Задание МА9 102012 РФ
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Ⱦɢɚɝɧɨɫɬɢɱɟɫɤɚɹ ɪɚɛɨɬɚ ʋ 1
ɩɨ ɆȺɌȿɆȺɌɂɄȿ
2 ɨɤɬɹɛɪɹ 2012 ɝɨɞɚ
9 ɤɥɚɫɫ
ȼɚɪɢɚɧɬ 5
Ɋɚɣɨɧ Ƚɨɪɨɞ (ɧɚɫɟɥɺɧɧɵɣ ɩɭɧɤɬ)
ɒɤɨɥɚ
Ʉɥɚɫɫ
Ɏɚɦɢɥɢɹ
ɂɦɹ
Ɉɬɱɟɫɬɜɨ
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 5 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 2 |
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ɂɧɫɬɪɭɤɰɢɹ ɩɨ ɜɵɩɨɥɧɟɧɢɸ ɪɚɛɨɬɵ |
Ɉɛɳɟɟ ɜɪɟɦɹ ɷɤɡɚɦɟɧɚ 4 ɱɚɫɚ (240 ɦɢɧɭɬ).
ȼɫɟɝɨ ɜ ɪɚɛɨɬɟ 26 ɡɚɞɚɧɢɣ, ɢɡ ɤɨɬɨɪɵɯ 20 ɡɚɞɚɧɢɣ ɛɚɡɨɜɨɝɨ ɭɪɨɜɧɹ (ɑɚɫɬɶ I) ɢ 6 ɡɚɞɚɧɢɣ ɩɨɜɵɲɟɧɧɨɝɨ ɭɪɨɜɧɹ (ɑɚɫɬɶ II).
Ɋɚɛɨɬɚ ɫɨɫɬɨɢɬ ɢɡ ɬɪɺɯ ɦɨɞɭɥɟɣ «Ⱥɥɝɟɛɪɚ», «Ƚɟɨɦɟɬɪɢɹ», «Ɋɟɚɥɶɧɚɹ ɦɚɬɟɦɚɬɢɤɚ». Ɇɨɞɭɥɶ «Ⱥɥɝɟɛɪɚ» ɫɨɞɟɪɠɢɬ 11 ɡɚɞɚɧɢɣ: ɜ ɱɚɫɬɢ I – 8 ɡɚɞɚɧɢɣ ɫ ɤɪɚɬɤɢɦ ɨɬɜɟɬɨɦ,
ɜɵɛɨɪɨɦ ɨɬɜɟɬɚ ɢ ɭɫɬɚɧɨɜɥɟɧɢɟɦ ɫɨɨɬɜɟɬɫɬɜɢɹ; ɜ ɱɚɫɬɢ II – 3 ɡɚɞɚɧɢɹ ɫ ɩɨɥɧɵɦ ɪɟɲɟɧɢɟɦ.
Ɇɨɞɭɥɶ «Ƚɟɨɦɟɬɪɢɹ» ɫɨɞɟɪɠɢɬ 8 ɡɚɞɚɧɢɣ: ɜ ɱɚɫɬɢ I – 5 ɡɚɞɚɧɢɣ ɫ ɤɪɚɬɤɢɦ ɨɬɜɟɬɨɦ, ɜ ɱɚɫɬɢ II – 3 ɡɚɞɚɧɢɹ ɫ ɩɨɥɧɵɦ ɪɟɲɟɧɢɟɦ.
Ɇɨɞɭɥɶ «Ɋɟɚɥɶɧɚɹ ɦɚɬɟɦɚɬɢɤɚ» ɫɨɞɟɪɠɢɬ 7 ɡɚɞɚɧɢɣ: ɜɫɟ ɡɚɞɚɧɢɹ – ɜ ɱɚɫɬɢ I, ɫ ɤɪɚɬɤɢɦ ɨɬɜɟɬɨɦ ɢ ɜɵɛɨɪɨɦ ɨɬɜɟɬɚ.
ɋɧɚɱɚɥɚ ɜɵɩɨɥɧɹɣɬɟ ɡɚɞɚɧɢɹ ɑɚɫɬɢ I. ɇɚɱɚɬɶ ɫɨɜɟɬɭɟɦ ɫ ɬɨɝɨ ɦɨɞɭɥɹ, ɡɚɞɚɧɢɹ ɤɨɬɨɪɨɝɨ ɜɵɡɵɜɚɸɬ ɭ ȼɚɫ ɦɟɧɶɲɟ ɡɚɬɪɭɞɧɟɧɢɣ, ɡɚɬɟɦ ɩɟɪɟɯɨɞɢɬɟ ɤ ɞɪɭɝɢɦ ɦɨɞɭɥɹɦ.
Ⱦɥɹ ɷɤɨɧɨɦɢɢ ɜɪɟɦɟɧɢ ɩɪɨɩɭɫɤɚɣɬɟ ɡɚɞɚɧɢɟ, ɤɨɬɨɪɨɟ ɧɟ ɭɞɚɺɬɫɹ ɜɵɩɨɥɧɢɬɶ ɫɪɚɡɭ, ɢ |
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ɩɟɪɟɯɨɞɢɬɟ ɤ ɫɥɟɞɭɸɳɟɦɭ. ȿɫɥɢ |
ɭ ȼɚɫ ɨɫɬɚɧɟɬɫɹ ɜɪɟɦɹ, ȼɵ ɫɦɨɠɟɬɟ ɜɟɪɧɭɬɶɫɹ |
ɤ ɩɪɨɩɭɳɟɧɧɵɦ ɡɚɞɚɧɢɹɦ. |
ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɬ.ɞ. ɜɵɩɨɥɧɹɣɬɟ ɜ ɱɟɪɧɨɜɢɤɟ. |
ȼɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɜɵɱɢɫɥɟɧɢɹ, |
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ȿɫɥɢ ɡɚɞɚɧɢɟ ɫɨɞɟɪɠɢɬ ɪɢɫɭɧɨɤ, |
ɬɨ ɧɚ ɧɺɦ ɦɨɠɧɨ ɜɵɩɨɥɧɹɬɶ ɧɟɨɛɯɨɞɢɦɵɟ ȼɚɦ |
ɩɨɫɬɪɨɟɧɢɹ. Ɉɛɪɚɳɚɟɦ ȼɚɲɟ ɜɧɢɦɚɧɢɟ ɧɚ ɬɨ, ɱɬɨ ɡɚɩɢɫɢ ɜ ɱɟɪɧɨɜɢɤɟ ɧɟ ɛɭɞɭɬ ɭɱɢɬɵɜɚɬɶɫɹ ɩɪɢ ɨɰɟɧɢɜɚɧɢɢ ɪɚɛɨɬɵ. Ɋɟɤɨɦɟɧɞɭɟɦ ɜɧɢɦɚɬɟɥɶɧɨ ɱɢɬɚɬɶ ɭɫɥɨɜɢɟ
ɢ ɩɪɨɜɨɞɢɬɶ ɩɪɨɜɟɪɤɭ ɩɨɥɭɱɟɧɧɨɝɨ ɨɬɜɟɬɚ.
ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ ɫ ɜɵɛɨɪɨɦ ɨɬɜɟɬɚ ɨɛɜɟɞɢɬɟ ɧɨɦɟɪ ɜɵɛɪɚɧɧɨɝɨ ɨɬɜɟɬɚ ɜ ɷɤɡɚɦɟɧɚɰɢɨɧɧɨɣ ɪɚɛɨɬɟ. ȿɫɥɢ ȼɵ ɨɛɜɟɥɢ ɧɟ ɬɨɬ ɧɨɦɟɪ, ɬɨ ɡɚɱɟɪɤɧɢɬɟ ɨɛɜɟɞɺɧɧɵɣ ɧɨɦɟɪ ɤɪɟɫɬɢɤɨɦ ɢ ɡɚɬɟɦ ɨɛɜɟɞɢɬɟ ɧɨɦɟɪ ɩɪɚɜɢɥɶɧɨɝɨ ɨɬɜɟɬɚ.
ȿɫɥɢ ɜɚɪɢɚɧɬɵ ɨɬɜɟɬɚ ɤ ɡɚɞɚɧɢɸ ɧɟ ɩɪɢɜɨɞɹɬɫɹ, ɩɨɥɭɱɟɧɧɵɣ ɨɬɜɟɬ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɨɬɜɟɞɺɧɧɨɦ ɞɥɹ ɷɬɨɝɨ ɦɟɫɬɟ. ȼ ɫɥɭɱɚɟ ɡɚɩɢɫɢ ɧɟɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɡɚɱɟɪɤɧɢɬɟ ɟɝɨ ɢ ɡɚɩɢɲɢɬɟ ɪɹɞɨɦ ɧɨɜɵɣ.
ȿɫɥɢ ɜ ɡɚɞɚɧɢɢ ɬɪɟɛɭɟɬɫɹ ɭɫɬɚɧɨɜɢɬɶ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɧɟɤɨɬɨɪɵɦɢ ɨɛɴɟɤɬɚɦɢ,
ɜɩɢɲɢɬɟ ɜ ɩɪɢɜɟɞɺɧɧɭɸ ɜ ɨɬɜɟɬɟ ɬɚɛɥɢɰɭ ɩɨɞ ɤɚɠɞɨɣ ɛɭɤɜɨɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɰɢɮɪɭ.
Ɋɟɲɟɧɢɹ ɡɚɞɚɧɢɣ ɑɚɫɬɢ II ɢ ɨɬɜɟɬɵ ɤ ɧɢɦ ɡɚɩɢɫɵɜɚɸɬɫɹ ɧɚ ɨɬɞɟɥɶɧɨɦ ɥɢɫɬɟ. Ɍɟɤɫɬ ɡɚɞɚɧɢɹ ɦɨɠɧɨ ɧɟ ɩɟɪɟɩɢɫɵɜɚɬɶ, ɧɟɨɛɯɨɞɢɦɨ ɥɢɲɶ ɭɤɚɡɚɬɶ ɟɝɨ ɧɨɦɟɪ.
Ȼɚɥɥɵ, ɩɨɥɭɱɟɧɧɵɟ ȼɚɦɢ ɡɚ ɜɟɪɧɨ ɜɵɩɨɥɧɟɧɧɵɟ ɡɚɞɚɧɢɹ, ɫɭɦɦɢɪɭɸɬɫɹ. Ⱦɥɹ
ɭɫɩɟɲɧɨɝɨ ɩɪɨɯɨɠɞɟɧɢɹ ɢɬɨɝɨɜɨɣ ɚɬɬɟɫɬɚɰɢɢ ɧɟɨɛɯɨɞɢɦɨ ɧɚɛɪɚɬɶ ɜ ɫɭɦɦɟ ɧɟ ɦɟɧɟɟ 8 ɛɚɥɥɨɜ, ɢɡ ɧɢɯ ɧɟ ɦɟɧɟɟ ɞɜɭɯ ɛɚɥɥɨɜ ɩɨ ɤɚɠɞɨɦɭ ɢɡ ɦɨɞɭɥɟɣ.
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© 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 |
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 5 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 3 |
ɑɚɫɬɶ 1
Ɇɨɞɭɥɶ "Ⱥɥɝɟɛɪɚ"
1ɇɚɣɞɢɬɟ ɡɧɚɱɟɧɢɹ ɜɵɪɚɠɟɧɢɣ. ȼ ɨɬɜɟɬɟ ɭɤɚɠɢɬɟ ɧɨɦɟɪ ɧɚɢɛɨɥɶɲɟɝɨ ɢɡ ɧɚɣɞɟɧɧɵɯ ɡɧɚɱɟɧɢɣ.
1)1, 8 |
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2)1 |
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Ɉɬɜɟɬ: 
2ȼɵɛɟɪɢɬɟ ɜɟɪɧɨɟ ɭɬɜɟɪɠɞɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɱɢɫɟɥ a ɢ b, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɧɚ ɱɢɫɥɨɜɨɣ ɩɪɹɦɨɣ.
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3 ɍɤɚɠɢɬɟ ɞɜɚ ɫɨɫɟɞɧɢɯ ɰɟɥɵɯ ɱɢɫɥɚ, ɦɟɠɞɭ ɤɨɬɨɪɵɦɢ ɡɚɤɥɸɱɟɧɨ ɱɢɫɥɨ 2 11.
1) 2 ɢ 3 2) 6 ɢ 7 3) 11 ɢ 12 4) 45 ɢ 46
4 ɇɚɣɞɢɬɟ ɤɨɪɧɢ ɭɪɚɜɧɟɧɢɹ 2x2 11x 6 0.
Ɉɬɜɟɬ: 
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 5 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 4 |
5ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɝɪɚɮɢɤɢ ɬɪɺɯ ɮɭɧɤɰɢɣ, ɡɚɞɚɜɚɟɦɵɯ ɮɨɪɦɭɥɚɦɢ ɜɢɞɚ y kx. ɍɤɚɠɢɬɟ ɞɥɹ ɤɚɠɞɨɝɨ ɝɪɚɮɢɤɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɟɦɭ ɮɨɪɦɭɥɭ, ɜɵɛɪɚɜ ɟɺ ɢɡ ɱɢɫɥɚ ɩɪɢɜɟɞɺɧɧɵɯ ɧɢɠɟ.
ȽɊȺɎɂɄɂ
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ɎɍɇɄɐɂɂ |
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Ɉɬɜɟɬ: |
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6Ɂɚɩɢɲɢɬɟ ɜ ɨɬɜɟɬɟ ɧɨɦɟɪɚ ɜɟɪɧɵɯ ɪɚɜɟɧɫɬɜ.
1) |
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Ɉɬɜɟɬ: 
7 ɍɩɪɨɫɬɢɬɟ ɜɵɪɚɠɟɧɢɟ |
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ɢ ɧɚɣɞɢɬɟ ɟɝɨ ɡɧɚɱɟɧɢɟ ɩɪɢ a |
0, 7, |
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Ɉɬɜɟɬ: 
© 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 |
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 5 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 5 |
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8 Ɋɟɲɢɬɟ ɭɪɚɜɧɟɧɢɟ |
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Ɉɬɜɟɬ: |
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Ɇɨɞɭɥɶ "Ƚɟɨɦɟɬɪɢɹ"
9ɉɟɪɢɦɟɬɪ ɪɚɜɧɨɫɬɨɪɨɧɧɟɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ABC ɪɚɜɟɧ 24 ɫɦ. ɇɚɣɞɢɬɟ ɞɥɢɧɭ ɫɪɟɞɧɟɣ ɥɢɧɢɢ ɷɬɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ.
Ɉɬɜɟɬ: 
10ɋɬɨɪɨɧɚ ɪɨɦɛɚ ɪɚɜɧɚ 32, ɚ ɨɫɬɪɵɣ ɭɝɨɥ ɪɚɜɟɧ 60q. ȼɵɫɨɬɚ ɪɨɦɛɚ, ɨɩɭɳɟɧɧɚɹ ɢɡ ɜɟɪɲɢɧɵ ɬɭɩɨɝɨ ɭɝɥɚ, ɞɟɥɢɬ ɫɬɨɪɨɧɭ ɧɚ ɞɜɚ ɨɬɪɟɡɤɚ. Ʉɚɤɨɜɵ ɞɥɢɧɵ ɷɬɢɯ ɨɬɪɟɡɤɨɜ?
Ɉɬɜɟɬ: 
11ɂɡ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ ɫɨ ɫɬɨɪɨɧɚɦɢ 10 ɫɦ ɢ 8 ɫɦ ɜɵɪɟɡɚɧ ɤɜɚɞɪɚɬ ɫɨ ɫɬɨɪɨɧɨɣ 5 ɫɦ. ɇɚɣɞɢɬɟ ɩɥɨɳɚɞɶ ɨɫɬɚɜɲɟɣɫɹ ɱɚɫɬɢ. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɫɦ2.
Ɉɬɜɟɬ: 
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 5 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 6 |
12Ʉ ɨɤɪɭɠɧɨɫɬɢ ɫ ɰɟɧɬɪɨɦ ɜ ɬɨɱɤɟ O ɩɪɨɜɟɞɟɧɵ ɤɚɫɚɬɟɥɶɧɚɹ AB ɢ ɫɟɤɭɳɚɹ AO. ɇɚɣɞɢɬɟ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ, ɟɫɥɢ AB=15 ɫɦ, AO=17 ɫɦ.
Ɉɬɜɟɬ: 
13ɍɤɚɠɢɬɟ ɜ ɨɬɜɟɬɟ ɧɨɦɟɪɚ ɜɟɪɧɵɯ ɭɬɜɟɪɠɞɟɧɢɣ.
1)ɋɭɳɟɫɬɜɭɟɬ ɩɪɹɦɨɭɝɨɥɶɧɢɤ, ɞɢɚɝɨɧɚɥɢ ɤɨɬɨɪɨɝɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵ.
2)ɑɟɪɟɡ ɬɨɱɤɭ, ɧɟ ɥɟɠɚɳɭɸ ɧɚ ɞɚɧɧɨɣ ɩɪɹɦɨɣ, ɦɨɠɧɨ ɩɪɨɜɟɫɬɢ ɩɪɹɦɭɸ, ɩɚɪɚɥɥɟɥɶɧɭɸ ɷɬɨɣ ɩɪɹɦɨɣ.
3)ȿɫɥɢ ɬɪɢ ɭɝɥɚ ɨɞɧɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ ɬɪɺɦ ɭɝɥɚɦ ɞɪɭɝɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ, ɬɨ ɬɚɤɢɟ ɬɪɟɭɝɨɥɶɧɢɤɢ ɪɚɜɧɵ.
Ɉɬɜɟɬ: 
Ɇɨɞɭɥɶ "Ɋɟɚɥɶɧɚɹ ɦɚɬɟɦɚɬɢɤɚ"
14Ʉɭɪɢɧɵɟ ɹɣɰɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɢɯ ɦɚɫɫɵ ɩɨɞɪɚɡɞɟɥɹɸɬ ɧɚ ɩɹɬɶ ɤɚɬɟɝɨɪɢɣ: ɜɵɫɲɚɹ, ɨɬɛɨɪɧɚɹ, ɩɟɪɜɚɹ, ɜɬɨɪɚɹ ɢ ɬɪɟɬɶɹ. ɂɫɩɨɥɶɡɭɹ ɞɚɧɧɵɟ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɜ ɬɚɛɥɢɰɟ, ɨɩɪɟɞɟɥɢɬɟ, ɤ ɤɚɤɨɣ ɤɚɬɟɝɨɪɢɢ ɨɬɧɨɫɢɬɫɹ ɹɣɰɨ, ɦɚɫɫɨɣ 60,7 ɝ.
Ʉ ɬɟɝɨ ɹ |
Ɇ ɫɫ ɨɞɧɨɝɨ ɹ , ɧɟ ɦɟɧɟɟ, ɝ |
ȼɵɫɲɚɹ |
75,0 ɢ ɜɵɲɟ |
Ɉɬɛɨɪɧɚɹ |
65,0 - 74,9 |
ɉɟɪɜɚɹ |
55,0 - 64,9 |
ȼɬɨɪɚɹ |
45,0 - 54,9 |
Ɍɪɟɬɶɹ |
35,0 - 44,9 |
Ɉɬɜɟɬ: 
© 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 |
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 5 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 7 |
15ɇɚ ɬɪɟɧɢɪɨɜɤɟ ɜ 50-ɦɟɬɪɨɜɨɦ ɛɚɫɫɟɣɧɟ ɩɥɨɜɟɰ ɩɪɨɩɥɵɥ 200-ɦɟɬɪɨɜɭɸ ɞɢɫɬɚɧɰɢɸ. ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɩɥɨɜɰɨɦ ɢ ɬɨɱɤɨɣ ɫɬɚɪɬɚ ɨɬ ɜɪɟɦɟɧɢ ɞɜɢɠɟɧɢɹ ɩɥɨɜɰɚ. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɫɫɬɨɹɧɢɟ (ɜ ɦɟɬɪɚɯ), ɤɨɬɨɪɨɟ ɩɪɨɩɥɵɥ ɩɥɨɜɟɰ ɡɚ ɩɟɪɜɭɸ ɦɢɧɭɬɭ ɡɚɩɥɵɜɚ.
Ɉɬɜɟɬ: 
16ɉɥɨɳɚɞɶ ɡɟɦɟɥɶ ɤɪɟɫɬɶɹɧɫɤɨɝɨ ɯɨɡɹɣɫɬɜɚ, ɡɚɧɹɬɚɹ ɩɨɞ ɩɨɫɚɞɤɭ ɫɟɥɶɫɤɨɯɨɡɹɣɫɬɜɟɧɧɵɯ ɤɭɥɶɬɭɪ, ɫɨɫɬɚɜɥɹɟɬ 49 ɝɚ ɢ ɪɚɫɩɪɟɞɟɥɟɧɚ ɦɟɠɞɭ ɡɟɪɧɨɜɵɦɢ ɤɭɥɶɬɭɪɚɦɢ ɢ ɤɚɪɬɨɮɟɥɟɦ ɜ ɨɬɧɨɲɟɧɢɢ 2:5. ɋɤɨɥɶɤɨ ɝɟɤɬɚɪɨɜ ɡɚɧɢɦɚɸɬ ɡɟɪɧɨɜɵɟ ɤɭɥɶɬɭɪɵ?
