d12mat101_9
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ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 11 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 7 |
ȿɣɛɞɨɩɬɭɣɲɠɬɥɛɺ ɫɛɜɩɭɛ ʌ 1 |
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ɪɩ ɇȻɍɀɇȻɍɃɅɀ |
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ɒɛɬɭɷ 2 |
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22 ɧɛɺ 2012 ɞɩɟɛ |
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ȿɦɺ ɢɛɪɣɬɣ ɫɠɳɠɨɣɤ ɣ ɩɭɝɠɭɩɝ ɨɛ ɢɛɟɛɨɣɺ C1–C6 ɣɬɪɩɦɷɢɮɤɭɠ |
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ɜɦɛɨɥ ɩɭɝɠɭɩɝ ʌ 2. ɂɛɪɣɳɣɭɠ ɬɨɛɲɛɦɛ ɨɩɧɠɫ ɝɶɪɩɦɨɺɠɧɩɞɩ |
10 ɥɦɛɬɬ |
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ɢɛɟɛɨɣɺ, ɛ ɢɛɭɠɧ ɪɩɦɨɩɠ ɩɜɩɬɨɩɝɛɨɨɩɠ ɫɠɳɠɨɣɠ ɣ ɩɭɝɠɭ. |
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C1 |
ɛ) ɋɠɳɣɭɠ ɮɫɛɝɨɠɨɣɠ sin2x 2 |
3 cos2x 6sinx 6 |
3 cosx |
0. |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
Ƚɛɫɣɛɨɭ 12 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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ªʌ; |
2ʌº. |
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¬2 |
¼ |
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C2 |
Ƚ ɪɫɛɝɣɦɷɨɩɤ ɲɠɭɶɫɻɰɮɞɩɦɷɨɩɤ ɪɣɫɛɧɣɟɠ SABCD ɝɬɠ ɫɻɜɫɛ ɫɛɝɨɶ 4. |
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ɍɩɲɥɣ M ɣ |
K – ɬɠɫɠɟɣɨɶ |
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ɜɩɥɩɝɶɰ |
ɫɻɜɠɫ SB ɣ SC ɬɩɩɭɝɠɭɬɭɝɠɨɨɩ. |
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Ɉɛɤɟɣɭɠ ɮɞɩɦ ɧɠɡɟɮ ɪɦɩɬɥɩɬɭɺɧɣ AMK ɣ ADS. |
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C3 |
ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ |
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(x |
2 |
5, 6x 7, 84)(x 2, 5) t 0, |
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° |
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d 5. |
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x |
2 |
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¯ |
x 3 |
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C4 |
Ɋɦɩɴɛɟɷ |
ɭɫɛɪɠɱɣɣ |
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ABCD ɫɛɝɨɛ |
270. |
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ȿɣɛɞɩɨɛɦɣ |
AB ɣ |
CD |
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ɪɠɫɠɬɠɥɛɹɭɬɺ ɝ ɭɩɲɥɠ O. ɉɭɫɠɢɥɣ, |
ɬɩɠɟɣɨɺɹɴɣɠ |
ɬɠɫɠɟɣɨɮ |
P |
ɋɛɤɩɨ |
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ɩɬɨɩɝɛɨɣɺ |
AD ɬ ɝɠɫɳɣɨɛɧɣ |
B ɣ C, |
ɪɠɫɠɬɠɥɛɹɭɬɺ |
ɬ ɟɣɛɞɩɨɛɦɺɧɣ |
Ⱦɩɫɩɟ (ɨɛɬɠɦɻɨɨɶɤ ɪɮɨɥɭ) |
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ɭɫɛɪɠɱɣɣ ɝ ɭɩɲɥɛɰ M ɣ N. Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɭɫɠɮɞɩɦɷɨɣɥɛ MON, |
ɠɬɦɣ |
ɓɥɩɦɛ |
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ɩɟɨɩ ɣɢ ɩɬɨɩɝɛɨɣɤ ɭɫɛɪɠɱɣɣ ɝɟɝɩɠ ɧɠɨɷɳɠ ɟɫɮɞɩɞɩ. |
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Ʌɦɛɬɬ |
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C5 |
Ɋɫɣ |
ɥɛɥɣɰ |
a ɮɫɛɝɨɠɨɣɠ |
x2 2x 3 2a |
x a 3 ɣɧɠɠɭ |
ɫɩɝɨɩ |
ɭɫɣ |
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ɥɩɫɨɺ? |
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C6 |
Ɍɮɧɧɛ ɪɺɭɣ ɨɛɣɧɠɨɷɳɣɰ ɨɛɭɮɫɛɦɷɨɶɰ ɟɠɦɣɭɠɦɠɤ ɨɛɭɮɫɛɦɷɨɩɞɩ ɲɣɬɦɛ |
ɏɛɧɣɦɣɺ |
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ɫɛɝɨɛ 17, ɛ ɬɮɧɧɛ ɲɠɭɶɫɠɰ ɨɛɣɜɩɦɷɳɣɰ ɠɞɩ ɟɠɦɣɭɠɦɠɤ ɫɛɝɨɛ 427. |
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Ɉɛɤɟɣɭɠ ɲɣɬɦɩ. |
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Ƀɧɺ |
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ɉɭɲɠɬɭɝɩ |
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© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ |
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ |
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ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 12 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 2
Ƀɨɬɭɫɮɥɱɣɺ ɪɩ ɝɶɪɩɦɨɠɨɣɹ ɫɛɜɩɭɶ
Ɉɛ ɝɶɪɩɦɨɠɨɣɠ ɸɥɢɛɧɠɨɛɱɣɩɨɨɩɤ ɫɛɜɩɭɶ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɟɛɻɭɬɺ 4 ɲɛɬɛ (240 ɧɣɨ). ɋɛɜɩɭɛ ɬɩɬɭɩɣɭ ɣɢ ɟɝɮɰ ɲɛɬɭɠɤ ɣ ɬɩɟɠɫɡɣɭ 20 ɢɛɟɛɨɣɤ.
ɒɛɬɭɷ 1 ɬɩɟɠɫɡɣɭ 14 ɢɛɟɛɨɣɤ ɬ ɥɫɛɭɥɣɧ ɩɭɝɠɭɩɧ (Ƚ1–Ƚ14) ɜɛɢɩɝɩɞɩ ɮɫɩɝɨɺ ɪɩ ɧɛɭɠɫɣɛɦɮ ɥɮɫɬɛ ɧɛɭɠɧɛɭɣɥɣ. ɂɛɟɛɨɣɺ ɲɛɬɭɣ 1 ɬɲɣɭɛɹɭɬɺ ɝɶɪɩɦɨɠɨɨɶɧɣ, ɠɬɦɣ ɸɥɢɛɧɠɨɮɠɧɶɤ ɟɛɦ ɝɠɫɨɶɤ ɩɭɝɠɭ ɝ ɝɣɟɠ ɱɠɦɩɞɩ ɲɣɬɦɛ ɣɦɣ ɥɩɨɠɲɨɩɤ ɟɠɬɺɭɣɲɨɩɤ ɟɫɩɜɣ.
ɒɛɬɭɷ 2 ɬɩɟɠɫɡɣɭ 6 ɜɩɦɠɠ ɬɦɩɡɨɶɰ ɢɛɟɛɨɣɤ (Ɍ1–Ɍ6) ɪɩ ɧɛɭɠɫɣɛɦɮ ɥɮɫɬɛ ɧɛɭɠɧɛɭɣɥɣ. Ɋɫɣ ɣɰ ɝɶɪɩɦɨɠɨɣɣ ɨɛɟɩ ɢɛɪɣɬɛɭɷ ɪɩɦɨɩɠ ɫɠɳɠɨɣɠ ɣ ɩɭɝɠɭ.
