ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɧɚ ɜɫɟɯ ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ ɬɟɫɬɚɯ. ɉɪɨɝɪɚɦɦɚ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɧɚ ɥɸɛɨɦ ɹɡɵɤɟ 2 ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɟɜɟɪɧɵɣ ɨɬɜɟɬ ɧɚ ɨɞɧɨɦ ɢɡ ɬɟɫɬɨɜ, ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ. ɇɚɩɪɢɦɟɪ, ɪɟɲɟɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɡɚɞɚɧɨ ɬɨɥɶɤɨ ɩɪɨɜɟɪɤɚ ɱɟɬɧɨɫɬɢ ɩɪɢ ɨɬɛɨɪɟ ɱɢɫɟɥ: (mod (ɚ,2) <> 0) ɢ (mod (ɚ,3) = 0) ɜɵɞɚɫɬ ɧɟɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ 1 ɬɟɫɬɟ ʋ 1. ɂɅɂ Ɉɬɛɢɪɚɸɬɫɹ ɧɟɱɺɬɧɵɟ ɱɢɫɥɚ. ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɜɫɟɯ ɬɟɫɬɚɯ ɨɬɜɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɧɟɱɺɬɧɨɟ ɱɢɫɥɨ ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɬɟɫɬɚɯ ɧɟɜɟɪɧɵɟ ɨɬɜɟɬɵ, ɨɬɥɢɱɧɵɟ ɨɬ ɨɩɢɫɚɧɧɵɯ ɜ 0 ɤɪɢɬɟɪɢɢ ɧɚ 1 ɛɚɥɥ Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ 2 © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 3 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 1 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 3 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 2 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ 19 ȼ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɡɚɧɟɫɥɢ ɪɟɡɭɥɶɬɚɬɵ ɬɟɫɬɢɪɨɜɚɧɢɹ ɭɱɚɳɢɯɫɹ ɩɨ ɪɚɡɥɢɱɧɵɦ ɩɪɟɞɦɟɬɚɦ. ɇɚ ɪɢɫɭɧɤɟ ɩɪɢɜɟɞɟɧɵ ɩɟɪɜɵɟ ɫɬɪɨɤɢ ɩɨɥɭɱɢɜɲɟɣɫɹ ɬɚɛɥɢɰɵ. A 1 2 3 4 5 6 7 8 Ɏɚɦɢɥɢɹ Ⱥɛɚɩɨɥɶɧɢɤɨɜ Ⱥɛɪɚɦɨɜ Ⱥɜɞɨɧɢɧ Ⱥɜɟɪɶɹɧɨɜ Ⱥɜɟɬɢɫɹɧ Ⱥɜɪɚɦɟɧɤɨ Ⱥɜɯɚɱɟɜ B ɂɦɹ Ɋɨɦɚɧ Ʉɢɪɢɥɥ ɇɢɤɨɥɚɣ ɇɢɤɢɬɚ Ⱦɚɧɢɢɥ Ⱥɥɟɤɫɟɣ Ʉɨɧɫɬɚɧɬɢɧ C D Ʉɥɚɫɫ Ɇɚɬɟɦɚɬɢɤɚ 11 5 7 6 4 6 7 4 3 0 5 5 4 0 E Ɋɭɫɫɤɢɣ ɹɡɵɤ 2 5 0 1 1 5 4 F ɂɧɨɫɬɪɚɧɧɵɣ ɹɡɵɤ 2 1 0 1 4 3 2 ɋɤɨɩɢɪɭɟɦ ɮɨɪɦɭɥɭ ɜɨ ɜɫɟ ɹɱɟɣɤɢ ɞɢɚɩɚɡɨɧɚ H2:H1001. Ȼɥɚɝɨɞɚɪɹ ɢɫɩɨɥɶɡɨɜɚɧɢɸ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɫɫɵɥɨɤ ɜ ɫɬɨɥɛɰɟ H ɜ ɫɬɪɨɤɚɯ 2–1001 ɛɭɞɭɬ ɡɚɩɢɫɚɧɵ ɥɢɛɨ 1 ɥɢɛɨ 0. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɧɚɣɬɢ ɫɭɦɦɭ, ɜ ɹɱɟɣɤɭ G1 ɜɧɟɫɺɦ ɮɨɪɦɭɥɭ =ɋɍɆɆ(H2:H1001) =SUM(H2:H1001) Ⱦɥɹ ɨɬɜɟɬɚ ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ ɹɱɟɣɤɟ, ɧɚɩɪɢɦɟɪ ɜ I2, ɧɚɩɢɲɟɦ ɮɨɪɦɭɥɭ, ɤɨɬɨɪɚɹ ɛɭɞɟɬ ɨɰɟɧɢɜɚɬɶ ɢɦɟɟɬ ɥɢ ɭɱɟɧɢɤ 0 ɛɚɥɥɨɜ ɩɨ ɤɚɤɨɦɭ-ɧɢɛɭɞɶ ɢɡ ɩɪɟɞɦɟɬɨɜ =ȿɋɅɂ(ɂɅɂ(D2=0;E2=0;F2=0);1;0) =IF(OR(D2=0;E2=0;F2=0);1;0) Ⱦɚɥɟɟ ɩɪɨɫɭɦɦɢɪɭɟɦ ɩɨɥɭɱɢɜɲɟɟɫɹ ɤɨɥɢɱɟɫɬɜɨ ɟɞɢɧɢɰ ɜ ɹɱɟɣɤɭ G3 =ɋɍɆɆ(I2:I1001) =SUM(I2:I1001) ȼɵɪɚɡɢɦ ɩɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɩɪɨɰɟɧɬɚɯ ɨɬ ɨɛɳɟɝɨ ɱɢɫɥɚ ɭɱɚɫɬɧɢɤɨɜ ɬɟɫɬɢɪɨɜɚɧɢɹ. Ɋɟɡɭɥɶɬɚɬ ɡɚɩɢɲɟɦ ɜ ɹɱɟɣɤɭ G2: =G3/1000*100 ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ. ȿɫɥɢ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɩɪɚɜɢɥɶɧɨ ɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɹ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɮɚɣɥɵ, ɫɩɟɰɢɚɥɶɧɨ ɩɨɞɝɨɬɨɜɥɟɧɧɵɟ ɞɥɹ ɩɪɨɜɟɪɤɢ ɜɵɩɨɥɧɟɧɢɹ ɞɚɧɧɨɝɨ ɡɚɞɚɧɢɹ, ɬɨ ɞɨɥɠɧɵ ɩɨɥɭɱɢɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɨɬɜɟɬɵ: ɧɚ ɩɟɪɜɵɣ ɜɨɩɪɨɫ – 20; ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ – 42,1 ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ ɉɨɥɭɱɟɧɵ ɩɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɚ ɨɛɚ ɜɨɩɪɨɫɚ. ɋɩɨɫɨɛ ɩɨɥɭɱɟɧɢɹ ɨɬɜɟɬɚ ɦɨɠɟɬ ɧɟ ɫɨɜɩɚɞɚɬɶ ɫ ɩɪɢɜɟɞɺɧɧɵɦ ɜɵɲɟ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɜ ɞɪɭɝɢɟ ɹɱɟɣɤɢ (ɨɬɥɢɱɧɵɟ ɨɬ ɬɟɯ, ɤɨɬɨɪɵɟ ɭɤɚɡɚɧɵ ɜ ɡɚɞɚɧɢɢ) ɩɪɢ ɭɫɥɨɜɢɢ 2 ɩɪɚɜɢɥɶɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɨɬɜɟɬɨɜ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɫ ɛɨɥɶɲɟɣ ɬɨɱɧɨɫɬɶɸ 1 ɉɨɥɭɱɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɬɨɥɶɤɨ ɧɚ ɨɞɢɧ ɢɡ ɞɜɭɯ ɜɨɩɪɨɫɨɜ ɉɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɟ ɩɨɥɭɱɟɧɵ ɧɢ ɧɚ ɨɞɢɧ ɢɡ ɜɨɩɪɨɫɨɜ 0 2 Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ ȼ ɫɬɨɥɛɰɟ A ɭɤɚɡɚɧɚ ɮɚɦɢɥɢɹ, ɜ ɫɬɨɥɛɰɟ B – ɢɦɹ ɭɱɚɳɟɝɨɫɹ, C – ɤɥɚɫɫ; ɜ ɫɬɨɥɛɰɚɯ D, E, F – ɛɚɥɥɵ, ɩɨɥɭɱɟɧɧɵɟ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨ ɦɚɬɟɦɚɬɢɤɟ, ɪɭɫɫɤɨɦɭ ɹɡɵɤɭ ɢ ɢɧɨɫɬɪɚɧɧɨɦɭ ɹɡɵɤɭ. ɉɨ ɤɚɠɞɨɦɭ ɩɪɟɞɦɟɬɭ ɦɨɠɧɨ ɛɵɥɨ ɧɚɛɪɚɬɶ ɨɬ 1 ɞɨ 5 ɛɚɥɥɨɜ, 0 ɛɚɥɥɨɜ – ɭɱɚɳɢɣɫɹ ɧɟ ɫɞɚɜɚɥ ɷɤɡɚɦɟɧ. ȼɫɟɝɨ ɜ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɛɵɥɢ ɡɚɧɟɫɟɧɵ ɞɚɧɧɵɟ ɩɨ 1000 ɭɱɚɳɢɯɫɹ. ɉɨɪɹɞɨɤ ɡɚɩɢɫɟɣ ɜ ɬɚɛɥɢɰɟ ɩɪɨɢɡɜɨɥɶɧɵɣ. ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ. Ɉɬɤɪɨɣɬɟ ɮɚɣɥ ɫ ɞɚɧɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɚɛɥɢɰɟɣ (ɪɚɫɩɨɥɨɠɟɧɢɟ ɮɚɣɥɚ ȼɚɦ ɫɨɨɛɳɚɬ ɨɪɝɚɧɢɡɚɬɨɪɵ ɷɤɡɚɦɟɧɚ). ɇɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɷɬɨɣ ɬɚɛɥɢɰɟ, ɨɬɜɟɬɶɬɟ ɧɚ ɞɜɚ ɜɨɩɪɨɫɚ. 1. ɋɤɨɥɶɤɨ ɭɱɟɧɢɤɨɜ 10 ɢ 11 ɤɥɚɫɫɨɜ, ɫɞɚɥɢ ɷɤɡɚɦɟɧɵ ɩɨ ɪɭɫɫɤɨɦɭ ɢ ɢɧɨɫɬɪɚɧɧɨɦɭ ɹɡɵɤɭ ɧɚ ɨɰɟɧɤɭ 4 ɢ 5 ɛɚɥɥɨɜ. Ɉɬɜɟɬ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ G1. 2. Ʉɚɤɨɣ ɩɪɨɰɟɧɬ ɭɱɟɧɢɤɨɜ ɧɟ ɫɞɚɜɚɥɢ ɷɤɡɚɦɟɧ ɯɨɬɹ ɛɵ ɩɨ ɨɞɧɨɦɭ ɩɪɟɞɦɟɬɭ? Ɉɬɜɟɬ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɨɞɧɨɝɨ ɡɧɚɤɚ ɩɨɫɥɟ ɡɚɩɹɬɨɣ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ G2 ɬɚɛɥɢɰɵ. ɉɨɥɭɱɟɧɧɭɸ ɬɚɛɥɢɰɭ ɧɟɨɛɯɨɞɢɦɨ ɫɨɯɪɚɧɢɬɶ ɩɨɞ ɢɦɟɧɟɦ, ɭɤɚɡɚɧɧɵɦ ɨɪɝɚɧɢɡɚɬɨɪɚɦɢ ɷɤɡɚɦɟɧɚ. ɉɪɢɦɟɱɚɧɢɟ. ɉɪɢ ɪɟɲɟɧɢɢ ɞɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɥɸɛɵɯ ɜɨɡɦɨɠɧɨɫɬɟɣ ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. Ⱥɥɝɨɪɢɬɦɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɞɥɹ OpenOffice.org Calc ɢ Microsoft Excel ɫɨɜɩɚɞɚɸɬ. Ɏɨɪɦɭɥɵ ɧɚɩɢɫɚɧɵ ɞɥɹ ɨɛɟɢɯ ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. ȼ ɫɬɨɥɛɰɟ H ɞɥɹ ɤɚɠɞɨɝɨ ɭɱɚɳɟɝɨɫɹ ɡɚɩɢɲɟɦ 1, ɟɫɥɢ ɨɧ ɭɱɢɬɫɹ 10 ɢ 11 ɤɥɚɫɫɟ ɢ ɫɞɚɥ ɷɤɡɚɦɟɧɵ ɩɨ ɪɭɫɫɤɨɦɭ ɢ ɢɧɨɫɬɪɚɧɧɨɦɭ ɹɡɵɤɭ ɧɚ ɨɰɟɧɤɭ 4 ɢ 5 ɛɚɥɥɨɜ, ɚ 0 ɜ ɞɪɭɝɢɯ ɫɥɭɱɚɹɯ. ȼ ɹɱɟɣɤɭ H2 ɡɚɩɢɲɟɦ ɮɨɪɦɭɥɭ =ȿɋɅɂ(ɂ(C2>9;E2>3;F2>3);1;0) =IF(AND(C2>9;E2>3;F2>3);1;0) © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 3 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 3 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 3 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 4 ȼɵɛɟɪɢɬɟ ɬɨɥɶɤɨ ɈȾɇɈ ɢɡ ɩɪɟɞɥɨɠɟɧɧɵɯ ɡɚɞɚɧɢɣ: 20.1 ɢɥɢ 20.2. 20.1 ɂɫɩɨɥɧɢɬɟɥɶ Ɋɨɛɨɬ ɭɦɟɟɬ ɩɟɪɟɦɟɳɚɬɶɫɹ ɩɨ ɥɚɛɢɪɢɧɬɭ, ɧɚɱɟɪɱɟɧɧɨɦɭ ɧɚ ɩɥɨɫɤɨɫɬɢ, ɪɚɡɛɢɬɨɣ ɧɚ ɤɥɟɬɤɢ. ɇɢɠɟ ɩɪɢɜɟɞɟɧɨ ɨɩɢɫɚɧɢɟ Ɋɨɛɨɬɚ. ɍ Ɋɨɛɨɬɚ ɟɫɬɶ ɱɟɬɵɪɟ ɤɨɦɚɧɞɵ ɩɟɪɟɦɟɳɟɧɢɹ: ɜɜɟɪɯ ɜɧɢɡ ɜɥɟɜɨ ɜɩɪɚɜɨ ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɤɨɦɚɧɞ Ɋɨɛɨɬ ɩɟɪɟɦɟɳɚɟɬɫɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: ɜɜɟɪɯ Ĺ, ɜɧɢɡ Ļ, ɜɥɟɜɨ ĸ, ɜɩɪɚɜɨ ĺ. Ɇɟɠɞɭ ɫɨɫɟɞɧɢɦɢ (ɩɨ ɫɬɨɪɨɧɚɦ) ɤɥɟɬɤɚɦɢ ɦɨɠɟɬ ɫɬɨɹɬɶ ɫɬɟɧɚ, ɱɟɪɟɡ ɤɨɬɨɪɭɸ Ɋɨɛɨɬ ɩɪɨɣɬɢ ɧɟ ɦɨɠɟɬ. ȿɫɥɢ Ɋɨɛɨɬ ɩɨɥɭɱɢɬ ɤɨɦɚɧɞɭ ɩɟɪɟɞɜɢɠɟɧɢɹ ɱɟɪɟɡ ɫɬɟɧɭ, ɬɨ ɨɧ ɪɚɡɪɭɲɢɬɫɹ. ɑɟɬɵɪɟ ɤɨɦɚɧɞɵ ɩɪɨɜɟɪɹɸɬ ɢɫɬɢɧɧɨɫɬɶ ɭɫɥɨɜɢɹ ɨɬɫɭɬɫɬɜɢɹ ɫɬɟɧɵ ɭ ɤɚɠɞɨɣ ɫɬɨɪɨɧɵ ɬɨɣ ɤɥɟɬɤɢ, ɝɞɟ ɧɚɯɨɞɢɬɫɹ Ɋɨɛɨɬ: ɫɜɟɪɯɭ ɫɜɨɛɨɞɧɨ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɗɬɢ ɤɨɦɚɧɞɵ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɦɟɫɬɟ ɫ ɭɫɥɨɜɢɟɦ «eɫɥɢ», ɢɦɟɸɳɢɦ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: ɟɫɥɢ <ɭɫɥɨɜɢɟ> ɬɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ ɜɫɟ «ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ» – ɷɬɨ ɨɞɧɚ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɸɛɵɯ ɤɨɦɚɧɞ, ɜɵɩɨɥɧɹɟɦɵɯ Ɋɨɛɨɬɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɟɪɟɞɜɢɠɟɧɢɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɜɩɪɚɜɨ, ɟɫɥɢ ɫɩɪɚɜɚ ɧɟɬ ɫɬɟɧɤɢ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɚɤɨɣ ɚɥɝɨɪɢɬɦ: ɟɫɥɢ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɬɨ ɜɩɪɚɜɨ ɜɫɟ ȼ ɨɞɧɨɦ ɭɫɥɨɜɢɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɟɫɤɨɥɶɤɨ ɤɨɦɚɧɞ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɣ, ɩɪɢɦɟɧɹɹ ɥɨɝɢɱɟɫɤɢɟ ɫɜɹɡɤɢ ɢ, ɢɥɢ, ɧɟ, ɧɚɩɪɢɦɟɪ: ɟɫɥɢ (ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ) ɢ (ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ) ɬɨ ɜɩɪɚɜɨ ɜɫɟ Ⱦɥɹ ɩɨɜɬɨɪɟɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɤɨɦɚɧɞ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɰɢɤɥ «ɩɨɤɚ», ɢɦɟɸɳɢɣ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: ɧɰ ɩɨɤɚ < ɭɫɥɨɜɢɟ > ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ ɤɰ ɇɚɩɪɢɦɟɪ, ɞɥɹ ɞɜɢɠɟɧɢɹ ɜɩɪɚɜɨ, ɩɨɤɚ ɷɬɨ ɜɨɡɦɨɠɧɨ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɣ ɚɥɝɨɪɢɬɦ: ɧɰ ɩɨɤɚ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɜɩɪɚɜɨ ɤɰ Ɍɚɤɠɟ ɭ Ɋɨɛɨɬɚ ɟɫɬɶ ɤɨɦɚɧɞɚ ɡɚɤɪɚɫɢɬɶ, ɡɚɤɪɚɲɢɜɚɸɳɚɹ ɤɥɟɬɤɭ, ɜ ɤɨɬɨɪɨɣ Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɜ ɧɚɫɬɨɹɳɢɣ ɦɨɦɟɧɬ. ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ. ɇɚ ɛɟɫɤɨɧɟɱɧɨɦ ɩɨɥɟ ɢɦɟɟɬɫɹ ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɬɟɧɚ, ɞɥɢɧɚ ɫɬɟɧɵ ɧɟɢɡɜɟɫɬɧɚ. Ɉɬ ɜɟɪɯɧɟɝɨ ɤɨɧɰɚ ɫɬɟɧɵ ɜɥɟɜɨ ɨɬɯɨɞɢɬ ɝɨɪɢɡɨɧɬɚɥɶɧɚɹ ɫɬɟɧɚ ɬɚɤɠɟ ɧɟɢɡɜɟɫɬɧɨɣ ɞɥɢɧɵ. Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɩɨɞ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɬɟɧɨɣ, ɜ ɤɥɟɬɤɟ, ɩɪɢɦɵɤɚɸɳɟɣ ɤ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɟɧɟ. ɇɚ ɪɢɫɭɧɤɟ ɭɤɚɡɚɧ ɨɞɢɧ ɢɡ ɜɨɡɦɨɠɧɵɯ ɫɩɨɫɨɛɨɜ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɬɟɧ ɢ Ɋɨɛɨɬɚ (Ɋɨɛɨɬ ɨɛɨɡɧɚɱɟɧ ɛɭɤɜɨɣ «Ɋ») . ɇɚɩɢɲɢɬɟ ɞɥɹ Ɋɨɛɨɬɚ ɚɥɝɨɪɢɬɦ, ɡɚɤɪɚɲɢɜɚɸɳɢɣ ɜɫɟ ɤɥɟɬɤɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɩɪɚɜɟɟ ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɭɱɚɫɬɤɚ ɫɬɟɧɵ ɢ ɧɚɞ ɝɨɪɢɡɨɧɬɚɥɶɧɵɦ ɭɱɚɫɬɤɨɦ ɫɬɟɧɵ. Ɋɨɛɨɬ ɞɨɥɠɟɧ ɡɚɤɪɚɫɢɬɶ ɬɨɥɶɤɨ ɤɥɟɬɤɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɞɚɧɧɨɦɭ ɭɫɥɨɜɢɸ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɪɢɜɟɞɺɧɧɨɝɨ ɜɵɲɟ ɪɢɫɭɧɤɚ Ɋɨɛɨɬ ɞɨɥɠɟɧ ɡɚɤɪɚɫɢɬɶ ɫɥɟɞɭɸɳɢɟ ɤɥɟɬɤɢ (ɫɦ. ɪɢɫɭɧɨɤ) . © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 3 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 5 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 3 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 6 Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.1 ɢɫɩɨɥɶɡɨɜɚɬɶ Ɋɨɛɨɬ ɚɥɝ ɧɚɱ ɧɰ ɩɨɤɚ ɧɟ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɜɧɢɡ ɤɰ ɜɩɪɚɜɨ ɜɜɟɪɯ ɧɰ ɩɨɤɚ ɧɟ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɡɚɤɪɚɫɢɬɶ ɜɜɟɪɯ ɤɰ ɜɥɟɜɨ ɧɰ ɩɨɤɚ ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɡɚɤɪɚɫɢɬɶ ɜɥɟɜɨ ɤɰ ɤɨɧ ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ Ɂɚɩɢɫɚɧ ɩɪɚɜɢɥɶɧɵɣ ɚɥɝɨɪɢɬɦ, ɧɟ ɩɪɢɜɨɞɹɳɢɣ ɤ ɭɧɢɱɬɨɠɟɧɢɸ Ɋɨɛɨɬɚ, ɩɨɥɧɨɫɬɶɸ ɪɟɲɚɸɳɢɣ ɩɨɫɬɚɜɥɟɧɧɭɸ ɡɚɞɚɱɭ. Ⱦɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ 2 ɢɧɨɝɨ ɫɢɧɬɚɤɫɢɫɚ ɢɧɫɬɪɭɤɰɢɣ ɢɫɩɨɥɧɢɬɟɥɹ, ɛɨɥɟɟ ɩɪɢɜɵɱɧɨɝɨ ɭɱɚɳɢɦɫɹ. Ⱥɥɝɨɪɢɬɦ ɜ ɰɟɥɨɦ ɡɚɩɢɫɚɧ ɜɟɪɧɨ, ɧɨ ɦɨɠɟɬ ɫɨɞɟɪɠɚɬɶ ɨɞɧɭ ɨɲɢɛɤɭ. ɉɪɢɦɟɪɵ ɨɲɢɛɨɤ: 1 1) Ɋɨɛɨɬ ɡɚɤɪɚɲɢɜɚɟɬ ɨɞɧɭ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɢɲɧɢɯ ɤɥɟɬɨɤ; 2) Ɋɨɛɨɬ ɧɟ ɡɚɤɪɚɲɢɜɚɟɬ ɨɞɧɭ ɢɡ ɤɥɟɬɨɤ Ɂɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɧɟɜɟɪɧɨ, ɢɥɢ ɜɨɡɦɨɠɧɵɯ ɨɲɢɛɨɤ ɜ ɚɥɝɨɪɢɬɦɟ ɛɨɥɶɲɟ 0 ɨɞɧɨɣ 2 Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ Ʉɨɧɟɱɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ Ɋɨɛɨɬɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɵɦ. Ⱥɥɝɨɪɢɬɦ ɞɨɥɠɟɧ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɪɚɡɦɟɪɚ ɩɨɥɹ ɢ ɥɸɛɨɝɨ ɞɨɩɭɫɬɢɦɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɬɟɧ ɜɧɭɬɪɢ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɩɨɥɹ. ɉɪɢ ɢɫɩɨɥɧɟɧɢɢ ɚɥɝɨɪɢɬɦɚ Ɋɨɛɨɬ ɧɟ ɞɨɥɠɟɧ ɪɚɡɪɭɲɢɬɶɫɹ. 