Ɉɬɜɟɬ: 
17ɑɟɥɨɜɟɤ, ɪɨɫɬ ɤɨɬɨɪɨɝɨ 1,6 ɦ, ɫɬɨɢɬ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 3 ɦ ɨɬ ɭɥɢɱɧɨɝɨ ɮɨɧɚɪɹ. ɉɪɢ ɷɬɨɦ ɞɥɢɧɚ ɟɝɨ ɬɟɧɢ ɪɚɜɧɚ 2 ɦ. Ɉɩɪɟɞɟɥɢɬɟ ɜɵɫɨɬɭ ɮɨɧɚɪɹ (ɜ ɦ).
Ɉɬɜɟɬ: 
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 5 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 8 |
18ɇɚ ɞɢɚɝɪɚɦɦɟ ɩɪɟɞɫɬɚɜɥɟɧɚ ɢɧɮɨɪɦɚɰɢɹ ɨ ɤɨɥɢɱɟɫɬɜɟ ɫɨɬɨɜɵɯ ɬɟɥɟɮɨɧɨɜ, ɩɪɨɞɚɧɧɵɯ ɱɟɬɵɪɶɦɹ ɜɟɞɭɳɢɦɢ ɬɨɪɝɨɜɵɦɢ ɤɨɦɩɚɧɢɹɦɢ ɜ 2004 ɝ. ɋɤɨɥɶɤɨ
ɬɟɥɟɮɨɧɨɜ ɛɵɥɨ ɩɪɨɞɚɧɨ ɜ ɷɬɨɦ ɝɨɞɭ ɞɜɭɦɹ ɜɟɞɭɳɢɦɢ ɤɨɦɩɚɧɢɹɦɢ ȿɜɪɨɫɟɬɶ ɢ ɋɜɹɡɧɨɣ? Ɉɬɜɟɬ ɭɤɚɠɢɬɟ ɜ ɦɢɥɥɢɨɧɚɯ ɲɬɭɤ.
Ɉɬɜɟɬ: 
19 ɇɚ ɫɬɨɥɟ ɫɬɨɹɬ |
ɫɬɚɤɚɧɵ ɫ ɮɪɭɤɬɨɜɵɦɢ ɣɨɝɭɪɬɚɦɢ, ɨɞɢɧɚɤɨɜɵɦɢ |
ɧɚ ɜɢɞ: |
9 ɫ ɜɢɲɧɺɜɵɦ ɢ |
6 ɫ ɤɥɭɛɧɢɱɧɵɦ. Ʉɚɬɹ ɧɚɭɝɚɞ ɛɟɪɟɬ ɨɞɢɧ ɫɬɚɤɚɧ. |
ɇɚɣɞɢɬɟ |
ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɷɬɨ ɛɭɞɟɬ ɜɢɲɧɟɜɵɣ ɣɨɝɭɪɬ. |
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Ɉɬɜɟɬ: 
20 ȼɵɫɨɬɭ h (ɜ ɦ), ɧɚ ɤɨɬɨɪɨɣ ɱɟɪɟɡ t ɫɟɤɭɧɞ ɨɤɚɠɟɬɫɹ ɬɟɥɨ, ɫɜɨɛɨɞɧɨ ɩɚɞɚɸɳɟɟ ɫ ɧɟɤɨɬɨɪɨɣ ɜɵɫɨɬɵ H (ɜ ɦ), ɦɨɠɧɨ ɩɪɢɛɥɢɠɟɧɧɨ ɜɵɱɢɫɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ
h H 5t2. ɇɚ ɤɚɤɨɣ ɜɵɫɨɬɟ ɨɤɚɠɟɬɫɹ ɬɟɥɨ ɱɟɪɟɡ 3 ɫɟɤɭɧɞɵ ɩɨɥɺɬɚ ɫ 50- ɬɢɦɟɬɪɨɜɨɣ ɜɵɫɨɬɵ?
Ɉɬɜɟɬ: 
© 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 |
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 5 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 9 |
ɑɚɫɬɶ 2
ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ 21–26 ɢɫɩɨɥɶɡɭɣɬɟ ɨɬɞɟɥɶɧɵɣ ɥɢɫɬ. ɋɧɚɱɚɥɚ ɭɤɚɠɢɬɟ ɧɨɦɟɪ ɡɚɞɚɧɢɹ, ɚ ɡɚɬɟɦ ɡɚɩɢɲɢɬɟ ɟɝɨ ɪɟɲɟɧɢɟ ɢ ɨɬɜɟɬ. ɉɢɲɢɬɟ ɱɺɬɤɨ ɢ ɪɚɡɛɨɪɱɢɜɨ.
Ɇ ɞ ɥɶ "Ⱥɥɝɟ ɪ "
21 |
ɍɩɪɨɫɬɢɬɟ ɜɵɪɚɠɟɧɢɟ |
10 |
2 |
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22 |
Ɉɞɢɧ ɢɡ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ 5x2 |
2x |
3p |
0 ɪɚɜɟɧ 1. ɇɚɣɞɢɬɟ ɜɬɨɪɨɣ ɤɨɪɟɧɶ. |
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23 |
ɇɚɣɞɢɬɟ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɟ ɜɵɪɚɠɟɧɢɹ ɢ ɡɧɚɱɟɧɢɹ x ɢ y, ɩɪɢ ɤɨɬɨɪɵɯ ɨɧɨ |
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ɞɨɫɬɢɝɚɟɬɫɹ |
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6x y 5 |
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3x 2y 1 |
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Ɇ ɞɭɥɶ "Ƚɟ ɦɟɬɪɢɹ"
24ɇɚɣɞɢɬɟ ɜɟɥɢɱɢɧɭ ɭɝɥɚ DOB, ɟɫɥɢ OE – ɛɢɫɫɟɤɬɪɢɫɚ ɭɝɥɚ AOC, OD – ɛɢɫɫɟɤɬɪɢɫɚ ɭɝɥɚ COB.
25 ȼ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦɟ ABCD ɬɨɱɤɚ M — ɫɟɪɟɞɢɧɚ ɫɬɨɪɨɧɵ AB. ɂɡɜɟɫɬɧɨ, ɱɬɨ MC MD. Ⱦɨɤɚɠɢɬɟ, ɱɬɨ ɞɚɧɧɵɣ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦ — ɩɪɹɦɨɭɝɨɥɶɧɢɤ.