Ɍɩɝɠɭɮɠɧ ɟɦɺ ɸɥɩɨɩɧɣɣ ɝɫɠɧɠɨɣ ɪɫɩɪɮɬɥɛɭɷ ɢɛɟɛɨɣɠ, ɥɩɭɩɫɩɠ ɨɠ ɮɟɛɠɭɬɺ ɝɶɪɩɦɨɣɭɷ ɬɫɛɢɮ, ɣ ɪɠɫɠɰɩɟɣɭɷ ɥ ɬɦɠɟɮɹɴɠɧɮ. Ʌ ɝɶɪɩɦɨɠɨɣɹ ɪɫɩɪɮɴɠɨɨɶɰ ɢɛɟɛɨɣɤ ɧɩɡɨɩ ɝɠɫɨɮɭɷɬɺ, ɠɬɦɣ ɮ Ƚɛɬ ɩɬɭɛɨɠɭɬɺ ɝɫɠɧɺ.
Ɂɠɦɛɠɧ ɮɬɪɠɰɛ!
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 12 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 3 |
ɒɛɬɭɷ 1
ɉɭɝɠɭɩɧ ɨɛ ɢɛɟɛɨɣɺ Ƚ1–Ƚ14 ɟɩɦɡɨɩ ɜɶɭɷ ɱɠɦɩɠ ɲɣɬɦɩ ɣɦɣ ɥɩɨɠɲɨɛɺ ɟɠɬɺɭɣɲɨɛɺ ɟɫɩɜɷ. ɉɭɝɠɭ ɬɦɠɟɮɠɭ ɢɛɪɣɬɛɭɷ ɝ ɜɦɛɨɥ ɩɭɝɠɭɩɝ ʌ 1 ɬɪɫɛɝɛ ɩɭ ɨɩɧɠɫɛ ɝɶɪɩɦɨɺɠɧɩɞɩ ɢɛɟɛɨɣɺ, ɨɛɲɣɨɛɺ ɬ ɪɠɫɝɩɤ ɥɦɠɭɩɲɥɣ. Ʌɛɡɟɮɹ ɱɣɯɫɮ, ɢɨɛɥ ɧɣɨɮɬ ɣ ɢɛɪɺɭɮɹ ɪɣɳɣɭɠ ɝ ɩɭɟɠɦɷɨɩɤ ɥɦɠɭɩɲɥɠ ɝ ɬɩɩɭɝɠɭɬɭɝɣɣ ɬ ɪɫɣɝɠɟɻɨɨɶɧɣ ɝ ɜɦɛɨɥɠ ɩɜɫɛɢɱɛɧɣ. ɀɟɣɨɣɱɶ ɣɢɧɠɫɠɨɣɤ ɪɣɬɛɭɷ ɨɠ ɨɮɡɨɩ.
B1 Ƚ ɥɝɛɫɭɣɫɠ, ɞɟɠ ɪɫɩɡɣɝɛɠɭ Ȼ., ɮɬɭɛɨɩɝɦɠɨ ɪɫɣɜɩɫ ɮɲɻɭɛ ɫɛɬɰɩɟɛ ɞɩɫɺɲɠɤ ɝɩɟɶ (ɬɲɻɭɲɣɥ). 1 ɧɛɫɭɛ ɬɲɻɭɲɣɥ ɪɩɥɛɢɶɝɛɦ ɫɛɬɰɩɟ 934 ɥɮɜ.ɧ. ɝɩɟɶ, ɛ 1 ɛɪɫɠɦɺ — 942 ɥɮɜ.ɧ. Ʌɛɥɮɹ ɬɮɧɧɮ ɟɩɦɡɠɨ ɢɛɪɦɛɭɣɭɷ Ȼ. ɢɛ ɞɩɫɺɲɮɹ ɝɩɟɮ ɢɛ ɧɛɫɭ, ɠɬɦɣ ɱɠɨɛ ɢɛ ɩɟɣɨ ɥɮɜ.ɧ. ɞɩɫɺɲɠɤ ɝɩɟɶ ɬɩɬɭɛɝɦɺɠɭ 82 ɫ. 50 ɥɩɪ? ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɫɮɜɦɺɰ.
ɉɭɝɠɭ: 
B2 Ɉɛ ɟɣɛɞɫɛɧɧɠ ɪɩɥɛɢɛɨ ɬɫɠɟɨɣɤ ɜɛɦɦ ɮɲɛɬɭɨɣɥɩɝ 10 ɬɭɫɛɨ ɝ ɭɠɬɭɣɫɩɝɛɨɣɣ ɮɲɛɴɣɰɬɺ 8-ɞɩ ɥɦɛɬɬɛ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɝ 2007 ɞɩɟɮ (ɪɩ 1000ɜɛɦɦɷɨɩɤ ɳɥɛɦɠ).
Ɋɩ ɟɛɨɨɶɧ ɟɣɛɞɫɛɧɧɶ ɨɛɤɟɣɭɠ ɬɫɠɟɨɣɤ ɜɛɦɦ ɮɲɛɬɭɨɣɥɩɝ ɣɢ ȼɩɦɞɛɫɣɣ.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 12 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 4 |
B3 Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɭɫɠɮɞɩɦɷɨɣɥɛ, |
ɣɢɩɜɫɛɡɻɨɨɩɞɩ ɨɛ |
ɥɦɠɭɲɛɭɩɤ ɜɮɧɛɞɠ ɬ ɫɛɢɧɠɫɩɧ ɥɦɠɭɥɣ 1 ɬɧ u 1 ɬɧ (ɬɧ. ɫɣɬ.). ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɝɛɟɫɛɭɨɶɰ ɬɛɨɭɣɧɠɭɫɛɰ.
ɉɭɝɠɭ: 
B4 Ƚ ɭɛɜɦɣɱɠ ɟɛɨɶ ɭɛɫɣɯɶ ɨɛ ɮɬɦɮɞɣ ɭɫɠɰ ɯɣɫɧ ɭɛɥɬɣ. Ɋɫɠɟɪɩɦɛɞɛɠɭɬɺ ɪɩɠɢɟɥɛ ɟɦɣɭɠɦɷɨɩɬɭɷɹ 60 ɧɣɨɮɭ. Ɉɮɡɨɩ ɝɶɜɫɛɭɷ ɯɣɫɧɮ, ɝ ɥɩɭɩɫɩɤ ɢɛɥɛɢ ɜɮɟɠɭ ɬɭɩɣɭɷ ɟɠɳɠɝɦɠ ɝɬɠɞɩ. Ɍɥɩɦɷɥɩ ɫɮɜɦɠɤ ɜɮɟɠɭ ɬɭɩɣɭɷ ɸɭɩɭ ɢɛɥɛɢ?