20.2 ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɫɭɦɦɭ ɱɺɬɧɵɯ ɱɢɫɟɥ, ɤɪɚɬɧɵɯ 3. ɉɪɨɝɪɚɦɦɚ ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɰɟɥɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ ɜɜɟɞɺɧɧɵɯ ɱɢɫɟɥ ɧɟɢɡɜɟɫɬɧɨ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɱɢɫɟɥ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 – ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ) . Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 1000. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɩɨ ɦɨɞɭɥɸ ɧɟ ɩɪɟɜɵɲɚɸɬ 30 000. ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɫɭɦɦɭ ɱɺɬɧɵɯ ɱɢɫɟɥ, ɤɪɚɬɧɵɯ 3. ɉɪɢɦɟɪ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ: ȼɯɨɞɧɵɟ ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ ɞɚɧɧɵɟ 40 18 6 9 12 0 © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 3 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 7 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 3 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 8 Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.2 ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɫɭɦɦɭ ɱɺɬɧɵɯ ɱɢɫɟɥ, ɤɪɚɬɧɵɯ 3. ɉɪɨɝɪɚɦɦɚ ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɰɟɥɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ ɜɜɟɞɺɧɧɵɯ ɱɢɫɟɥ ɧɟɢɡɜɟɫɬɧɨ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɱɢɫɟɥ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 – ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ). Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 1000. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɩɨ ɦɨɞɭɥɸ ɧɟ ɩɪɟɜɵɲɚɸɬ 30 000. ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɫɭɦɦɭ ɱɺɬɧɵɯ ɱɢɫɟɥ, ɤɪɚɬɧɵɯ 3. ɧɚɱ ɰɟɥ ɚ,answer answer:=0; ɜɜɨɞ ɚ ɧɰ ɩɨɤɚ ɚ<>0 ɟɫɥɢ (mod (ɚ,2) = 0) ɢ (mod (ɚ,3) = 0) ɬɨ answer:=answer+a ɜɫɟ ɜɜɨɞ ɚ ɤɰ ɜɵɜɨɞ answer ɤɨɧ ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɜɚɪɢɚɧɬɵ ɪɟɲɟɧɢɹ. ɇɚɩɪɢɦɟɪ, ɜɦɟɫɬɨ ɭɫɥɨɜɢɹ (mod ( ɚ,2) = 0) ɢ (mod (ɚ,3) = 0) ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɭɫɥɨɜɢɟ mod (a,6) = 0. Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ ɬɟɫɬɵ: Ɍɚɛɥɢɰɚ ɬɟɫɬɢɪɨɜɚɧɢɹ ʋ 1 7 8 25 27 9 0 18 12 0 10 24 10051 36 0 ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ 0 ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ ɉɪɟɞɥɨɠɟɧɨ ɜɟɪɧɨɟ ɪɟɲɟɧɢɟ. ɉɪɨɝɪɚɦɦɚ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɧɚ ɜɫɟɯ ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ ɬɟɫɬɚɯ. ɉɪɨɝɪɚɦɦɚ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɧɚ ɥɸɛɨɦ ɹɡɵɤɟ 2 ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɟɜɟɪɧɵɣ ɨɬɜɟɬ ɧɚ ɨɞɧɨɦ ɢɡ ɬɟɫɬɨɜ, ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ. ɇɚɩɪɢɦɟɪ, ɪɟɲɟɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɡɚɞɚɧɨ ɬɨɥɶɤɨ ɩɪɨɜɟɪɤɚ ɱɟɬɧɨɫɬɢ ɩɪɢ ɨɬɛɨɪɟ ɱɢɫɟɥ: (mod (ɚ,2) <> 0) ɢ (mod (ɚ,3) = 0) ɜɵɞɚɫɬ ɧɟɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ 1 ɬɟɫɬɟ ʋ 1. ɂɅɂ Ɉɬɛɢɪɚɸɬɫɹ ɧɟɱɺɬɧɵɟ ɱɢɫɥɚ. ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɜɫɟɯ ɬɟɫɬɚɯ ɨɬɜɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɧɟɱɺɬɧɨɟ ɱɢɫɥɨ ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɬɟɫɬɚɯ ɧɟɜɟɪɧɵɟ ɨɬɜɟɬɵ, ɨɬɥɢɱɧɵɟ ɨɬ ɨɩɢɫɚɧɧɵɯ ɜ 0 ɤɪɢɬɟɪɢɢ ɧɚ 1 ɛɚɥɥ Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ 2 2 30 3 60 © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 4 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 1 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 4 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 2 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ 19 ȼ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɡɚɧɟɫɥɢ ɪɟɡɭɥɶɬɚɬɵ ɬɟɫɬɢɪɨɜɚɧɢɹ ɭɱɚɳɢɯɫɹ 8Ť11 ɤɥɚɫɫɨɜ ɩɨ ɪɚɡɥɢɱɧɵɦ ɩɪɟɞɦɟɬɚɦ. ɇɚ ɪɢɫɭɧɤɟ ɩɪɢɜɟɞɟɧɵ ɩɟɪɜɵɟ ɫɬɪɨɤɢ ɩɨɥɭɱɢɜɲɟɣɫɹ ɬɚɛɥɢɰɵ. 