26Ɉɫɧɨɜɚɧɢɟ AC ɪɚɜɧɨɛɟɞɪɟɧɧɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ABC ɪɚɜɧɨ 12. Ɉɤɪɭɠɧɨɫɬɶ ɪɚɞɢɭɫɚ 8 ɫ ɰɟɧɬɪɨɦ ɜɧɟ ɷɬɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɤɚɫɚɟɬɫɹ ɩɪɨɞɨɥɠɟɧɢɹ ɛɨɤɨɜɵɯ ɫɬɨɪɨɧ ɬɪɟɭɝɨɥɶɧɢɤɚ ɢ ɤɚɫɚɟɬɫɹ ɨɫɧɨɜɚɧɢɹ AC ɜ ɟɝɨ ɫɟɪɟɞɢɧɟ. ɇɚɣɞɢɬɟ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ, ɜɩɢɫɚɧɧɨɣ ɜ ɬɪɟɭɝɨɥɶɧɢɤ ABC.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
Ⱦɢɚɝɧɨɫɬɢɱɟɫɤɚɹ ɪɚɛɨɬɚ ʋ 1
ɩɨ ɆȺɌȿɆȺɌɂɄȿ
2 ɨɤɬɹɛɪɹ 2012 ɝɨɞɚ
9 ɤɥɚɫɫ
ȼɚɪɢɚɧɬ 6
Ɋɚɣɨɧ Ƚɨɪɨɞ (ɧɚɫɟɥɺɧɧɵɣ ɩɭɧɤɬ)
ɒɤɨɥɚ
Ʉɥɚɫɫ
Ɏɚɦɢɥɢɹ
ɂɦɹ
Ɉɬɱɟɫɬɜɨ
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 6 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 2 |
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ɂɧɫɬɪɭɤɰɢɹ ɩɨ ɜɵɩɨɥɧɟɧɢɸ ɪɚɛɨɬɵ |
Ɉɛɳɟɟ ɜɪɟɦɹ ɷɤɡɚɦɟɧɚ 4 ɱɚɫɚ (240 ɦɢɧɭɬ).
ȼɫɟɝɨ ɜ ɪɚɛɨɬɟ 26 ɡɚɞɚɧɢɣ, ɢɡ ɤɨɬɨɪɵɯ 20 ɡɚɞɚɧɢɣ ɛɚɡɨɜɨɝɨ ɭɪɨɜɧɹ (ɑɚɫɬɶ I) ɢ 6 ɡɚɞɚɧɢɣ ɩɨɜɵɲɟɧɧɨɝɨ ɭɪɨɜɧɹ (ɑɚɫɬɶ II).
Ɋɚɛɨɬɚ ɫɨɫɬɨɢɬ ɢɡ ɬɪɺɯ ɦɨɞɭɥɟɣ «Ⱥɥɝɟɛɪɚ», «Ƚɟɨɦɟɬɪɢɹ», «Ɋɟɚɥɶɧɚɹ ɦɚɬɟɦɚɬɢɤɚ». Ɇɨɞɭɥɶ «Ⱥɥɝɟɛɪɚ» ɫɨɞɟɪɠɢɬ 11 ɡɚɞɚɧɢɣ: ɜ ɱɚɫɬɢ I – 8 ɡɚɞɚɧɢɣ ɫ ɤɪɚɬɤɢɦ ɨɬɜɟɬɨɦ,
ɜɵɛɨɪɨɦ ɨɬɜɟɬɚ ɢ ɭɫɬɚɧɨɜɥɟɧɢɟɦ ɫɨɨɬɜɟɬɫɬɜɢɹ; ɜ ɱɚɫɬɢ II – 3 ɡɚɞɚɧɢɹ ɫ ɩɨɥɧɵɦ ɪɟɲɟɧɢɟɦ.
Ɇɨɞɭɥɶ «Ƚɟɨɦɟɬɪɢɹ» ɫɨɞɟɪɠɢɬ 8 ɡɚɞɚɧɢɣ: ɜ ɱɚɫɬɢ I – 5 ɡɚɞɚɧɢɣ ɫ ɤɪɚɬɤɢɦ ɨɬɜɟɬɨɦ, ɜ ɱɚɫɬɢ II – 3 ɡɚɞɚɧɢɹ ɫ ɩɨɥɧɵɦ ɪɟɲɟɧɢɟɦ.
Ɇɨɞɭɥɶ «Ɋɟɚɥɶɧɚɹ ɦɚɬɟɦɚɬɢɤɚ» ɫɨɞɟɪɠɢɬ 7 ɡɚɞɚɧɢɣ: ɜɫɟ ɡɚɞɚɧɢɹ – ɜ ɱɚɫɬɢ I, ɫ ɤɪɚɬɤɢɦ ɨɬɜɟɬɨɦ ɢ ɜɵɛɨɪɨɦ ɨɬɜɟɬɚ.
ɋɧɚɱɚɥɚ ɜɵɩɨɥɧɹɣɬɟ ɡɚɞɚɧɢɹ ɑɚɫɬɢ I. ɇɚɱɚɬɶ ɫɨɜɟɬɭɟɦ ɫ ɬɨɝɨ ɦɨɞɭɥɹ, ɡɚɞɚɧɢɹ ɤɨɬɨɪɨɝɨ ɜɵɡɵɜɚɸɬ ɭ ȼɚɫ ɦɟɧɶɲɟ ɡɚɬɪɭɞɧɟɧɢɣ, ɡɚɬɟɦ ɩɟɪɟɯɨɞɢɬɟ ɤ ɞɪɭɝɢɦ ɦɨɞɭɥɹɦ.
Ⱦɥɹ ɷɤɨɧɨɦɢɢ ɜɪɟɦɟɧɢ ɩɪɨɩɭɫɤɚɣɬɟ ɡɚɞɚɧɢɟ, ɤɨɬɨɪɨɟ ɧɟ ɭɞɚɺɬɫɹ ɜɵɩɨɥɧɢɬɶ ɫɪɚɡɭ, ɢ |
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ɩɟɪɟɯɨɞɢɬɟ ɤ ɫɥɟɞɭɸɳɟɦɭ. ȿɫɥɢ |
ɭ ȼɚɫ ɨɫɬɚɧɟɬɫɹ ɜɪɟɦɹ, ȼɵ ɫɦɨɠɟɬɟ ɜɟɪɧɭɬɶɫɹ |
ɤ ɩɪɨɩɭɳɟɧɧɵɦ ɡɚɞɚɧɢɹɦ. |
ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɬ.ɞ. ɜɵɩɨɥɧɹɣɬɟ ɜ ɱɟɪɧɨɜɢɤɟ. |
ȼɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɜɵɱɢɫɥɟɧɢɹ, |
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ȿɫɥɢ ɡɚɞɚɧɢɟ ɫɨɞɟɪɠɢɬ ɪɢɫɭɧɨɤ, |
ɬɨ ɧɚ ɧɺɦ ɦɨɠɧɨ ɜɵɩɨɥɧɹɬɶ ɧɟɨɛɯɨɞɢɦɵɟ ȼɚɦ |
ɩɨɫɬɪɨɟɧɢɹ. Ɉɛɪɚɳɚɟɦ ȼɚɲɟ ɜɧɢɦɚɧɢɟ ɧɚ ɬɨ, ɱɬɨ ɡɚɩɢɫɢ ɜ ɱɟɪɧɨɜɢɤɟ ɧɟ ɛɭɞɭɬ ɭɱɢɬɵɜɚɬɶɫɹ ɩɪɢ ɨɰɟɧɢɜɚɧɢɢ ɪɚɛɨɬɵ. Ɋɟɤɨɦɟɧɞɭɟɦ ɜɧɢɦɚɬɟɥɶɧɨ ɱɢɬɚɬɶ ɭɫɥɨɜɢɟ
ɢ ɩɪɨɜɨɞɢɬɶ ɩɪɨɜɟɪɤɭ ɩɨɥɭɱɟɧɧɨɝɨ ɨɬɜɟɬɚ.
ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ ɫ ɜɵɛɨɪɨɦ ɨɬɜɟɬɚ ɨɛɜɟɞɢɬɟ ɧɨɦɟɪ ɜɵɛɪɚɧɧɨɝɨ ɨɬɜɟɬɚ ɜ ɷɤɡɚɦɟɧɚɰɢɨɧɧɨɣ ɪɚɛɨɬɟ. ȿɫɥɢ ȼɵ ɨɛɜɟɥɢ ɧɟ ɬɨɬ ɧɨɦɟɪ, ɬɨ ɡɚɱɟɪɤɧɢɬɟ ɨɛɜɟɞɺɧɧɵɣ ɧɨɦɟɪ ɤɪɟɫɬɢɤɨɦ ɢ ɡɚɬɟɦ ɨɛɜɟɞɢɬɟ ɧɨɦɟɪ ɩɪɚɜɢɥɶɧɨɝɨ ɨɬɜɟɬɚ.
ȿɫɥɢ ɜɚɪɢɚɧɬɵ ɨɬɜɟɬɚ ɤ ɡɚɞɚɧɢɸ ɧɟ ɩɪɢɜɨɞɹɬɫɹ, ɩɨɥɭɱɟɧɧɵɣ ɨɬɜɟɬ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɨɬɜɟɞɺɧɧɨɦ ɞɥɹ ɷɬɨɝɨ ɦɟɫɬɟ. ȼ ɫɥɭɱɚɟ ɡɚɩɢɫɢ ɧɟɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɡɚɱɟɪɤɧɢɬɟ ɟɝɨ ɢ ɡɚɩɢɲɢɬɟ ɪɹɞɨɦ ɧɨɜɵɣ.
ȿɫɥɢ ɜ ɡɚɞɚɧɢɢ ɬɪɟɛɭɟɬɫɹ ɭɫɬɚɧɨɜɢɬɶ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɧɟɤɨɬɨɪɵɦɢ ɨɛɴɟɤɬɚɦɢ,
ɜɩɢɲɢɬɟ ɜ ɩɪɢɜɟɞɺɧɧɭɸ ɜ ɨɬɜɟɬɟ ɬɚɛɥɢɰɭ ɩɨɞ ɤɚɠɞɨɣ ɛɭɤɜɨɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɰɢɮɪɭ.
Ɋɟɲɟɧɢɹ ɡɚɞɚɧɢɣ ɑɚɫɬɢ II ɢ ɨɬɜɟɬɵ ɤ ɧɢɦ ɡɚɩɢɫɵɜɚɸɬɫɹ ɧɚ ɨɬɞɟɥɶɧɨɦ ɥɢɫɬɟ. Ɍɟɤɫɬ ɡɚɞɚɧɢɹ ɦɨɠɧɨ ɧɟ ɩɟɪɟɩɢɫɵɜɚɬɶ, ɧɟɨɛɯɨɞɢɦɨ ɥɢɲɶ ɭɤɚɡɚɬɶ ɟɝɨ ɧɨɦɟɪ.
Ȼɚɥɥɵ, ɩɨɥɭɱɟɧɧɵɟ ȼɚɦɢ ɡɚ ɜɟɪɧɨ ɜɵɩɨɥɧɟɧɧɵɟ ɡɚɞɚɧɢɹ, ɫɭɦɦɢɪɭɸɬɫɹ. Ⱦɥɹ
ɭɫɩɟɲɧɨɝɨ ɩɪɨɯɨɠɞɟɧɢɹ ɢɬɨɝɨɜɨɣ ɚɬɬɟɫɬɚɰɢɢ ɧɟɨɛɯɨɞɢɦɨ ɧɚɛɪɚɬɶ ɜ ɫɭɦɦɟ ɧɟ ɦɟɧɟɟ 8 ɛɚɥɥɨɜ, ɢɡ ɧɢɯ ɧɟ ɦɟɧɟɟ ɞɜɭɯ ɛɚɥɥɨɜ ɩɨ ɤɚɠɞɨɦɭ ɢɡ ɦɨɞɭɥɟɣ.
ɀɟɥɚɟɦ ɭɫɩɟɯɚ!
ȼɧɢɦɚɧɢɟ! ȼɢɞɟɨɪɚɡɛɨɪ ɞɚɧɧɨɣ ɪɚɛɨɬɵ ɩɪɨɣɞɟɬ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
© 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 |
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 6 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 3 |
ɑɚɫɬɶ 1
Ɇɨɞɭɥɶ "Ⱥɥɝɟɛɪɚ"
1ɇɚɣɞɢɬɟ ɡɧɚɱɟɧɢɹ ɜɵɪɚɠɟɧɢɣ. ȼ ɨɬɜɟɬɟ ɭɤɚɠɢɬɟ ɧɨɦɟɪ ɧɚɢɦɟɧɶɲɟɝɨ ɢɡ ɧɚɣɞɟɧɧɵɯ ɡɧɚɱɟɧɢɣ.
1)1, 8 |
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Ɉɬɜɟɬ: 
2ȼɵɛɟɪɢɬɟ ɜɟɪɧɨɟ ɭɬɜɟɪɠɞɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɱɢɫɟɥ a ɢ b, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɧɚ ɱɢɫɥɨɜɨɣ ɩɪɹɦɨɣ.
1) a b 0 |
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3 ɍɤɚɠɢɬɟ ɞɜɚ ɫɨɫɟɞɧɢɯ ɰɟɥɵɯ ɱɢɫɥɚ, ɦɟɠɞɭ ɤɨɬɨɪɵɦɢ ɡɚɤɥɸɱɟɧɨ ɱɢɫɥɨ 3 11.
1) 3 ɢ 4 2) 9 ɢ 10 3) 11 ɢ 12 4) 99 ɢ 100
4 ɇɚɣɞɢɬɟ ɤɨɪɧɢ ɭɪɚɜɧɟɧɢɹ 2x2 13x 7 0.
Ɉɬɜɟɬ: 
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 6 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 4 |
5ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɝɪɚɮɢɤɢ ɬɪɺɯ ɮɭɧɤɰɢɣ, ɡɚɞɚɜɚɟɦɵɯ ɮɨɪɦɭɥɚɦɢ ɜɢɞɚ y kx. ɍɤɚɠɢɬɟ ɞɥɹ ɤɚɠɞɨɝɨ ɝɪɚɮɢɤɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɟɦɭ ɮɨɪɦɭɥɭ, ɜɵɛɪɚɜ ɟɺ ɢɡ ɱɢɫɥɚ ɩɪɢɜɟɞɺɧɧɵɯ ɧɢɠɟ.
ȽɊȺɎɂɄɂ
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6Ɂɚɩɢɲɢɬɟ ɜ ɨɬɜɟɬɟ ɧɨɦɟɪɚ ɜɟɪɧɵɯ ɪɚɜɟɧɫɬɜ.
1) (2 b)(b 2) 4 b2
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7 ɍɩɪɨɫɬɢɬɟ ɜɵɪɚɠɟɧɢɟ |
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b2, 1.