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Ɋɫɩɟɩɦɡɣɭɠɦɷɨɩɬɭɷ |
Ɍɭɩɣɧɩɬɭɷ 1 ɧɣɨɮɭɶ |
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ɏɣɫɧɛ |
Ɋɩɟɛɲɛ |
ɬɝɠɫɰ |
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ɣ ɬɭɩɣɧɩɬɭɷ |
ɪɫɩɟɩɦɡɣɭɠɦɷɨɩɬɭɣ |
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ɭɛɥɬɣ |
ɧɛɳɣɨɶ |
ɧɣɨɣɧɛɦɷɨɩɤ |
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ɧɣɨɣɧɛɦɷɨɩɤ |
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ɪɩɠɢɟɥɣ |
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ɪɩɠɢɟɥɣ (ɝ ɫɮɜ.) |
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Ȼ |
350 |
ɨɠɭ |
12 |
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ȼ |
ȼɠɬɪɦɛɭɨɩ |
10 ɧɣɨɮɭ – 200 ɫɮɜɦɠɤ |
19 |
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Ƚ |
180 |
15 ɧɣɨɮɭ – 300 ɫɮɜɦɠɤ |
15 |
* ɀɬɦɣ ɪɩɠɢɟɥɛ ɪɫɩɟɩɦɡɛɠɭɬɺ ɧɠɨɷɳɠ ɮɥɛɢɛɨɨɩɞɩ ɝɫɠɧɠɨɣ, ɩɨɛ ɩɪɦɛɲɣɝɛɠɭɬɺ ɪɩ ɬɭɩɣɧɩɬɭɣ ɧɣɨɣɧɛɦɷɨɩɤ ɪɩɠɢɟɥɣ.
ɉɭɝɠɭ: 
B5 Ɉɛɤɟɣɭɠ ɥɩɫɠɨɷ ɮɫɛɝɨɠɨɣɺ: 32 4x 2.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 12 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5
B6 Ƚ ɭɫɠɮɞɩɦɷɨɣɥɠ ABC ɮɞɩɦ A ɫɛɝɠɨ 15q, ɛ ɮɞɦɶ B ɣ C ɩɬɭɫɶɠ. BD ɣ CE –
ɝɶɬɩɭɶ, ɪɠɫɠɬɠɥɛɹɴɣɠɬɺ ɝ ɭɩɲɥɠ O. Ɉɛɤɟɣɭɠ ɮɞɩɦ DOE. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɞɫɛɟɮɬɛɰ.
ɉɭɝɠɭ:
B7 Ɉɛɤɟɣɭɠ ɢɨɛɲɠɨɣɠ ɝɶɫɛɡɠɨɣɺ (1812 112) : 192.
ɉɭɝɠɭ: 
B8 Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ |
y f (x), ɩɪɫɠɟɠɦɻɨɨɩɤ ɨɛ |
ɣɨɭɠɫɝɛɦɠ ( 4; 7). Ɉɛɤɟɣɭɠ ɥɩɦɣɲɠɬɭɝɩ ɭɩɲɠɥ, ɝ ɥɩɭɩɫɶɰ ɥɛɬɛɭɠɦɷɨɛɺ ɥ |
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ɞɫɛɯɣɥɮ ɯɮɨɥɱɣɣ ɪɛɫɛɦɦɠɦɷɨɛ ɪɫɺɧɩɤ y |
11. |
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 12 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 6
B9 Ƚ |
ɪɫɺɧɩɮɞɩɦɷɨɩɧ |
ɪɛɫɛɦɦɠɦɠɪɣɪɠɟɠ ABCDA B C D ɣɢɝɠɬɭɨɩ, ɲɭɩ |
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1 |
1 |
1 |
1 |
BB1 |
4, AB 18, AD |
12. Ɉɛɤɟɣɭɠ ɟɦɣɨɮ ɟɣɛɞɩɨɛɦɣ DB1. |
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ɉɭɝɠɭ: 
B10 Ƚ ɬɜɩɫɨɣɥɠ ɜɣɦɠɭɩɝ ɪɩ ɜɣɩɦɩɞɣɣ ɝɬɠɞɩ 55 ɜɣɦɠɭɩɝ, ɝ 11 ɣɢ ɨɣɰ ɝɬɭɫɠɲɛɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɢɩɩɦɩɞɣɣ. Ɉɛɤɟɣɭɠ ɝɠɫɩɺɭɨɩɬɭɷ ɭɩɞɩ, ɲɭɩ ɝ ɬɦɮɲɛɤɨɩ ɝɶɜɫɛɨɨɩɧ ɨɛ ɸɥɢɛɧɠɨɠ ɜɣɦɠɭɠ ɳɥɩɦɷɨɣɥɮ ɨɠ ɟɩɬɭɛɨɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɢɩɩɦɩɞɣɣ.
ɉɭɝɠɭ: 
B11 Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɪɩɝɠɫɰɨɩɬɭɣ ɧɨɩɞɩɞɫɛɨɨɣɥɛ, ɣɢɩɜɫɛɡɠɨɨɩɞɩ ɨɛ ɫɣɬɮɨɥɠ. Ƚɬɠ ɟɝɮɞɫɛɨɨɶɠ ɮɞɦɶ ɧɨɩɞɩɞɫɛɨɨɣɥɛ ɪɫɺɧɶɠ.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 12 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 7 |
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B12 Ɉɠɜɩɦɷɳɩɤ ɧɺɲɣɥ ɜɫɩɬɛɹɭ ɪɩɟ ɩɬɭɫɶɧ ɮɞɦɩɧ |
Į ɥ ɪɦɩɬɥɩɤ |
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ɞɩɫɣɢɩɨɭɛɦɷɨɩɤ ɪɩɝɠɫɰɨɩɬɭɣ ɢɠɧɦɣ. ɇɛɥɬɣɧɛɦɷɨɛɺ ɝɶɬɩɭɛ ɪɩɦɻɭɛ |
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ɧɺɲɣɥɛ, |
ɝɶɫɛɡɠɨɨɛɺ |
ɝ ɧɠɭɫɛɰ, ɩɪɫɠɟɠɦɺɠɭɬɺ |
ɯɩɫɧɮɦɩɤ |
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Ȟ2 |
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H |
0 |
(1 cos2Į), ɞɟɠ Ȟ |
14 ɧ/ɬ — ɨɛɲɛɦɷɨɛɺ ɬɥɩɫɩɬɭɷ ɧɺɲɣɥɛ, ɛ g — |
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4g |
0 |
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(ɬɲɣɭɛɤɭɠ g 10 ɦ/ɫ2). |
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ɮɬɥɩɫɠɨɣɠ |
ɬɝɩɜɩɟɨɩɞɩ |
ɪɛɟɠɨɣɺ |
Ɋɫɣ ɥɛɥɩɧ |
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ɨɛɣɧɠɨɷɳɠɧ ɢɨɛɲɠɨɣɣ ɮɞɦɛ Į (ɝ ɞɫɛɟɮɬɛɰ) ɧɺɲɣɥ ɪɫɩɦɠɭɣɭ ɨɛɟ ɬɭɠɨɩɤ ɝɶɬɩɭɩɤ 6, 35 ɧ ɨɛ ɫɛɬɬɭɩɺɨɣɣ 1 ɧ?
ɉɭɝɠɭ: 
B13 ɇɩɭɩɫɨɛɺ ɦɩɟɥɛ ɪɫɩɳɦɛ ɪɫɩɭɣɝ ɭɠɲɠɨɣɺ ɫɠɥɣ 143 ɥɧ ɣ ɝɠɫɨɮɦɛɬɷ ɝ ɪɮɨɥɭ ɩɭɪɫɛɝɦɠɨɣɺ, ɢɛɭɫɛɭɣɝ ɨɛ ɩɜɫɛɭɨɶɤ ɪɮɭɷ ɨɛ 2 ɲɛɬɛ ɧɠɨɷɳɠ. Ɉɛɤɟɣɭɠ ɬɥɩɫɩɬɭɷ ɭɠɲɠɨɣɺ, ɠɬɦɣ ɬɥɩɫɩɬɭɷ ɦɩɟɥɣ ɝ ɨɠɪɩɟɝɣɡɨɩɤ ɝɩɟɠ ɫɛɝɨɛ 12 ɥɧ/ɲ. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɧ/ɲ.
ɉɭɝɠɭ:
B14 Ɉɛɤɟɣɭɠ ɭɩɲɥɮ ɧɣɨɣɧɮɧɛ ɯɮɨɥɱɣɣ y |
x2 4x 26. |
ɉɭɝɠɭ:
ɒɛɬɭɷ 2
ȿɦɺ ɢɛɪɣɬɣ ɫɠɳɠɨɣɤ ɣ ɩɭɝɠɭɩɝ ɨɛ ɢɛɟɛɨɣɺ C1–C6 ɣɬɪɩɦɷɢɮɤɭɠ ɜɦɛɨɥ ɩɭɝɠɭɩɝ ʌ 2. ɂɛɪɣɳɣɭɠ ɬɨɛɲɛɦɛ ɨɩɧɠɫ ɝɶɪɩɦɨɺɠɧɩɞɩ ɢɛɟɛɨɣɺ, ɛ ɢɛɭɠɧ ɪɩɦɨɩɠ ɩɜɩɬɨɩɝɛɨɨɩɠ ɫɠɳɠɨɣɠ ɣ ɩɭɝɠɭ.
C1 |
ɛ) ɋɠɳɣɭɠ ɮɫɛɝɨɠɨɣɠ sin2x 2 3 sin2x 6cosx 6 3 sinx 0. |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
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ª 3ʌ; |
3ʌ |
º. |
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« |
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¬ |
2 ¼ |
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C2 |
Ƚ ɪɫɛɝɣɦɷɨɩɤ ɲɠɭɶɫɻɰɮɞɩɦɷɨɩɤ ɪɣɫɛɧɣɟɠ SABCD ɝɬɻ ɫɠɜɫɛ ɫɛɝɨɶ 4. |
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ɍɩɲɥɣ |
M ɣ K – ɬɠɫɠɟɣɨɶ ɜɩɥɩɝɶɰ ɫɻɜɠɫ SB ɣ SC ɬɩɩɭɝɠɭɬɭɝɠɨɨɩ. |
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Ɉɛɤɟɣɭɠ ɮɞɩɦ ɧɠɡɟɮ ɪɦɩɬɥɩɬɭɺɧɣ AMK ɣ BCS. |
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© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 12 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 8 |
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C3 |
ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ ɨɠɫɛɝɠɨɬɭɝ |
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2 |
3, 6x 3, 24)(x 1, 5) t 0, |
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d 5. |
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x 2 |
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C4 |
Ɋɦɩɴɛɟɷ |
ɭɫɛɪɠɱɣɣ |
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ABCD ɫɛɝɨɛ 675. |
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ȿɣɛɞɩɨɛɦɣ |
AC ɣ |
BD |
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ɪɠɫɠɬɠɥɛɹɭɬɺ ɝ ɭɩɲɥɠ O. ɉɭɫɠɢɥɣ, |
ɬɩɠɟɣɨɺɹɴɣɠ ɬɠɫɠɟɣɨɮ P ɩɬɨɩɝɛɨɣɺ |
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AD ɬ ɝɠɫɳɣɨɛɧɣ B ɣ C , ɪɠɫɠɬɠɥɛɹɭɬɺ ɬ |
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ɟɣɛɞɩɨɛɦɺɧɣ |
ɭɫɛɪɠɱɣɣ ɝ |
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ɭɩɲɥɛɰ M ɣ N. Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɭɫɠɮɞɩɦɷɨɣɥɛ MON, ɠɬɦɣ ɩɟɨɩ ɣɢ |
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ɩɬɨɩɝɛɨɣɤ ɭɫɛɪɠɱɣɣ ɝɟɝɩɠ ɧɠɨɷɳɠ ɟɫɮɞɩɞɩ. |
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C5 |
Ɋɫɣ ɥɛɥɣɰ |
a ɮɫɛɝɨɠɨɣɠ |
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x2 2x 3 |
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3 ɣɧɠɠɭ |
ɫɩɝɨɩ |
ɭɫɣ |
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ɥɩɫɨɺ? |
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C6 Ɍɮɧɧɛ ɪɺɭɣ ɨɛɣɧɠɨɷɳɣɰ ɨɛɭɮɫɛɦɷɨɶɰ ɟɠɦɣɭɠɦɠɤ ɨɛɭɮɫɛɦɷɨɩɞɩ ɲɣɬɦɛ ɫɛɝɨɛ 17, ɛ ɬɮɧɧɛ ɲɠɭɶɫɠɰ ɨɛɣɜɩɦɷɳɣɰ ɠɞɩ ɟɠɦɣɭɠɦɠɤ ɫɛɝɨɛ 671. Ɉɛɤɟɣɭɠ ɲɣɬɦɩ.
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ȿɣɛɞɨɩɬɭɣɲɠɬɥɛɺ ɫɛɜɩɭɛ ʌ 1
ɪɩ ɇȻɍɀɇȻɍɃɅɀ
22 ɧɛɺ 2012 ɞɩɟɛ
10 ɥɦɛɬɬ
Ƚɛɫɣɛɨɭ 13 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ)
ɋɛɤɩɨ Ⱦɩɫɩɟ (ɨɛɬɠɦɻɨɨɶɤ ɪɮɨɥɭ) ɓɥɩɦɛ Ʌɦɛɬɬ
ɏɛɧɣɦɣɺ
Ƀɧɺ
ɉɭɲɠɬɭɝɩ
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 13 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 2
Ƀɨɬɭɫɮɥɱɣɺ ɪɩ ɝɶɪɩɦɨɠɨɣɹ ɫɛɜɩɭɶ
Ɉɛ ɝɶɪɩɦɨɠɨɣɠ ɸɥɢɛɧɠɨɛɱɣɩɨɨɩɤ ɫɛɜɩɭɶ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɟɛɻɭɬɺ 4 ɲɛɬɛ (240 ɧɣɨ). ɋɛɜɩɭɛ ɬɩɬɭɩɣɭ ɣɢ ɟɝɮɰ ɲɛɬɭɠɤ ɣ ɬɩɟɠɫɡɣɭ 20 ɢɛɟɛɨɣɤ.
ɒɛɬɭɷ 1 ɬɩɟɠɫɡɣɭ 14 ɢɛɟɛɨɣɤ ɬ ɥɫɛɭɥɣɧ ɩɭɝɠɭɩɧ (Ƚ1–Ƚ14) ɜɛɢɩɝɩɞɩ ɮɫɩɝɨɺ ɪɩ ɧɛɭɠɫɣɛɦɮ ɥɮɫɬɛ ɧɛɭɠɧɛɭɣɥɣ. ɂɛɟɛɨɣɺ ɲɛɬɭɣ 1 ɬɲɣɭɛɹɭɬɺ ɝɶɪɩɦɨɠɨɨɶɧɣ, ɠɬɦɣ ɸɥɢɛɧɠɨɮɠɧɶɤ ɟɛɦ ɝɠɫɨɶɤ ɩɭɝɠɭ ɝ ɝɣɟɠ ɱɠɦɩɞɩ ɲɣɬɦɛ ɣɦɣ ɥɩɨɠɲɨɩɤ ɟɠɬɺɭɣɲɨɩɤ ɟɫɩɜɣ.
ɒɛɬɭɷ 2 ɬɩɟɠɫɡɣɭ 6 ɜɩɦɠɠ ɬɦɩɡɨɶɰ ɢɛɟɛɨɣɤ (Ɍ1–Ɍ6) ɪɩ ɧɛɭɠɫɣɛɦɮ ɥɮɫɬɛ ɧɛɭɠɧɛɭɣɥɣ. Ɋɫɣ ɣɰ ɝɶɪɩɦɨɠɨɣɣ ɨɛɟɩ ɢɛɪɣɬɛɭɷ ɪɩɦɨɩɠ ɫɠɳɠɨɣɠ ɣ ɩɭɝɠɭ.
Ɍɩɝɠɭɮɠɧ ɟɦɺ ɸɥɩɨɩɧɣɣ ɝɫɠɧɠɨɣ ɪɫɩɪɮɬɥɛɭɷ ɢɛɟɛɨɣɠ, ɥɩɭɩɫɩɠ ɨɠ ɮɟɛɠɭɬɺ ɝɶɪɩɦɨɣɭɷ ɬɫɛɢɮ, ɣ ɪɠɫɠɰɩɟɣɭɷ ɥ ɬɦɠɟɮɹɴɠɧɮ. Ʌ ɝɶɪɩɦɨɠɨɣɹ ɪɫɩɪɮɴɠɨɨɶɰ ɢɛɟɛɨɣɤ ɧɩɡɨɩ ɝɠɫɨɮɭɷɬɺ, ɠɬɦɣ ɮ Ƚɛɬ ɩɬɭɛɨɠɭɬɺ ɝɫɠɧɺ.
Ɂɠɦɛɠɧ ɮɬɪɠɰɛ!
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 13 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 3 |
ɒɛɬɭɷ 1
ɉɭɝɠɭɩɧ ɨɛ ɢɛɟɛɨɣɺ Ƚ1–Ƚ14 ɟɩɦɡɨɩ ɜɶɭɷ ɱɠɦɩɠ ɲɣɬɦɩ ɣɦɣ ɥɩɨɠɲɨɛɺ ɟɠɬɺɭɣɲɨɛɺ ɟɫɩɜɷ. ɉɭɝɠɭ ɬɦɠɟɮɠɭ ɢɛɪɣɬɛɭɷ ɝ ɜɦɛɨɥ ɩɭɝɠɭɩɝ ʌ 1 ɬɪɫɛɝɛ ɩɭ ɨɩɧɠɫɛ ɝɶɪɩɦɨɺɠɧɩɞɩ ɢɛɟɛɨɣɺ, ɨɛɲɣɨɛɺ ɬ ɪɠɫɝɩɤ ɥɦɠɭɩɲɥɣ. Ʌɛɡɟɮɹ ɱɣɯɫɮ, ɢɨɛɥ ɧɣɨɮɬ ɣ ɢɛɪɺɭɮɹ ɪɣɳɣɭɠ ɝ ɩɭɟɠɦɷɨɩɤ ɥɦɠɭɩɲɥɠ ɝ ɬɩɩɭɝɠɭɬɭɝɣɣ ɬ ɪɫɣɝɠɟɻɨɨɶɧɣ ɝ ɜɦɛɨɥɠ ɩɜɫɛɢɱɛɧɣ. ɀɟɣɨɣɱɶ ɣɢɧɠɫɠɨɣɤ ɪɣɬɛɭɷ ɨɠ ɨɮɡɨɩ.
B1 |
ɍɛɥɬɣɬɭ ɢɛ ɧɠɬɺɱ ɪɫɩɠɰɛɦ 6000 ɥɧ. Ɍɭɩɣɧɩɬɭɷ 1 ɦɣɭɫɛ ɜɠɨɢɣɨɛ |
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22,5 ɫɮɜɦɺ. Ɍɫɠɟɨɣɤ ɫɛɬɰɩɟ ɜɠɨɢɣɨɛ ɨɛ 100 ɥɧ ɬɩɬɭɛɝɦɺɠɭ 8 ɦ. Ɍɥɩɦɷɥɩ |
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ɫɮɜɦɠɤ ɪɩɭɫɛɭɣɦ ɭɛɥɬɣɬɭ ɨɛ ɜɠɨɢɣɨ ɢɛ ɸɭɩɭ ɧɠɬɺɱ? |
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ɉɭɝɠɭ: |
B2 |
Ɉɛ ɟɣɛɞɫɛɧɧɠ ɪɩɥɛɢɛɨ ɬɫɠɟɨɣɤ ɜɛɦɦ ɮɲɛɬɭɨɣɥɩɝ 8 ɬɭɫɛɨ ɝ ɭɠɬɭɣ- |
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ɫɩɝɛɨɣɣ ɮɲɛɴɣɰɬɺ 4-ɞɩ ɥɦɛɬɬɛ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɝ 2007 ɞɩɟɮ (ɪɩ 1000- |
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ɜɛɦɦɷɨɩɤ ɳɥɛɦɠ). |
Ɋɩ ɟɛɨɨɶɧ ɟɣɛɞɫɛɧɧɶ ɨɛɤɟɣɭɠ ɲɣɬɦɩ ɬɭɫɛɨ, ɝ ɥɩɭɩɫɶɰ ɬɫɠɟɨɣɤ ɜɛɦɦ ɝɶɳɠ, ɲɠɧ ɝ Ɍɦɩɝɛɥɣɣ.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 13 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 4 |
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B3 |
Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɭɫɛɪɠɱɣɣ, ɣɢɩɜɫɛɡɠɨɨɩɤ ɨɛ |
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ɥɦɠɭɲɛɭɩɤ ɜɮɧɛɞɠ ɬ ɫɛɢɧɠɫɩɧ ɥɦɠɭɥɣ 1 ɬɧ u 1 ɬɧ |
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(ɬɧ. ɫɣɬ.). ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɝɛɟɫɛɭɨɶɰ |
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ɬɛɨɭɣɧɠɭɫɛɰ. |
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ɉɭɝɠɭ: |
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B4 |
Ƚ ɬɫɠɟɨɠɧ ɞɫɛɡɟɛɨɣɨ Ȼ. ɝ ɟɨɠɝɨɩɠ ɝɫɠɧɺ ɫɛɬɰɩɟɮɠɭ 110 ɥȽɭ·ɲ |
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ɸɦɠɥɭɫɩɸɨɠɫɞɣɣ ɝ ɧɠɬɺɱ, ɛ ɝ ɨɩɲɨɩɠ ɝɫɠɧɺ — 155 ɥȽɭ·ɲ ɸɦɠɥɭɫɩ- |
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ɸɨɠɫɞɣɣ. ɋɛɨɷɳɠ ɮ Ȼ. ɝ ɥɝɛɫɭɣɫɠ ɜɶɦ ɮɬɭɛɨɩɝɦɠɨ ɩɟɨɩɭɛɫɣɯɨɶɤ |
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ɬɲɻɭɲɣɥ, ɣ |
ɝɬɹ |
ɸɦɠɥɭɫɩɸɨɠɫɞɣɹ |
ɩɨ |
ɩɪɦɛɲɣɝɛɦ |
ɪɩ |
ɭɛɫɣɯɮ |
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2,6 ɫɮɜ. ɢɛ ɥȽɭ·ɲ. Ⱦɩɟ ɨɛɢɛɟ Ȼ. ɮɬɭɛɨɩɝɣɦ ɟɝɮɰɭɛɫɣɯɨɶɤ ɬɲeɭɲɣɥ, ɪɫɣ |
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ɸɭɩɧ ɟɨɠɝɨɩɤ |