1 2 3 4 5 6 7 8 9 10 A Ɏɚɦɢɥɢɹ ɢɦɹ ɀɢɥɢɧɫɤɚɹ Ⱥɥɟɤɫɚɧɞɪɚ Ʉɨɦɚɯɢɧ Ⱥɥɟɤɫɚɧɞɪ ɒɢɬɨɜɚ Ɇɚɪɢɹ əɲɢɧ Ⱥɧɞɪɟɣ Ɏɨɦɢɧ Ⱦɟɧɢɫ ɒɚɣɤɨɜɚ Ⱥɧɧɚ ɋɬɟɩɚɧɨɜ ȼɥɚɞɢɫɥɚɜ Ʉɨɥɭɩɚɟɜɚ Ɍɚɬɶɹɧɚ Ɍɢɬɟɟɜɚ Ɇɚɪɢɹ B C Ʉɥɚɫɫ Ɋɭɫɫɤɢɣ ɹɡɵɤ 8 60 11 9 8 62 8 65 9 56 10 80 9 92 11 7 8 11 D Ɇɚɬɟɦɚɬɢɤɚ 57 61 37 94 66 96 43 62 76 E Ɏɢɡɤɭɥɶɬɭɪɚ 69 11 49 23 50 49 74 28 51 ɋɤɨɩɢɪɭɟɦ ɮɨɪɦɭɥɭ ɜɨ ɜɫɟ ɹɱɟɣɤɢ ɞɢɚɩɚɡɨɧɚ F3:F368. Ȼɥɚɝɨɞɚɪɹ ɢɫɩɨɥɶɡɨɜɚɧɢɸ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɫɫɵɥɨɤ ɜ ɫɬɨɥɛɰɟ F ɜ ɫɬɪɨɤɚɯ 2 – 368 ɛɭɞɭɬ ɡɚɩɢɫɚɧɵ ɥɢɛɨ 1 ɥɢɛɨ 0. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɧɚɣɬɢ ɫɭɦɦɭ, ɜ ɹɱɟɣɤɭ G1 ɜɧɟɫɺɦ ɮɨɪɦɭɥɭ =ɋɍɆɆ(F2:F368) =SUM(F2:F368) Ⱦɥɹ ɨɬɜɟɬɚ ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ ɜ ɹɱɟɣɤɟ, ɧɚɩɪɢɦɟɪ ɜ H2, ɧɚɩɢɲɟɦ ɮɨɪɦɭɥɭ, ɤɨɬɨɪɚɹ ɛɭɞɟɬ ɨɰɟɧɢɜɚɬɶ ɩɨɥɭɱɢɥ ɥɢ ɭɱɟɧɢɤ 10 ɢɥɢ 11 ɤɥɚɫɫɚ ɫɪɟɞɧɢɣ ɛɚɥ ɛɨɥɶɲɟ 50 ɩɨ ɬɪɺɦ ɷɤɡɚɦɟɧɚɦ. =ȿɋɅɂ(ɂ(B2>9;ɋɊɁɇȺɑ(C2:E2)>50);1;0) =IF(AND(B2>9;AVERAGE(C2:E2)>50);1;0) Ⱦɚɥɟɟ ɩɪɨɫɭɦɦɢɪɭɟɦ ɩɨɥɭɱɢɜɲɟɟɫɹ ɤɨɥɢɱɟɫɬɜɨ ɟɞɢɧɢɰ ɜ ɹɱɟɣɤɭ G3 =ɋɍɆɆ(H2:H368) =SUM(H2:H368) ȼɵɪɚɡɢɦ ɩɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɩɪɨɰɟɧɬɚɯ ɨɬ ɨɛɳɟɝɨ ɱɢɫɥɚ ɭɱɚɫɬɧɢɤɨɜ ɬɟɫɬɢɪɨɜɚɧɢɹ. Ɋɟɡɭɥɶɬɚɬ ɡɚɩɢɲɟɦ ɜ ɹɱɟɣɤɭ G2: =G3/368*100 ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ. ȿɫɥɢ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɩɪɚɜɢɥɶɧɨ ɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɹ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɮɚɣɥɵ, ɫɩɟɰɢɚɥɶɧɨ ɩɨɞɝɨɬɨɜɥɟɧɧɵɟ ɞɥɹ ɩɪɨɜɟɪɤɢ ɜɵɩɨɥɧɟɧɢɹ ɞɚɧɧɨɝɨ ɡɚɞɚɧɢɹ, ɬɨ ɞɨɥɠɧɵ ɩɨɥɭɱɢɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɨɬɜɟɬɵ: ɧɚ ɩɟɪɜɵɣ ɜɨɩɪɨɫ – 75; ɧɚ ɜɬɨɪɨɣ ɜɨɩɪɨɫ – 22,8. ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ ɉɨɥɭɱɟɧɵ ɩɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɚ ɨɛɚ ɜɨɩɪɨɫɚ. ɋɩɨɫɨɛ ɩɨɥɭɱɟɧɢɹ ɨɬɜɟɬɚ ɦɨɠɟɬ ɧɟ ɫɨɜɩɚɞɚɬɶ ɫ ɩɪɢɜɟɞɺɧɧɵɦ ɜɵɲɟ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɜ ɞɪɭɝɢɟ ɹɱɟɣɤɢ (ɨɬɥɢɱɧɵɟ ɨɬ ɬɟɯ, ɤɨɬɨɪɵɟ ɭɤɚɡɚɧɵ ɜ ɡɚɞɚɧɢɢ) ɩɪɢ ɭɫɥɨɜɢɢ 2 ɩɪɚɜɢɥɶɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɨɬɜɟɬɨɜ. Ⱦɨɩɭɫɬɢɦɚ ɡɚɩɢɫɶ ɨɬɜɟɬɚ ɫ ɛɨɥɶɲɟɣ ɬɨɱɧɨɫɬɶɸ ɉɨɥɭɱɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɬɨɥɶɤɨ ɧɚ ɨɞɢɧ ɢɡ ɞɜɭɯ ɜɨɩɪɨɫɨɜ 1 0 ɉɪɚɜɢɥɶɧɵɟ ɨɬɜɟɬɵ ɧɟ ɩɨɥɭɱɟɧɵ ɧɢ ɧɚ ɨɞɢɧ ɢɡ ɜɨɩɪɨɫɨɜ 2 Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ ȼ ɫɬɨɥɛɰɟ A ɭɤɚɡɚɧɵ ɮɚɦɢɥɢɹ ɢ ɢɦɹ, ɜ ɫɬɨɥɛɰɟ B – ɤɥɚɫɫ ɭɱɚɳɟɝɨɫɹ; ɜ ɫɬɨɥɛɰɚɯ C, D, E – ɛɚɥɥɵ, ɩɨɥɭɱɟɧɧɵɟ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨ ɪɭɫɫɤɨɦɭ ɹɡɵɤɭ, ɦɚɬɟɦɚɬɢɤɟ ɢ ɮɢɡɤɭɥɶɬɭɪɟ. ɉɨ ɤɚɠɞɨɦɭ ɩɪɟɞɦɟɬɭ ɦɨɠɧɨ ɛɵɥɨ ɧɚɛɪɚɬɶ ɨɬ 1 ɞɨ 100 ɛɚɥɥɨɜ. ȼɫɟɝɨ ɜ ɷɥɟɤɬɪɨɧɧɭɸ ɬɚɛɥɢɰɭ ɛɵɥɢ ɡɚɧɟɫɟɧɵ ɞɚɧɧɵɟ ɩɨ 367 ɭɱɚɳɢɦɫɹ. ɉɨɪɹɞɨɤ ɡɚɩɢɫɟɣ ɜ ɬɚɛɥɢɰɟ ɩɪɨɢɡɜɨɥɶɧɵɣ. ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ. Ɉɬɤɪɨɣɬɟ ɮɚɣɥ ɫ ɞɚɧɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɚɛɥɢɰɟɣ (ɪɚɫɩɨɥɨɠɟɧɢɟ ɮɚɣɥɚ ȼɚɦ ɫɨɨɛɳɚɬ ɨɪɝɚɧɢɡɚɬɨɪɵ ɷɤɡɚɦɟɧɚ). ɇɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɷɬɨɣ ɬɚɛɥɢɰɟ, ɨɬɜɟɬɶɬɟ ɧɚ ɞɜɚ ɜɨɩɪɨɫɚ. 1. ɋɤɨɥɶɤɨ ɭɱɟɧɢɤɨɜ ɢɡ 8 ɢ 9 ɤɥɚɫɫɨɜ ɩɨɥɭɱɢɥɢ ɨɰɟɧɤɭ ɩɨ ɪɭɫɫɤɨɦɭ ɹɡɵɤɭ ɛɨɥɶɲɟ, ɱɟɦ ɨɰɟɧɤɭ ɩɨ ɦɚɬɟɦɚɬɢɤɟ ɢ ɩɨ ɮɢɡɤɭɥɶɬɭɪɟ. Ɉɬɜɟɬ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ G1. 