Ɉɬɜɟɬ: 
© 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 |
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 6 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 5 |
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8 Ɋɟɲɢɬɟ ɭɪɚɜɧɟɧɢɟ |
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Ɇɨɞɭɥɶ "Ƚɟɨɦɟɬɪɢɹ"
9ɉɟɪɢɦɟɬɪ ɪɚɜɧɨɫɬɨɪɨɧɧɟɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ABC ɪɚɜɟɧ 36 ɫɦ. ɇɚɣɞɢɬɟ ɞɥɢɧɭ ɫɪɟɞɧɟɣ ɥɢɧɢɢ ɷɬɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ.
Ɉɬɜɟɬ: 
10ɋɬɨɪɨɧɚ ɪɨɦɛɚ ɪɚɜɧɚ 20, ɚ ɨɫɬɪɵɣ ɭɝɨɥ ɪɚɜɟɧ 60q. ɇɚɣɞɢɬɟ ɞɥɢɧɭ ɦɟɧɶɲɟɣ ɞɢɚɝɨɧɚɥɢ ɪɨɦɛɚ.
Ɉɬɜɟɬ: 
11ɂɡ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ ɫɨ ɫɬɨɪɨɧɚɦɢ 6 ɫɦ ɢ 8 ɫɦ ɜɵɪɟɡɚɧ ɤɜɚɞɪɚɬ ɫɨ ɫɬɨɪɨɧɨɣ 4 ɫɦ. ɇɚɣɞɢɬɟ ɩɥɨɳɚɞɶ ɨɫɬɚɜɲɟɣɫɹ ɱɚɫɬɢ. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɫɦ2.
Ɉɬɜɟɬ: 
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 6 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 6 |
12 Ɍɨɱɤɚ O – ɰɟɧɬɪ ɨɤɪɭɠɧɨɫɬɢ, BAC |
70q (ɫɦ. ɪɢɫɭɧɨɤ). |
ɇɚɣɞɢɬɟ ɜɟɥɢɱɢɧɭ ɭɝɥɚ BOC (ɜ ɝɪɚɞɭɫɚɯ). |
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Ɉɬɜɟɬ: 
13ɍɤɚɠɢɬɟ ɜ ɨɬɜɟɬɟ ɧɨɦɟɪɚ ɧɟɜɟɪɧɵɯ ɭɬɜɟɪɠɞɟɧɢɣ.
1)Ⱦɜɚ ɭɝɥɚ ɫ ɨɛɳɟɣ ɫɬɨɪɨɧɨɣ ɧɚɡɵɜɚɸɬɫɹ ɫɦɟɠɧɵɦɢ.
2)ɇɚ ɩɪɹɦɨɣ ɦɨɠɧɨ ɨɬɥɨɠɢɬɶ ɬɨɥɶɤɨ ɨɞɢɧ ɨɬɪɟɡɨɤ ɡɚɞɚɧɧɨɣ ɞɥɢɧɵ.
3)ȿɫɥɢ ɬɪɢ ɫɬɨɪɨɧɵ ɨɞɧɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ ɬɪɺɦ ɫɬɨɪɨɧɚɦ ɞɪɭɝɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ, ɬɨ ɬɚɤɢɟ ɬɪɟɭɝɨɥɶɧɢɤɢ ɪɚɜɧɵ.
Ɉɬɜɟɬ: 
Ɇɨɞɭɥɶ "Ɋɟɚɥɶɧɚɹ ɦɚɬɟɦɚɬɢɤɚ"
14Ʉɭɪɢɧɵɟ ɹɣɰɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɢɯ ɦɚɫɫɵ ɩɨɞɪɚɡɞɟɥɹɸɬ ɧɚ ɩɹɬɶ ɤɚɬɟɝɨɪɢɣ: ɜɵɫɲɚɹ, ɨɬɛɨɪɧɚɹ, ɩɟɪɜɚɹ, ɜɬɨɪɚɹ ɢ ɬɪɟɬɶɹ. ɂɫɩɨɥɶɡɭɹ ɞɚɧɧɵɟ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɜ ɬɚɛɥɢɰɟ, ɨɩɪɟɞɟɥɢɬɟ, ɤ ɤɚɤɨɣ ɤɚɬɟɝɨɪɢɢ ɨɬɧɨɫɢɬɫɹ ɹɣɰɨ, ɦɚɫɫɨɣ 41,4 ɝ.
Ʉ ɬɟɝɨ ɹ |
Ɇ ɫɫ ɨɞɧɨɝɨ ɹ , ɧɟ ɦɟɧɟɟ, ɝ |
ȼɵɫɲɚɹ |
75,0 ɢ ɜɵɲɟ |
Ɉɬɛɨɪɧɚɹ |
65,0 - 74,9 |
ɉɟɪɜɚɹ |
55,0 - 64,9 |
ȼɬɨɪɚɹ |
45,0 - 54,9 |
Ɍɪɟɬɶɹ |
35,0 - 44,9 |
Ɉɬɜɟɬ: 
© 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 |
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 6 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 7 |
15ɇɚ ɬɪɟɧɢɪɨɜɤɟ ɜ 50-ɦɟɬɪɨɜɨɦ ɛɚɫɫɟɣɧɟ ɩɥɨɜɟɰ ɩɪɨɩɥɵɥ 200-ɦɟɬɪɨɜɭɸ ɞɢɫɬɚɧɰɢɸ. ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɩɥɨɜɰɨɦ ɢ ɬɨɱɤɨɣ ɫɬɚɪɬɚ ɨɬ ɜɪɟɦɟɧɢ ɞɜɢɠɟɧɢɹ ɩɥɨɜɰɚ. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɫɫɬɨɹɧɢɟ (ɜ ɦɟɬɪɚɯ), ɤɨɬɨɪɨɟ ɨɫɬɚɥɨɫɶ ɩɪɨɩɥɵɬɶ ɩɥɨɜɰɭ ɱɟɪɟɡ 2 ɦɢɧɭɬɵ ɨɬ ɧɚɱɚɥɚ ɡɚɩɥɵɜɚ.
Ɉɬɜɟɬ: 
16ɋɩɨɪɬɢɜɧɵɣ ɦɚɝɚɡɢɧ ɩɪɨɜɨɞɢɬ ɚɤɰɢɸ: «Ʌɸɛɚɹ ɮɭɬɛɨɥɤɚ ɩɨ ɰɟɧɟ 200 ɪ. ɉɪɢ ɩɨɤɭɩɤɟ ɞɜɭɯ ɮɭɬɛɨɥɨɤ – ɫɤɢɞɤɚ ɧɚ ɜɬɨɪɭɸ 80%». ɋɤɨɥɶɤɨ ɪɭɛɥɟɣ ɩɪɢɞɺɬɫɹ ɡɚɩɥɚɬɢɬɶ ɡɚ ɩɨɤɭɩɤɭ ɞɜɭɯ ɮɭɬɛɨɥɨɤ?