ɫɛɬɰɩɟ ɸɦɠɥɭɫɩɸɨɠɫɞɣɣ |
ɩɪɦɛɲɣɝɛɠɭɬɺ |
ɪɩ |
ɭɛɫɣɯɮ |
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2,6 ɫɮɜ. ɢɛ ɥȽɭ·ɲ, |
ɛ ɨɩɲɨɩɤ ɫɛɬɰɩɟ |
ɩɪɦɛɲɣɝɛɠɭɬɺ |
ɪɩ |
ɭɛɫɣɯɮ |
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0,8 ɫɮɜ. ɢɛ ɥȽɭ·ɲ. |
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Ƚ ɭɠɲɠɨɣɠ 12 ɧɠɬɺɱɠɝ ɫɠɡɣɧ ɪɩɭɫɠɜɦɠɨɣɺ ɣ ɭɛɫɣɯɶ ɩɪɦɛɭɶ |
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ɸɦɠɥɭɫɩɸɨɠɫɞɣɣ ɨɠ ɧɠɨɺɦɣɬɷ. Ɉɛ ɬɥɩɦɷɥɩ ɜɩɦɷɳɠ ɢɛɪɦɛɭɣɦ ɜɶ Ȼ. ɢɛ |
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ɸɭɩɭ ɪɠɫɣɩɟ, ɠɬɦɣ ɜɶ ɨɠ ɪɩɧɠɨɺɦɬɺ ɬɲɻɭɲɣɥ? ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɫɮɜɦɺɰ. |
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ɉɭɝɠɭ: |
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B5 |
Ɉɛɤɟɣɭɠ ɥɩɫɠɨɷ ɮɫɛɝɨɠɨɣɺ: log |
(2 x) |
2. |
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7 |
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ɉɭɝɠɭ: |
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B6 |
ɒɠɭɶɫɠɰɮɞɩɦɷɨɣɥ |
ABCD ɝɪɣɬɛɨ ɝ ɩɥɫɮɡɨɩɬɭɷ. Ɏɞɩɦ ABC ɫɛɝɠɨ 76q, |
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ɮɞɩɦCAD ɫɛɝɠɨ52q. Ɉɛɤɟɣɭɠ ɮɞɩɦ ABD. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɞɫɛɟɮɬɛɰ. |
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ɉɭɝɠɭ: 
B7 Ɉɛɤɟɣɭɠ ɢɨɛɲɠɨɣɠ ɝɶɫɛɡɠɨɣɺ (1812 112) : 192.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 13 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5
B8 ɇɛɭɠɫɣɛɦɷɨɛɺ ɭɩɲɥɛ M ɨɛɲɣɨɛɠɭ ɟɝɣɡɠɨɣɠ ɣɢ ɭɩɲɥɣ A ɣ ɟɝɣɡɠɭɬɺ ɪɩ ɪɫɺɧɩɤ ɨɛ ɪɫɩɭɺɡɠɨɣɣ 12 ɬɠɥɮɨɟ. Ⱦɫɛɯɣɥ ɪɩɥɛɢɶɝɛɠɭ, ɥɛɥ ɧɠɨɺɦɩɬɷ ɫɛɬɬɭɩɺɨɣɠ ɩɭ ɭɩɲɥɣ A ɟɩ ɭɩɲɥɣ M ɬɩ ɝɫɠɧɠɨɠɧ. Ɉɛ ɩɬɣ ɛɜɬɱɣɬɬ
ɩɭɥɦɛɟɶɝɛɠɭɬɺ ɝɫɠɧɺ t ɝ ɬɠɥɮɨɟɛɰ, ɨɛ ɩɬɣ ɩɫɟɣɨɛɭ – ɫɛɬɬɭɩɺɨɣɠ s ɝ ɧɠɭɫɛɰ.
ɉɪɫɠɟɠɦɣɭɠ, ɬɥɩɦɷɥɩ ɫɛɢ ɢɛ ɝɫɠɧɺ ɟɝɣɡɠɨɣɺ ɬɥɩɫɩɬɭɷ ɭɩɲɥɣ M ɩɜɫɛɴɛɦɛɬɷ ɝ ɨɩɦɷ (ɨɛɲɛɦɩ ɣ ɥɩɨɠɱ ɟɝɣɡɠɨɣɺ ɨɠ ɮɲɣɭɶɝɛɤɭɠ).
ɉɭɝɠɭ:
B9 Ƚ |
ɪɫɺɧɩɮɞɩɦɷɨɩɧ |
ɪɛɫɛɦɦɠɦɠɪɣɪɠɟɠ ABCDA B C D ɣɢɝɠɬɭɨɩ, ɲɭɩ |
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1 |
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BB1 |
4, AB 18, AD |
12. Ɉɛɤɟɣɭɠ ɟɦɣɨɮ ɟɣɛɞɩɨɛɦɣ DB1. |
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ɉɭɝɠɭ:
B10 Ƚ ɬɜɩɫɨɣɥɠ ɜɣɦɠɭɩɝ ɪɩ ɜɣɩɦɩɞɣɣ ɝɬɠɞɩ 55 ɜɣɦɠɭɩɝ, ɝ 11 ɣɢ ɨɣɰ ɝɬɭɫɠɲɛɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɢɩɩɦɩɞɣɣ. Ɉɛɤɟɣɭɠ ɝɠɫɩɺɭɨɩɬɭɷ ɭɩɞɩ, ɲɭɩ ɝ ɬɦɮɲɛɤɨɩ ɝɶɜɫɛɨɨɩɧ ɨɛ ɸɥɢɛɧɠɨɠ ɜɣɦɠɭɠ ɳɥɩɦɷɨɣɥɮ ɨɠ ɟɩɬɭɛɨɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɢɩɩɦɩɞɣɣ.
ɉɭɝɠɭ:
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 13 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 6 |
B11 Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɪɩɝɠɫɰɨɩɬɭɣ ɧɨɩɞɩɞɫɛɨɨɣɥɛ, ɣɢɩɜɫɛɡɠɨɨɩɞɩ ɨɛ ɫɣɬɮɨɥɠ. Ƚɬɠ ɟɝɮɞɫɛɨɨɶɠ ɮɞɦɶ ɧɨɩɞɩɞɫɛɨɨɣɥɛ ɪɫɺɧɶɠ.