2. Ʉɚɤɨɣ ɩɪɨɰɟɧɬ ɭɱɟɧɢɤɨɜ 10 ɢ 11 ɤɥɚɫɫɨɜ ɩɨɥɭɱɢɥɢ ɫɪɟɞɧɢɣ ɛɚɥ ɛɨɥɶɲɟ 50 ɩɨ ɬɪɺɦ ɷɤɡɚɦɟɧɚɦ? Ɉɬɜɟɬ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɨɞɧɨɝɨ ɡɧɚɤɚ ɩɨɫɥɟ ɡɚɩɹɬɨɣ ɡɚɩɢɲɢɬɟ ɜ ɹɱɟɣɤɭ G2 ɬɚɛɥɢɰɵ. ɉɨɥɭɱɟɧɧɭɸ ɬɚɛɥɢɰɭ ɧɟɨɛɯɨɞɢɦɨ ɫɨɯɪɚɧɢɬɶ ɩɨɞ ɢɦɟɧɟɦ, ɭɤɚɡɚɧɧɵɦ ɨɪɝɚɧɢɡɚɬɨɪɚɦɢ ɷɤɡɚɦɟɧɚ. ɉɪɢɦɟɱɚɧɢɟ. ɉɪɢ ɪɟɲɟɧɢɢ ɞɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɥɸɛɵɯ ɜɨɡɦɨɠɧɨɫɬɟɣɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. Ⱥɥɝɨɪɢɬɦɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɞɥɹ OpenOffice.org Calc ɢ Microsoft Excel ɫɨɜɩɚɞɚɸɬ. Ɏɨɪɦɭɥɵ ɧɚɩɢɫɚɧɵ ɞɥɹ ɨɛɟɢɯ ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰ. ȼɬɨɪɨɣ ɜɚɪɢɚɧɬ – ɞɥɹ OpenOffice.org Calc. ȼ ɫɬɨɥɛɰɟ F ɞɥɹ ɤɚɠɞɨɝɨ ɭɱɚɳɟɝɨɫɹ ɡɚɩɢɲɟɦ 1, ɟɫɥɢ ɨɧ ɭɱɢɬɫɹ 8 ɢɥɢ 9 ɤɥɚɫɫɟ, ɢ ɩɨɥɭɱɢɥ ɨɰɟɧɤɭ ɩɨ ɪɭɫɫɤɨɦɭ ɹɡɵɤɭ ɛɨɥɶɲɟ, ɱɟɦ ɨɰɟɧɤɭ ɩɨ ɦɚɬɟɦɚɬɢɤɟ ɢ ɩɨ ɮɢɡɤɭɥɶɬɭɪɟ, ɢ 0 - ɜ ɨɛɪɚɬɧɨɦ ɫɥɭɱɚɟ. ȼ ɹɱɟɣɤɭ F2 ɡɚɩɢɲɟɦ ɮɨɪɦɭɥɭ =ȿɋɅɂ(ɂ(B2<10;C2>D2;C2>E2);1;0) =IF(AND (B2<10;C2>D2;C2>E2);1;0) © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 4 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 3 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 4 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 4 ȼɵɛɟɪɢɬɟ ɬɨɥɶɤɨ ɈȾɇɈ ɢɡ ɩɪɟɞɥɨɠɟɧɧɵɯ ɡɚɞɚɧɢɣ: 20.1 ɢɥɢ 20.2. 20.1 ɂɫɩɨɥɧɢɬɟɥɶ Ɋɨɛɨɬ ɭɦɟɟɬ ɩɟɪɟɦɟɳɚɬɶɫɹ ɩɨ ɥɚɛɢɪɢɧɬɭ, ɧɚɱɟɪɱɟɧɧɨɦɭ ɧɚ ɩɥɨɫɤɨɫɬɢ, ɪɚɡɛɢɬɨɣ ɧɚ ɤɥɟɬɤɢ. ɇɢɠɟ ɩɪɢɜɟɞɟɧɨ ɨɩɢɫɚɧɢɟ Ɋɨɛɨɬɚ. ɍ Ɋɨɛɨɬɚ ɟɫɬɶ ɱɟɬɵɪɟ ɤɨɦɚɧɞɵ ɩɟɪɟɦɟɳɟɧɢɹ: ɜɜɟɪɯ ɜɧɢɡ ɜɥɟɜɨ ɜɩɪɚɜɨ ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɤɨɦɚɧɞ Ɋɨɛɨɬ ɩɟɪɟɦɟɳɚɟɬɫɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: ɜɜɟɪɯ Ĺ, ɜɧɢɡ Ļ, ɜɥɟɜɨ ĸ, ɜɩɪɚɜɨ ĺ. Ɇɟɠɞɭ ɫɨɫɟɞɧɢɦɢ (ɩɨ ɫɬɨɪɨɧɚɦ) ɤɥɟɬɤɚɦɢ ɦɨɠɟɬ ɫɬɨɹɬɶ ɫɬɟɧɚ, ɱɟɪɟɡ ɤɨɬɨɪɭɸ Ɋɨɛɨɬ ɩɪɨɣɬɢ ɧɟ ɦɨɠɟɬ. ȿɫɥɢ Ɋɨɛɨɬ ɩɨɥɭɱɢɬ ɤɨɦɚɧɞɭ ɩɟɪɟɞɜɢɠɟɧɢɹ ɱɟɪɟɡ ɫɬɟɧɭ, ɬɨ ɨɧ ɪɚɡɪɭɲɢɬɫɹ. ɑɟɬɵɪɟ ɤɨɦɚɧɞɵ ɩɪɨɜɟɪɹɸɬ ɢɫɬɢɧɧɨɫɬɶ ɭɫɥɨɜɢɹ ɨɬɫɭɬɫɬɜɢɹ ɫɬɟɧɵ ɭ ɤɚɠɞɨɣ ɫɬɨɪɨɧɵ ɬɨɣ ɤɥɟɬɤɢ, ɝɞɟ ɧɚɯɨɞɢɬɫɹ Ɋɨɛɨɬ: ɫɜɟɪɯɭ ɫɜɨɛɨɞɧɨ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɗɬɢ ɤɨɦɚɧɞɵ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɦɟɫɬɟ ɫ ɭɫɥɨɜɢɟɦ «eɫɥɢ», ɢɦɟɸɳɢɦ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: ɟɫɥɢ <ɭɫɥɨɜɢɟ> ɬɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ ɜɫɟ «ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ» – ɷɬɨ ɨɞɧɚ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɸɛɵɯ ɤɨɦɚɧɞ, ɜɵɩɨɥɧɹɟɦɵɯ Ɋɨɛɨɬɨɦ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɟɪɟɞɜɢɠɟɧɢɹ ɧɚ ɨɞɧɭ ɤɥɟɬɤɭ ɜɩɪɚɜɨ, ɟɫɥɢ ɫɩɪɚɜɚ ɧɟɬ ɫɬɟɧɤɢ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɚɤɨɣ ɚɥɝɨɪɢɬɦ: ɟɫɥɢ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɬɨ ɜɩɪɚɜɨ ɜɫɟ ȼ ɨɞɧɨɦ ɭɫɥɨɜɢɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɟɫɤɨɥɶɤɨ ɤɨɦɚɧɞ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɣ, ɩɪɢɦɟɧɹɹ ɥɨɝɢɱɟɫɤɢɟ ɫɜɹɡɤɢ ɢ, ɢɥɢ, ɧɟ, ɧɚɩɪɢɦɟɪ: ɟɫɥɢ (ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ) ɢ (ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ) ɬɨ ɜɩɪɚɜɨ ɜɫɟ Ⱦɥɹ ɩɨɜɬɨɪɟɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɤɨɦɚɧɞ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɰɢɤɥ «ɩɨɤɚ», ɢɦɟɸɳɢɣ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: ɧɰ ɩɨɤɚ < ɭɫɥɨɜɢɟ > ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɤɨɦɚɧɞ ɤɰ ɇɚɩɪɢɦɟɪ, ɞɥɹ ɞɜɢɠɟɧɢɹ ɜɩɪɚɜɨ, ɩɨɤɚ ɷɬɨ ɜɨɡɦɨɠɧɨ, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɣ ɚɥɝɨɪɢɬɦ: ɧɰ ɩɨɤɚ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɜɩɪɚɜɨ ɤɰ Ɍɚɤɠɟ ɭ Ɋɨɛɨɬɚ ɟɫɬɶ ɤɨɦɚɧɞɚ ɡɚɤɪɚɫɢɬɶ, ɡɚɤɪɚɲɢɜɚɸɳɚɹ ɤɥɟɬɤɭ, ɜ ɤɨɬɨɪɨɣ Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɜ ɧɚɫɬɨɹɳɢɣ ɦɨɦɟɧɬ. ȼɵɩɨɥɧɢɬɟ ɡɚɞɚɧɢɟ. ɇɚ ɛɟɫɤɨɧɟɱɧɨɦ ɩɨɥɟ ɢɦɟɟɬɫɹ ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɬɟɧɚ, ɞɥɢɧɚ ɫɬɟɧɵ ɧɟɢɡɜɟɫɬɧɚ. Ɉɬ ɜɟɪɯɧɟɝɨ ɤɨɧɰɚ ɫɬɟɧɵ ɜɩɪɚɜɨ ɨɬɯɨɞɢɬ ɝɨɪɢɡɨɧɬɚɥɶɧɚɹ ɫɬɟɧɚ ɬɚɤɠɟ ɧɟɢɡɜɟɫɬɧɨɣ ɞɥɢɧɵ, ɚ ɩɨɬɨɦ ɫɧɨɜɚ ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɬɟɧɚ ɧɟɢɡɜɟɫɬɧɨɣ ɞɥɢɧɵ. Ɋɨɛɨɬ ɧɚɯɨɞɢɬɫɹ ɜ ɤɥɟɬɤɟ, ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɫɩɪɚɜɚ ɨɬ ɧɢɠɧɟɝɨ ɤɪɚɹ ɩɟɪɜɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɟɧɵ. ɇɚ ɪɢɫɭɧɤɟ ɭɤɚɡɚɧ ɨɞɢɧ ɢɡ ɜɨɡɦɨɠɧɵɯ ɫɩɨɫɨɛɨɜ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɬɟɧ ɢ Ɋɨɛɨɬɚ (Ɋɨɛɨɬ ɨɛɨɡɧɚɱɟɧ ɛɭɤɜɨɣ «Ɋ») . ɇɚɩɢɲɢɬɟ ɞɥɹ Ɋɨɛɨɬɚ ɚɥɝɨɪɢɬɦ, ɡɚɤɪɚɲɢɜɚɸɳɢɣ ɜɫɟ ɤɥɟɬɤɢ, ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɥɟɜɟɟ ɥɟɜɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɟɧɵ ɢ ɩɪɚɜɟɟ ɩɪɚɜɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɫɬɟɧɵ. Ɋɨɛɨɬ ɞɨɥɠɟɧ ɡɚɤɪɚɫɢɬɶ ɬɨɥɶɤɨ ɤɥɟɬɤɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɞɚɧɧɨɦɭ ɭɫɥɨɜɢɸ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɪɢɜɟɞɺɧɧɨɝɨ ɜɵɲɟ ɪɢɫɭɧɤɚ Ɋɨɛɨɬ ɞɨɥɠɟɧ ɡɚɤɪɚɫɢɬɶ ɫɥɟɞɭɸɳɢɟ ɤɥɟɬɤɢ (ɫɦ. ɪɢɫɭɧɨɤ) . © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 4 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 5 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 4 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 6 Ʉɨɧɟɱɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ Ɋɨɛɨɬɚ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɵɦ. Ⱥɥɝɨɪɢɬɦ ɞɨɥɠɟɧ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɪɚɡɦɟɪɚ ɩɨɥɹ ɢ ɥɸɛɨɝɨ ɞɨɩɭɫɬɢɦɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɬɟɧ ɜɧɭɬɪɢ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɩɨɥɹ. ɉɪɢ ɢɫɩɨɥɧɟɧɢɢ ɚɥɝɨɪɢɬɦɚ Ɋɨɛɨɬ ɧɟ ɞɨɥɠɟɧ ɪɚɡɪɭɲɢɬɶɫɹ. 20.2 ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɺɬɧɨɟ ɱɢɫɥɨ. ɉɪɨɝɪɚɦɦɚ ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɰɟɥɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ ɜɜɟɞɺɧɧɵɯ ɱɢɫɟɥ ɧɟɢɡɜɟɫɬɧɨ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɱɢɫɟɥ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 – ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ) . Ƚɚɪɚɧɬɢɪɭɟɬɫɹ, ɱɬɨ ɯɨɬɹ ɛɵ ɨɞɧɨ ɱɺɬɧɨɟ ɱɢɫɥɨ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɟɫɬɶ. Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 1000. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɩɨ ɦɨɞɭɥɸ ɧɟ ɩɪɟɜɵɲɚɸɬ 30 000. ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɺɬɧɨɟ ɱɢɫɥɨ. ɉɪɢɦɟɪ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ: ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ 40 Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.1 ɢɫɩɨɥɶɡɨɜɚɬɶ Ɋɨɛɨɬ ɚɥɝ ɧɚɱ ɜɧɢɡ ɜɥɟɜɨ ɜɜɟɪɯ ɧɰ ɩɨɤɚ ɧɟ ɫɩɪɚɜɚ ɫɜɨɛɨɞɧɨ ɡɚɤɪɚɫɢɬɶ ɜɜɟɪɯ ɤɰ ɜɩɪɚɜɨ ɧɰ ɩɨɤɚ ɧɟ ɫɧɢɡɭ ɫɜɨɛɨɞɧɨ ɜɩɪɚɜɨ ɤɰ ɜɧɢɡ ɧɰ ɩɨɤɚ ɧɟ ɫɥɟɜɚ ɫɜɨɛɨɞɧɨ ɡɚɤɪɚɫɢɬɶ ɜɧɢɡ ɤɰ ɤɨɧ ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ Ɂɚɩɢɫɚɧ ɩɪɚɜɢɥɶɧɵɣ ɚɥɝɨɪɢɬɦ, ɧɟ ɩɪɢɜɨɞɹɳɢɣ ɤ ɭɧɢɱɬɨɠɟɧɢɸ Ɋɨɛɨɬɚ, ɩɨɥɧɨɫɬɶɸ ɪɟɲɚɸɳɢɣ ɩɨɫɬɚɜɥɟɧɧɭɸ ɡɚɞɚɱɭ. Ⱦɨɩɭɫɤɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ 2 ɢɧɨɝɨ ɫɢɧɬɚɤɫɢɫɚ ɢɧɫɬɪɭɤɰɢɣ ɢɫɩɨɥɧɢɬɟɥɹ, ɛɨɥɟɟ ɩɪɢɜɵɱɧɨɝɨ ɭɱɚɳɢɦɫɹ. Ⱥɥɝɨɪɢɬɦ ɜ ɰɟɥɨɦ ɡɚɩɢɫɚɧ ɜɟɪɧɨ, ɧɨ ɦɨɠɟɬ ɫɨɞɟɪɠɚɬɶ ɨɞɧɭ ɨɲɢɛɤɭ. ɉɪɢɦɟɪɵ ɨɲɢɛɨɤ: 1) Ɋɨɛɨɬ ɡɚɤɪɚɲɢɜɚɟɬ ɨɞɧɭ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɥɢɲɧɢɯ ɤɥɟɬɨɤ; 1 2) Ɋɨɛɨɬ ɧɟ ɡɚɤɪɚɲɢɜɚɟɬ ɨɞɧɭ ɢɡ ɤɥɟɬɨɤ (ɧɚɩɪɢɦɟɪ, ɤɥɟɬɤɭ ɩɨɞ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɬɟɧɨɣ) Ɂɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɧɟɜɟɪɧɨ, ɢɥɢ ɜɨɡɦɨɠɧɵɯ ɨɲɢɛɨɤ 0 ɜ ɚɥɝɨɪɢɬɦɟ ɛɨɥɶɲɟ ɨɞɧɨɣ 2 Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ Ɋɟɲɟɧɢɟ ɡɚɞɚɧɢɹ 20.2 