Ɉɬɜɟɬ: 
17ɑɟɥɨɜɟɤ, ɪɨɫɬ ɤɨɬɨɪɨɝɨ 2 ɦ, ɫɬɨɢɬ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 3,5 ɦ ɨɬ ɭɥɢɱɧɨɝɨ ɮɨɧɚɪɹ. ɉɪɢ ɷɬɨɦ ɞɥɢɧɚ ɟɝɨ ɬɟɧɢ ɪɚɜɧɚ 1 ɦ. Ɉɩɪɟɞɟɥɢɬɟ ɜɵɫɨɬɭ ɮɨɧɚɪɹ (ɜ ɦ).
Ɉɬɜɟɬ: 
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 6 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 8 |
18ɇɚ ɞɢɚɝɪɚɦɦɟ ɩɪɟɞɫɬɚɜɥɟɧɚ ɢɧɮɨɪɦɚɰɢɹ ɨ ɤɨɥɢɱɟɫɬɜɟ ɫɨɬɨɜɵɯ ɬɟɥɟɮɨɧɨɜ, ɩɪɨɞɚɧɧɵɯ ɱɟɬɵɪɶɦɹ ɜɟɞɭɳɢɦɢ ɬɨɪɝɨɜɵɦɢ ɤɨɦɩɚɧɢɹɦɢ ɜ 2004 ɝ. ɉɪɢɦɟɪɧɨ ɜɨ ɫɤɨɥɶɤɨ ɪɚɡ ɤɨɦɩɚɧɢɟɣ ȿɜɪɨɫɟɬɶ ɛɵɥɨ ɩɪɨɞɚɧɨ ɛɨɥɶɲɟ ɬɟɥɟɮɨɧɨɜ, ɱɟɦ ɤɨɦɩɚɧɢɟɣ Ⱦɢɤɫɢɫ?
Ɉɬɜɟɬ: 
19 ɇɚ ɫɬɨɥɟ ɫɬɨɹɬ |
ɫɬɚɤɚɧɵ ɫ ɮɪɭɤɬɨɜɵɦɢ ɣɨɝɭɪɬɚɦɢ, ɨɞɢɧɚɤɨɜɵɦɢ |
ɧɚ ɜɢɞ: |
9 ɫ ɜɢɲɧɺɜɵɦ ɢ |
6 ɫ ɤɥɭɛɧɢɱɧɵɦ. Ʉɚɬɹ ɧɚɭɝɚɞ ɛɟɪɟɬ ɨɞɢɧ ɫɬɚɤɚɧ. |
ɇɚɣɞɢɬɟ |
ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɷɬɨ ɛɭɞɟɬ ɤɥɭɛɧɢɱɧɵɣ ɣɨɝɭɪɬ. |
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Ɉɬɜɟɬ: 
20ȼɵɫɨɬɭ H (ɜ ɦ), ɧɚ ɤɨɬɨɪɨɣ ɱɟɪɟɡ T Cɟɤɭɧɞ ɨɤɚɠɟɬɫɹ ɬɟɥɨ, ɛɪɨɲɟɧɧɨɟ ɜɟɪɬɢɤɚɥɶɧɨ ɜɜɟɪɯ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ V ɦ/ɫ, ɦɨɠɧɨ ɩɪɢɛɥɢɠɟɧɧɨ
ɜɵɱɢɫɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ H VT |
5T2. ɇɚ ɫɤɨɥɶɤɨ |
ɦɟɬɪɨɜ ɜɵɲɟ ɜɡɥɟɬɢɬ ɡɚ |
1 ɫɟɤɭɧɞɭ ɬɟɥɨ, ɩɨɞɛɪɨɲɟɧɧɨɟ |
ɜɟɪɬɢɤɚɥɶɧɨ ɜɜɟɪɯ, |
ɩɪɢ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ |
15 ɦ/ɫ, ɱɟɦ ɩɪɢ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ 10 ɦ/ɫ? |
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Ɉɬɜ ɬ: 
© 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 |
Ɇɚɬɟɦɚɬɢɤɚ. 9 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 6 |
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 9 |
ɑɚɫɬɶ 2
ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ 21–26 ɢɫɩɨɥɶɡɭɣɬɟ ɨɬɞɟɥɶɧɵɣ ɥɢɫɬ. ɋɧɚɱɚɥɚ ɭɤɚɠɢɬɟ ɧɨɦɟɪ ɡɚɞɚɧɢɹ, ɚ ɡɚɬɟɦ ɡɚɩɢɲɢɬɟ ɟɝɨ ɪɟɲɟɧɢɟ ɢ ɨɬɜɟɬ. ɉɢɲɢɬɟ ɱɺɬɤɨ ɢ ɪɚɡɛɨɪɱɢɜɨ.
Ɇ ɞ ɥɶ "Ⱥɥɝɟ ɪ "
21 |
ɍɩɪɨɫɬɢɬɟ ɜɵɪɚɠɟɧɢɟ |
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15 3 |
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Ɉɞɢɧ ɢɡ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ 4x2 |
x |
3m 0 ɪɚɜɟɧ 1. ɇɚɣɞɢɬɟ ɜɬɨɪɨɣ ɤɨɪɟɧɶ. |
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23 |
ɇɚɣɞɢɬɟ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɟ ɜɵɪɚɠɟɧɢɹ ɢ ɡɧɚɱɟɧɢɹ x ɢ y, ɩɪɢ ɤɨɬɨɪɵɯ ɨɧɨ |
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ɞɨɫɬɢɝɚɟɬɫɹ: |
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3x 4y 1 |
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x 5y |
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Ɇ ɞɭɥɶ "Ƚɟ ɦɟɬɪɢɹ"
24ɇɚɣɞɢɬɟ ɜɟɥɢɱɢɧɭ ɭɝɥɚ AOE, ɟɫɥɢ OE – ɛɢɫɫɟɤɬɪɢɫɚ ɭɝɥɚ AOC, OD – ɛɢɫɫɟɤɬɪɢɫɚ ɭɝɥɚ COB.
25 ȼ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦɟ ABCD ɬɨɱɤɚ K — ɫɟɪɟɞɢɧɚ ɫɬɨɪɨɧɵ AB. ɂɡɜɟɫɬɧɨ, ɱɬɨ KC KD. Ⱦɨɤɚɠɢɬɟ, ɱɬɨ ɞɚɧɧɵɣ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦ — ɩɪɹɦɨɭɝɨɥɶɧɢɤ.
26Ɉɫɧɨɜɚɧɢɟ AC ɪɚɜɧɨɛɟɞɪɟɧɧɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ABC ɪɚɜɧɨ 8. Ɉɤɪɭɠɧɨɫɬɶ ɪɚɞɢɭɫɚ 6 ɫ ɰɟɧɬɪɨɦ ɜɧɟ ɷɬɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɤɚɫɚɟɬɫɹ ɩɪɨɞɨɥɠɟɧɢɹ ɛɨɤɨɜɵɯ ɫɬɨɪɨɧ ɬɪɟɭɝɨɥɶɧɢɤɚ ɢ ɤɚɫɚɟɬɫɹ ɨɫɧɨɜɚɧɢɹ AC ɜ ɟɝɨ ɫɟɪɟɞɢɧɟ. ɇɚɣɞɢɬɟ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ, ɜɩɢɫɚɧɧɨɣ ɜ ɬɪɟɭɝɨɥɶɧɢɤ ABC.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