ɉɭɝɠɭ: 
B12 Ɍɥɩɫɩɬɭɷ ɛɝɭɩɧɩɜɣɦɺ, ɫɛɢɞɩɨɺɹɴɠɞɩɬɺ ɬ ɧɠɬɭɛ ɬɭɛɫɭɛ ɪɩ ɪɫɺɧɩɦɣɨɠɤɨɩɧɮ ɩɭɫɠɢɥɮ ɪɮɭɣ ɟɦɣɨɩɤ l ɥɧ ɬ ɪɩɬɭɩɺɨɨɶɧ ɮɬɥɩɫɠɨɣɠɧ
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a ɤɦ/ɱ2, ɝɶɲɣɬɦɺɠɭɬɺ ɪɩ ɯɩɫɧɮɦɠ Ȟ |
2la. |
ɉɪɫɠɟɠɦɣɭɠ ɨɛɣɧɠɨɷɳɠɠ |
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ɮɬɥɩɫɠɨɣɠ, ɬ ɥɩɭɩɫɶɧ ɟɩɦɡɠɨ ɟɝɣɞɛɭɷɬɺ ɛɝɭɩɧɩɜɣɦɷ, ɲɭɩɜɶ, ɪɫɩɠɰɛɝ |
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0, 8 ɥɣɦɩɧɠɭɫɛ, ɪɫɣɩɜɫɠɬɭɣ ɬɥɩɫɩɬɭɷ ɨɠ ɧɠɨɠɠ 60 ɥɧ/ɲ. ɉɭɝɠɭ ɝɶɫɛɢɣɭɠ |
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ɝ ɤɦ/ɱ2. |
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ɉɭɝɠɭ: |
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B13 |
ɇɩɭɩɫɨɛɺ ɦɩɟɥɛ ɪɫɩɳɦɛ ɪɫɩɭɣɝ ɭɠɲɠɨɣɺ ɫɠɥɣ 143 ɥɧ ɣ ɝɠɫɨɮɦɛɬɷ ɝ |
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ɪɮɨɥɭ ɩɭɪɫɛɝɦɠɨɣɺ, ɢɛɭɫɛɭɣɝ ɨɛ ɩɜɫɛɭɨɶɤ ɪɮɭɷ ɨɛ 2 ɲɛɬɛ ɧɠɨɷɳɠ. |
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Ɉɛɤɟɣɭɠ ɬɥɩɫɩɬɭɷ ɭɠɲɠɨɣɺ, ɠɬɦɣ ɬɥɩɫɩɬɭɷ ɦɩɟɥɣ ɝ ɨɠɪɩɟɝɣɡɨɩɤ ɝɩɟɠ |
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ɫɛɝɨɛ 12 ɥɧ/ɲ. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɧ/ɲ. |
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ɉɭɝɠɭ: |
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B14 |
Ɉɛɤɟɣɭɠ ɨɛɣɜɩɦɷɳɠɠ ɢɨɛɲɠɨɣɠ ɯɮɨɥɱɣɣ y |
99 20x x2 |
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3 |
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ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 13 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 7
ɒɛɬɭɷ 2
ȿɦɺ ɢɛɪɣɬɣ ɫɠɳɠɨɣɤ ɣ ɩɭɝɠɭɩɝ ɨɛ ɢɛɟɛɨɣɺ C1–C6 ɣɬɪɩɦɷɢɮɤɭɠ ɜɦɛɨɥ ɩɭɝɠɭɩɝ ʌ 2. ɂɛɪɣɳɣɭɠ ɬɨɛɲɛɦɛ ɨɩɧɠɫ ɝɶɪɩɦɨɺɠɧɩɞɩ ɢɛɟɛɨɣɺ, ɛ ɢɛɭɠɧ ɪɩɦɨɩɠ ɩɜɩɬɨɩɝɛɨɨɩɠ ɫɠɳɠɨɣɠ ɣ ɩɭɝɠɭ.
C1 |
ɛ) ɋɠɳɣɭɠ ɮɫɛɝɨɠɨɣɠ sin2x 2 |
3 cos2x 6sinx 6 3 cosx |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
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ª |
ʌ |
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2ʌº. |
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¬2 |
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C2 |
Ƚ ɪɫɛɝɣɦɷɨɩɤ ɲɠɭɶɫɻɰɮɞɩɦɷɨɩɤ ɪɣɫɛɧɣɟɠ SABCD ɝɬɠ ɫɻɜɫɛ ɫɛɝɨɶ 4. |
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ɍɩɲɥɣ M ɣ |
K – |
ɬɠɫɠɟɣɨɶ ɜɩɥɩɝɶɰ |
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ɫɻɜɠɫ |
SB ɣ SC ɬɩɩɭɝɠɭɬɭɝɠɨɨɩ. |
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Ɉɛɤɟɣɭɠ ɮɞɩɦ ɧɠɡɟɮ ɪɦɩɬɥɩɬɭɺɧɣ AMK ɣ ADS. |
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C3 |
ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ |
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(5x 6) log |
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(4x 1) d 2, |
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° log |
4x 1 |
5x 6 |
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® |
x |
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d 0. |
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25 |
15 10 9 |
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C4 |
Ɋɦɩɴɛɟɷ |
ɭɫɛɪɠɱɣɣ |
ABCD |
ɫɛɝɨɛ |
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ȿɣɛɞɩɨɛɦɣ |
AB ɣ |
CD |
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ɪɠɫɠɬɠɥɛɹɭɬɺ |
ɝ |
ɭɩɲɥɠ |
O. ɉɭɫɠɢɥɣ, |
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ɬɩɠɟɣɨɺɹɴɣɠ |
ɬɠɫɠɟɣɨɮ |
P |
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ɩɬɨɩɝɛɨɣɺ |
AD |
ɬ |
ɝɠɫɳɣɨɛɧɣ |
B ɣ |
C, |
ɪɠɫɠɬɠɥɛɹɭɬɺ |
ɬ ɟɣɛɞɩɨɛɦɺɧɣ |
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ɭɫɛɪɠɱɣɣ ɝ ɭɩɲɥɛɰ M ɣ N. Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɭɫɠɮɞɩɦɷɨɣɥɛ MON, |
ɠɬɦɣ |
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ɩɟɨɩ ɣɢ ɩɬɨɩɝɛɨɣɤ ɭɫɛɪɠɱɣɣ ɝɟɝɩɠ ɧɠɨɷɳɠ ɟɫɮɞɩɞɩ. |
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C5 |
Ɋɫɣ |
ɥɛɥɣɰ |
a ɮɫɛɝɨɠɨɣɠ |
x2 2x 3 2a |
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3 ɣɧɠɠɭ |
ɫɩɝɨɩ |
ɭɫɣ |
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ɥɩɫɨɺ?
C6 Ɍɮɧɧɛ ɪɺɭɣ ɨɛɣɧɠɨɷɳɣɰ ɨɛɭɮɫɛɦɷɨɶɰ ɟɠɦɣɭɠɦɠɤ ɨɛɭɮɫɛɦɷɨɩɞɩ ɲɣɬɦɛ ɫɛɝɨɛ 17, ɛ ɬɮɧɧɛ ɲɠɭɶɫɠɰ ɨɛɣɜɩɦɷɳɣɰ ɠɞɩ ɟɠɦɣɭɠɦɠɤ ɫɛɝɨɛ 427. Ɉɛɤɟɣɭɠ ɲɣɬɦɩ.
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ȿɣɛɞɨɩɬɭɣɲɠɬɥɛɺ ɫɛɜɩɭɛ ʌ 1
ɪɩ ɇȻɍɀɇȻɍɃɅɀ
22 ɧɛɺ 2012 ɞɩɟɛ
10 ɥɦɛɬɬ
Ƚɛɫɣɛɨɭ 14 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ)
ɋɛɤɩɨ Ⱦɩɫɩɟ (ɨɛɬɠɦɻɨɨɶɤ ɪɮɨɥɭ) ɓɥɩɦɛ Ʌɦɛɬɬ
ɏɛɧɣɦɣɺ
Ƀɧɺ
ɉɭɲɠɬɭɝɩ
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 14 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 2
Ƀɨɬɭɫɮɥɱɣɺ ɪɩ ɝɶɪɩɦɨɠɨɣɹ ɫɛɜɩɭɶ
Ɉɛ ɝɶɪɩɦɨɠɨɣɠ ɸɥɢɛɧɠɨɛɱɣɩɨɨɩɤ ɫɛɜɩɭɶ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɟɛɻɭɬɺ 4 ɲɛɬɛ (240 ɧɣɨ). ɋɛɜɩɭɛ ɬɩɬɭɩɣɭ ɣɢ ɟɝɮɰ ɲɛɬɭɠɤ ɣ ɬɩɟɠɫɡɣɭ 20 ɢɛɟɛɨɣɤ.
ɒɛɬɭɷ 1 ɬɩɟɠɫɡɣɭ 14 ɢɛɟɛɨɣɤ ɬ ɥɫɛɭɥɣɧ ɩɭɝɠɭɩɧ (Ƚ1–Ƚ14) ɜɛɢɩɝɩɞɩ ɮɫɩɝɨɺ ɪɩ ɧɛɭɠɫɣɛɦɮ ɥɮɫɬɛ ɧɛɭɠɧɛɭɣɥɣ. ɂɛɟɛɨɣɺ ɲɛɬɭɣ 1 ɬɲɣɭɛɹɭɬɺ ɝɶɪɩɦɨɠɨɨɶɧɣ, ɠɬɦɣ ɸɥɢɛɧɠɨɮɠɧɶɤ ɟɛɦ ɝɠɫɨɶɤ ɩɭɝɠɭ ɝ ɝɣɟɠ ɱɠɦɩɞɩ ɲɣɬɦɛ ɣɦɣ ɥɩɨɠɲɨɩɤ ɟɠɬɺɭɣɲɨɩɤ ɟɫɩɜɣ.