ɇɚɩɢɲɢɬɟ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɨɩɪɟɞɟɥɹɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɺɬɧɨɟ ɱɢɫɥɨ. ɉɪɨɝɪɚɦɦɚ ɩɨɥɭɱɚɟɬ ɧɚ ɜɯɨɞ ɰɟɥɵɟ ɱɢɫɥɚ, ɤɨɥɢɱɟɫɬɜɨ ɜɜɟɞɺɧɧɵɯ ɱɢɫɟɥ ɧɟɢɡɜɟɫɬɧɨ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɱɢɫɟɥ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɱɢɫɥɨɦ 0 (0 – ɩɪɢɡɧɚɤ ɨɤɨɧɱɚɧɢɹ ɜɜɨɞɚ, ɧɟ ɜɯɨɞɢɬ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ). Ƚɚɪɚɧɬɢɪɭɟɬɫɹ, ɱɬɨ ɯɨɬɹ ɛɵ ɨɞɧɨ ɱɺɬɧɨɟ ɱɢɫɥɨ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɟɫɬɶ. Ʉɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɧɟ ɩɪɟɜɵɲɚɟɬ 1000. ȼɜɟɞɺɧɧɵɟ ɱɢɫɥɚ ɩɨ ɦɨɞɭɥɸ ɧɟ ɩɪɟɜɵɲɚɸɬ 30 000. ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ: ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɺɬɧɨɟ ɱɢɫɥɨ. 40 45 11 -25 77 0 © 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. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 4 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 7 ɂɧɮɨɪɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 4 ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 8 ɧɚɱ ɰɟɥ ɚ,answer answer:=0; ɜɜɨɞ ɚ ɧɰ ɩɨɤɚ ɚ<>0 ɟɫɥɢ (mod (ɚ,2) = 0) ɢ (a > answer) ɬɨ answer:=a ɜɫɟ ɜɜɨɞ ɚ ɤɰ ɜɵɜɨɞ answer ɤɨɧ ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɜɚɪɢɚɧɬɵ ɪɟɲɟɧɢɹ. Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɵ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ ɬɟɫɬɵ: Ɍɚɛɥɢɰɚ ɬɟɫɬɢɪɨɜɚɧɢɹ ʋ ȼɯɨɞɧɵɟ ɞɚɧɧɵɟ ȼɵɯɨɞɧɵɟ ɞɚɧɧɵɟ 1 1 2 2 0 2 4 4 5 2 3 0 3 2 2 1023 11111 2121 0 ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ Ȼɚɥɥɵ ɉɪɟɞɥɨɠɟɧɨ ɜɟɪɧɨɟ ɪɟɲɟɧɢɟ. ɉɪɨɝɪɚɦɦɚ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɧɚ ɜɫɟɯ ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ ɬɟɫɬɚɯ. ɉɪɨɝɪɚɦɦɚ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɧɚ ɥɸɛɨɦ ɹɡɵɤɟ 2 ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɟɜɟɪɧɵɣ ɨɬɜɟɬ ɧɚ ɨɞɧɨɦ ɢɡ ɬɟɫɬɨɜ, ɩɪɢɜɟɞɺɧɧɵɯ ɜɵɲɟ. ɇɚɩɪɢɦɟɪ, ɪɟɲɟɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɡɚɞɚɧɨ ɬɨɥɶɤɨ ɩɪɨɜɟɪɤɚ ɱɟɬɧɨɫɬɢ ɩɪɢ ɨɬɛɨɪɟ ɱɢɫɟɥ: mod (ɚ,2) = 0) 1 ɜɵɞɚɫɬ ɧɟɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɬɟɫɬɟ ʋ 2. ɂɅɂ Ɉɬɛɢɪɚɸɬɫɹ ɧɟɱɺɬɧɵɟ ɱɢɫɥɚ. ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɜɫɟɯ ɬɟɫɬɚɯ ɨɬɜɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɧɟɱɺɬɧɨɟ ɱɢɫɥɨ. ɉɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ ɧɚ ɬɟɫɬɚɯ ɧɟɜɟɪɧɵɟ ɨɬɜɟɬɵ, ɨɬɥɢɱɧɵɟ ɨɬ ɨɩɢɫɚɧɧɵɯ ɜ 0 ɤɪɢɬɟɪɢɢ ɧɚ 1 ɛɚɥɥ. Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ 2 © 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 Информатика. 9 класс. Видеоразбор на сайте www.statgrad.cde.ru Информатика. 9 класс. Видеоразбор на сайте www.statgrad.cde.ru Вариант 1 Ответы к заданиям Вариант 3 Ответы к заданиям № задания 1. 2 3. 4 5 6. 7. 8. 9. Ответ 3 1 2 3 2 4 Е 9 29 № задания 10. 11 12. 13 14 15. 16 17. 18. Вариант 2 Ответы к заданиям Вариант 4 Ответы к заданиям № задания 1 2. 3 4 5 6 7 8 9 Ответ 2 4 3 4 1 3 Д 2 60 № задания 10 11 12 13 14 15 16 17 18 Ответ 19 9 5 6 2212 2048 ВФРНГУ ЖДАГЕВБ ВБАГ Ответ 45 10 2 5 12122 3072 АОВТА АГВЖДЕБ ВАБГ № задания 1 2 3 4 5 6 7 8 9 Ответ 3 4 2 4 2 3 Е 2 29 № задания 10 11 12 13 14 15 16 17 18 Ответ 19 10 5 5 2212 3072 ВФРНГУ АГВЖДЕБ ВБАГ № задания 1 2 3 4 5 6 7 8 9 Ответ 2 1 3 3 1 4 Д 9 60 № задания 10 11 12 13 14 15 16 17 18 Ответ 45 9 2 6 12122 2048 АОВТА ЖДАГЕВБ ВАБГ © МИОО 2012 г. Публикация в Интернете или печатных изданиях без письменного согласия МИОО запрещена © МИОО 2012 г. Публикация в Интернете или печатных изданиях без письменного согласия МИОО запрещена
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