Ⱥ.Ȼ. Ƚɟɞɪɚɧɨɜɢɱ, ȼ.ȼ. Ƚɟɞɪɚɧɨɜɢɱ – Ɏɢɧɚɧɫɨɜɚɹ ɢɧɮɨɪɦɚɬɢɤɚ – Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ʋ 10 Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ 10. Ɋɟɲɟɧɢɟ ɨɩɬɢɦɢɡɚɰɢɨɧɧɵɯ ɡɚɞɚɱ ɫ ɩɨɦɨɳɶɸ ɧɚɞɫɬɪɨɣɤɢ «ɉɨɢɫɤ ɪɟɲɟɧɢɹ» ɜ MS Excel ɐɟɥɶ ɪɚɛɨɬɵ – ɧɚɭɱɢɬɶɫɹ ɪɟɲɚɬɶ ɡɚɞɚɱɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɩɨɪɬɮɟɥɹ ɰɟɧɧɵɯ ɛɭɦɚɝ ɫ ɩɨɦɨɳɶɸ ɧɚɞɫɬɪɨɣɤɢ ɉɨɢɫɤ ɪɟɲɟɧɢɹ. Ʉ ɡɚɳɢɬɟ ɥɚɛɨɪɚɬɨɪɧɨɣ ɪɚɛɨɬɵ ɫɬɭɞɟɧɬ ɞɨɥɠɟɧ ɩɪɟɞɫɬɚɜɢɬɶ ɮɚɣɥɵ ɅɊ10_Ɏɚɦɢɥɢɹ.xls ɢ Ɉɬɱɟɬ_ɅɊ10_Ɏɚɦɢɥɢɹ.doc. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ Ɂɚɞɚɱɚ 1 Ɋɟɲɢɬɟ ɡɚɞɚɱɭ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɨɪɬɮɟɥɹ ɞɥɹ ɭɫɥɨɜɢɣ, ɡɚɞɚɧɧɵɯ ɧɚ ɪɢɫɭɧɤɟ 10.1: Ɋɢɫɭɧɨɤ 10.1 – ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɡɚɞɚɱɢ ɨɩɬɢɦɢɡɚɰɢɢ ɉɨɪɹɞɨɤ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ Ɂɧɚɱɟɧɢɹ ɫɬɨɥɛɰɚ ɉɪɢɛɵɥɶ ɪɚɫɫɱɢɬɚɣɬɟ ɤɚɤ ɩɪɨɢɡɜɟɞɟɧɢɟ Ⱦɨɯɨɞɧɨɫɬɢ ɢ ɋɭɦɦɵ ɜɥɨɠɟɧɢɣ. Ɂɧɚɱɟɧɢɟ ɋɭɦɦɚ ɜ ɧɚɞɟɠɧɵɯ ɚɤɬɢɜɚɯ ɪɚɫɫɱɢɬɚɣɬɟ ɤɚɤ ɫɭɦɦɭ ɜɥɨɠɟɧɢɣ, ɭ ɤɨɬɨɪɵɯ ɡɧɚɱɟɧɢɟ ɇɚɞɟɠɧɨɫɬɢ ɧɟ ɦɟɧɟɟ 4. Ɂɧɚɱɟɧɢɟ ɋɭɦɦɚ ɜ ɞɨɥɝɨɫɪɨɱɧɵɯ ɚɤɬɢɜɚɯ ɪɚɫɫɱɢɬɚɣɬɟ ɤɚɤ ɫɭɦɦɭ ɜɥɨɠɟɧɢɣ, ɋɪɨɤ ɜɵɤɭɩɚ ɩɨ ɤɨɬɨɪɵɦ ɧɚɫɬɭɩɚɟɬ ɩɨɡɞɧɟɟ 2015 ɝɨɞɚ. Ɂɧɚɱɟɧɢɟ Ⱦɨɯɨɞɧɨɫɬɶ ɩɨɪɬɮɟɥɹ ɪɚɫɫɱɢɬɚɣɬɟ ɤɚɤ ɨɬɧɨɲɟɧɢɟ ɢɬɨɝɨɜɨɣ ɩɪɢɛɵɥɢ ɤ ɢɬɨɝɨɜɨɣ ɫɭɦɦɟ ɜɥɨɠɟɧɢɣ (ɜ %). ɋ ɩɨɦɨɳɶɸ ɧɚɞɫɬɪɨɣɤɢ ɉɨɢɫɤ ɪɟɲɟɧɢɹ ɧɚɣɞɢɬɟ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɭɸ Ⱦɨɯɨɞɧɨɫɬɶ ɩɨɪɬɮɟɥɹ ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɨɝɪɚɧɢɱɟɧɢɹɯ: a) Ɉɛɳɚɹ ɫɭɦɦɚ ɜɥɨɠɟɧɢɣ ɪɚɜɧɚ $200 000. b) ɋɭɦɦɚ ɜɥɨɠɟɧɢɣ ɜ ɤɚɠɞɵɣ ɚɤɬɢɜ ɧɟ ɩɪɟɜɵɲɚɟɬ ɱɟɬɜɟɪɬɢ ɨɬ Ɉɛɳɟɣ ɫɭɦɦɵ ɜɥɨɠɟɧɢɣ. c) ɋɭɦɦɚ ɜ ɧɚɞɟɠɧɵɯ ɚɤɬɢɜɚɯ ɫɨɫɬɚɜɥɹɟɬ ɧɟ ɦɟɧɟɟ 2/3 ɨɬ Ɉɛɳɟɣ ɋɭɦɦɵ ɜɥɨɠɟɧɢɣ. d) ɋɭɦɦɚ ɜ ɞɨɥɝɨɫɪɨɱɧɵɯ ɚɤɬɢɜɚɯ ɫɨɫɬɚɜɥɹɟɬ ɧɟ ɦɟɧɟɟ ɩɨɥɨɜɢɧɵ ɨɬ Ɉɛɳɟɣ ɫɭɦɦɵ ɜɥɨɠɟɧɢɣ. ɉɊɂɆȿɑȺɇɂȿ: 1. Ⱦɥɹ ɪɚɫɱɟɬɚ ɡɧɚɱɟɧɢɣ ɋɭɦɦɚ ɜ ɧɚɞɟɠɧɵɯ ɚɤɬɢɜɚɯ ɢ ɋɭɦɦɚ ɜ ɞɨɥɝɨɫɪɨɱɧɵɯ ɚɤɬɢɜɚɯ ɢɫɩɨɥɶɡɭɣɬɟ ɮɭɧɤɰɢɸ ɋɍɆɆȿɋɅɂ: ɋɢɧɬɚɤɫɢɫ ɮɭɧɤɰɢɢ: ɋɍɆɆȿɋɅɂ(ɞɢɚɩɚɡɨɧ; ɤɪɢɬɟɪɢɣ; ɞɢɚɩɚɡɨɧ_ɫɭɦɦɢɪɨɜɚɧɢɹ) ɞɢɚɩɚɡɨɧ – ɞɢɚɩɚɡɨɧ ɩɪɨɜɟɪɹɟɦɵɯ ɹɱɟɟɤ; ɤɪɢɬɟɪɢɣ – ɤɪɢɬɟɪɢɣ ɜ ɮɨɪɦɟ ɱɢɫɥɚ, ɜɵɪɚɠɟɧɢɹ ɢɥɢ ɬɟɤɫɬɚ, ɨɩɪɟɞɟɥɹɸɳɟɝɨ ɫɭɦɦɢɪɭɟɦɵɟ ɹɱɟɣɤɢ; ɞɢɚɩɚɡɨɧ_ɫɭɦɦɢɪɨɜɚɧɢɹ – ɮɚɤɬɢɱɟɫɤɢɟ ɹɱɟɣɤɢ ɞɥɹ ɫɭɦɦɢɪɨɜɚɧɢɹ. 2. Ⱦɥɹ ɜɤɥɸɱɟɧɢɹ ɧɚɞɫɬɪɨɣɤɢ ɉɨɢɫɤ ɪɟɲɟɧɢɹ ɜɵɩɨɥɧɢɬɟ ɤɨɦɚɧɞɭ ɋɟɪɜɢɫ – ɇɚɞɫɬɪɨɣɤɢ, ɜ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɇɚɞɫɬɪɨɣɤɢ ɫɪɟɞɢ ɞɨɫɬɭɩɧɵɯ ɢɧɫɬɪɭɦɟɧɬɨɜ ɜɵɛɟɪɢɬɟ ɉɨɢɫɤ ɪɟɲɟɧɢɹ. ȼɵɩɨɥɧɢɬɟ ɤɨɦɚɧɞɭ ɋɟɪɜɢɫ – ɉɨɢɫɤ ɪɟɲɟɧɢɹ. ȼ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɉɨɢɫɤ ɪɟɲɟɧɢɹ ɜ ɤɚɱɟɫɬɜɟ ɰɟɥɟɜɨɣ ɹɱɟɣɤɢ ɜɵɛɟɪɢɬɟ Ⱦɨɯɨɞ1 Ⱥ.Ȼ. Ƚɟɞɪɚɧɨɜɢɱ, ȼ.ȼ. Ƚɟɞɪɚɧɨɜɢɱ – Ɏɢɧɚɧɫɨɜɚɹ ɢɧɮɨɪɦɚɬɢɤɚ – Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ʋ 10 ɧɨɫɬɶ ɩɨɪɬɮɟɥɹ (ȿ11), ɭɫɬɚɧɨɜɢɬɟ ɟɟ ɪɚɜɧɨɣ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ. ȼ ɤɚɱɟɫɬɜɟ ɹɱɟɟɤ ɞɥɹ ɢɡɦɟɧɟɧɢɹ ɜɵɛɟɪɢɬɟ ɫɬɨɥɛɟɰ, ɫɨɞɟɪɠɚɳɢɣ ɡɧɚɱɟɧɢɹ ɋɭɦɦɚ ɜɥɨɠɟɧɢɣ (ȿ2:ȿ7). Ⱦɨɛɚɜɶɬɟ ɨɝɪɚɧɢɱɟɧɢɹ a) – d) ɢ ɞɥɹ ɋɭɦɦɚ ɜɥɨɠɟɧɢɣ (ȿ2:ȿ7) – ɧɟɨɬɪɢɰɚɬɟɥɶɧɨɟ ɱɢɫɥɨ (ɤɧɨɩɤɚ Ⱦɨɛɚɜɢɬɶ). ɇɚɠɦɢɬɟ ɤɧɨɩɤɭ ȼɵɩɨɥɧɢɬɶ. ɋɨɯɪɚɧɢɬɟ ɢ ɩɪɨɚɧɚɥɢɡɢɪɭɣɬɟ ɧɚɣɞɟɧɧɨɟ ɪɟɲɟɧɢɟ. Ɂɚɞɚɱɚ 2 Ɋɟɲɢɬɟ ɡɚɞɚɱɭ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɩɨɪɬɮɟɥɹ ɞɥɹ ɞɚɧɧɵɯ, ɭɤɚɡɚɧɧɵɯ ɧɚ ɪɢɫɭɧɤɟ 10.2, ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɞɨɥɢ ɚɤɬɢɜɨɜ ɧɟ ɦɨɝɭɬ ɩɪɢɧɢɦɚɬɶ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɢ ɪɢɫɤ ɧɟ ɩɪɟɜɵɲɚɟɬ 0,35. Ɋɢɫɭɧɨɤ 10.2 – ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɡɚɞɚɱɢ 2 ɉɨɪɹɞɨɤ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɉɭɫɬɶ ɩɟɪɜɨɧɚɱɚɥɶɧɵɟ ɞɨɥɢ ɚɤɬɢɜɨɜ Ⱥ, ȼ ɢ ɋ ɜ ɩɨɪɬɮɟɥɟ ɪɚɜɧɵ 0, 0 ɢ 1 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ȼ ɹɱɟɣɤɭ F5 ɜɜɟɞɢɬɟ ɮɨɪɦɭɥɭ ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ ɫɭɦɦɵ ɞɨɥɟɣ. Ɉɠɢɞɚɟɦɭɸ ɞɨɯɨɞɧɨɫɬɶ ɩɨɪɬɮɟɥɹ ɪɚɫɫɱɢɬɚɣɬɟ ɜ ɹɱɟɣɤɟ ɋ6 ɩɨ ɮɨɪɦɭɥɟ: =ɋɍɆɆɉɊɈɂɁȼ(B2:B4;F2:F4) Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɞɢɫɩɟɪɫɢɢ ɞɨɯɨɞɚ (ɹɱɟɣɤɚ ɋ7) ɜɜɟɞɢɬɟ ɮɨɪɦɭɥɭ: =C2*F2^2+D3*F3^2+E4*F4^2+2*F2*F3*C3+2*F2*F4*C4+2*F3*F4*D4 ɋɬɚɧɞɚɪɬɧɨɟ ɨɬɤɥɨɧɟɧɢɟ (ɪɢɫɤ) ɜɵɱɢɫɥɢɬɟ ɩɨ ɮɨɪɦɭɥɟ =ɄɈɊȿɇɖ(C7) ɢ ɩɨɦɟɫɬɢɬɟ ɜ ɹɱɟɣɤɭ ɋ8. ɐɟɥɟɜɨɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɪɢɫɤɚ (0,35) ɜɜɟɞɢɬɟ ɜ ɹɱɟɣɤɭ I2. ɋ ɩɨɦɨɳɶɸ ɧɚɞɫɬɪɨɣɤɢ ɉɨɢɫɤ ɪɟɲɟɧɢɹ ɧɚɣɞɢɬɟ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɭɸ Ⱦɨɯɨɞɧɨɫɬɶ ɩɨɪɬɮɟɥɹ (ɰɟɥɟɜɚɹ ɹɱɟɣɤɚ $C$6) ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɨɝɪɚɧɢɱɟɧɢɹɯ: a) ɋɭɦɦɚ ɞɨɥɟɣ ɚɤɬɢɜɨɜ ɪɚɜɧɚ 1. b) Ⱦɨɥɢ ɚɤɬɢɜɨɜ – ɧɟɨɬɪɢɰɚɬɟɥɶɧɵɟ ɱɢɫɥɚ. c) Ɋɢɫɤ ɧɟ ɩɪɟɜɵɲɚɟɬ ɡɧɚɱɟɧɢɹ, ɡɚɞɚɧɧɨɝɨ ɜ ɹɱɟɣɤɟ I2. ɋɨɯɪɚɧɢɬɟ ɢ ɩɪɨɚɧɚɥɢɡɢɪɭɣɬɟ ɧɚɣɞɟɧɧɨɟ ɪɟɲɟɧɢɟ. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ȿɫɥɢ ɩɨɪɬɮɟɥɶ ɧɚɫɱɢɬɵɜɚɟɬ ɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɛɭɦɚɝ, ɬɨ ɜ ɪɚɦɤɚɯ ɩɪɟɞɫɬɚɜɥɟɧɧɨɝɨ ɜɵɲɟ ɚɥɝɨɪɢɬɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɟ ɨɱɟɧɶ ɭɞɨɛɧɨ ɜɜɨɞɢɬɶ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ ɞɢɫɩɟɪɫɢɢ ɞɨɯɨɞɚ. Ɉɞɧɚɤɨ ɷɬɭ ɩɪɨɛɥɟɦɭ ɥɟɝɤɨ ɫɧɹɬɶ, ɟɫɥɢ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɦɚɬɪɢɱɧɵɦ ɢɫɱɢɫɥɟɧɢɟɦ. Ɂɚɞɚɱɚ 3 Ɋɟɲɢɬɟ ɡɚɞɚɱɭ 2, ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɦɚɬɪɢɱɧɵɦɢ ɮɭɧɤɰɢɹɦɢ ɞɥɹ ɪɚɫɱɟɬɚ ɞɢɫɩɟɪɫɢɢ ɞɨɯɨɞɚ. ɉɊɂɆȿɑȺɇɂȿ: 1. ȼ ɹɱɟɣɤɚɯ ɋ10:ȿ10 ɪɚɡɦɟɫɬɢɬɟ ɬɪɚɧɫɩɨɧɢɪɨɜɚɧɧɭɸ ɦɚɬɪɢɰɭ ɞɨɥɟɣ ɚɤɬɢɜɨɜ. 2. Ⱦɢɫɩɟɪɫɢɸ ɞɨɯɨɞɚ ɜɵɱɢɫɥɢɬɟ ɩɨ ɮɨɪɦɭɥɟ: =ɆɍɆɇɈɀ(ɆɍɆɇɈɀ(C10:E10;C2:E4);F2:F4). Ɂɚɞɚɱɚ 4 Ɋɟɲɢɬɟ ɡɚɞɚɱɭ ɮɨɪɦɢɪɨɜɚɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɩɨɪɬɮɟɥɹ ɞɥɹ ɞɚɧɧɵɯ, ɭɤɚɡɚɧɧɵɯ ɧɚ ɪɢɫɭɧɤɟ 10.2, ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɞɨɥɢ ɚɤɬɢɜɨɜ ɧɟ ɦɨɝɭɬ ɩɪɢɧɢɦɚɬɶ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɢ ɨɠɢɞɚɟɦɚɹ ɞɨɯɨɞɧɨɫɬɶ ɩɨɪɬɮɟɥɹ ɧɟ ɧɢɠɟ 0,21. 2