ɒɛɬɭɷ 2 ɬɩɟɠɫɡɣɭ 6 ɜɩɦɠɠ ɬɦɩɡɨɶɰ ɢɛɟɛɨɣɤ (Ɍ1–Ɍ6) ɪɩ ɧɛɭɠɫɣɛɦɮ ɥɮɫɬɛ ɧɛɭɠɧɛɭɣɥɣ. Ɋɫɣ ɣɰ ɝɶɪɩɦɨɠɨɣɣ ɨɛɟɩ ɢɛɪɣɬɛɭɷ ɪɩɦɨɩɠ ɫɠɳɠɨɣɠ ɣ ɩɭɝɠɭ.
Ɍɩɝɠɭɮɠɧ ɟɦɺ ɸɥɩɨɩɧɣɣ ɝɫɠɧɠɨɣ ɪɫɩɪɮɬɥɛɭɷ ɢɛɟɛɨɣɠ, ɥɩɭɩɫɩɠ ɨɠ ɮɟɛɠɭɬɺ ɝɶɪɩɦɨɣɭɷ ɬɫɛɢɮ, ɣ ɪɠɫɠɰɩɟɣɭɷ ɥ ɬɦɠɟɮɹɴɠɧɮ. Ʌ ɝɶɪɩɦɨɠɨɣɹ ɪɫɩɪɮɴɠɨɨɶɰ ɢɛɟɛɨɣɤ ɧɩɡɨɩ ɝɠɫɨɮɭɷɬɺ, ɠɬɦɣ ɮ Ƚɛɬ ɩɬɭɛɨɠɭɬɺ ɝɫɠɧɺ.
Ɂɠɦɛɠɧ ɮɬɪɠɰɛ!
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 14 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 3 |
ɒɛɬɭɷ 1
ɉɭɝɠɭɩɧ ɨɛ ɢɛɟɛɨɣɺ Ƚ1–Ƚ14 ɟɩɦɡɨɩ ɜɶɭɷ ɱɠɦɩɠ ɲɣɬɦɩ ɣɦɣ ɥɩɨɠɲɨɛɺ ɟɠɬɺɭɣɲɨɛɺ ɟɫɩɜɷ. ɉɭɝɠɭ ɬɦɠɟɮɠɭ ɢɛɪɣɬɛɭɷ ɝ ɜɦɛɨɥ ɩɭɝɠɭɩɝ ʌ 1 ɬɪɫɛɝɛ ɩɭ ɨɩɧɠɫɛ ɝɶɪɩɦɨɺɠɧɩɞɩ ɢɛɟɛɨɣɺ, ɨɛɲɣɨɛɺ ɬ ɪɠɫɝɩɤ ɥɦɠɭɩɲɥɣ. Ʌɛɡɟɮɹ ɱɣɯɫɮ, ɢɨɛɥ ɧɣɨɮɬ ɣ ɢɛɪɺɭɮɹ ɪɣɳɣɭɠ ɝ ɩɭɟɠɦɷɨɩɤ ɥɦɠɭɩɲɥɠ ɝ ɬɩɩɭɝɠɭɬɭɝɣɣ ɬ ɪɫɣɝɠɟɻɨɨɶɧɣ ɝ ɜɦɛɨɥɠ ɩɜɫɛɢɱɛɧɣ. ɀɟɣɨɣɱɶ ɣɢɧɠɫɠɨɣɤ ɪɣɬɛɭɷ ɨɠ ɨɮɡɨɩ.
B1 Ƚ ɥɝɛɫɭɣɫɠ, ɞɟɠ ɪɫɩɡɣɝɛɠɭ Ȼ., ɮɬɭɛɨɩɝɦɠɨ ɪɫɣɜɩɫ ɮɲɻɭɛ ɫɛɬɰɩɟɛ ɰɩɦɩɟɨɩɤ ɝɩɟɶ (ɬɲɻɭɲɣɥ). 1 ɟɠɥɛɜɫɺ ɬɲɻɭɲɣɥ ɪɩɥɛɢɶɝɛɦ ɫɛɬɰɩɟ 75 ɥɮɜ.ɧ. ɝɩɟɶ, ɛ 1 ɺɨɝɛɫɺ — 83 ɥɮɜ.ɧ. Ʌɛɥɮɹ ɬɮɧɧɮ ɟɩɦɡɠɨ ɢɛɪɦɛɭɣɭɷ Ȼ. ɢɛ ɰɩɦɩɟɨɮɹ ɝɩɟɮ ɢɛ ɟɠɥɛɜɫɷ, ɠɬɦɣ ɱɠɨɛ ɢɛ ɩɟɣɨ ɥɮɜ.ɧ. ɰɩɦɩɟɨɩɤ ɝɩɟɶ ɬɩɬɭɛɝɦɺɠɭ 26 ɫ. 50 ɥɩɪ? ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɫɮɜɦɺɰ.
ɉɭɝɠɭ: 
B2 Ɉɛ ɟɣɛɞɫɛɧɧɠ ɪɩɥɛɢɛɨ ɬɫɠɟɨɣɤ ɜɛɦɦ ɮɲɛɬɭɨɣɥɩɝ 10 ɬɭɫɛɨ ɝ ɭɠɬɭɣɫɩɝɛɨɣɣ ɮɲɛɴɣɰɬɺ 8-ɞɩ ɥɦɛɬɬɛ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɝ 2007 ɞɩɟɮ (ɪɩ 1000ɜɛɦɦɷɨɩɤ ɳɥɛɦɠ).
Ɋɩ ɟɛɨɨɶɧ ɟɣɛɞɫɛɧɧɶ ɨɛɤɟɣɭɠ ɬɫɠɟɨɣɤ ɜɛɦɦ ɮɲɛɬɭɨɣɥɩɝ ɣɢ ȼɩɦɞɛɫɣɣ.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 14 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 4 |
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B3 |
Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɭɫɛɪɠɱɣɣ, ɣɢɩɜɫɛɡɠɨɨɩɤ ɨɛ |
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ɥɦɠɭɲɛɭɩɤ ɜɮɧɛɞɠ ɬ ɫɛɢɧɠɫɩɧ ɥɦɠɭɥɣ 1 ɬɧ u 1 ɬɧ |
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(ɬɧ. ɫɣɬ.). ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɝɛɟɫɛɭɨɶɰ |
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ɬɛɨɭɣɧɠɭɫɛɰ. |
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ɉɭɝɠɭ: |
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B4 |
Ɍɝɩɠɧɮ ɪɩɬɭɩɺɨɨɩɧɮ ɥɦɣɠɨɭɮ ɥɩɧɪɛɨɣɺ ɬɩɭɩɝɩɤ ɬɝɺɢɣ ɫɠɳɣɦɛ |
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ɪɫɠɟɩɬɭɛɝɣɭɷ ɨɛ ɝɶɜɩɫ ɩɟɨɮ ɣɢ ɬɥɣɟɩɥ. Ɇɣɜɩ ɬɥɣɟɥɮ 25% ɨɛ ɢɝɩɨɥɣ |
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ɛɜɩɨɠɨɭɛɧ ɟɫɮɞɣɰ ɬɩɭɩɝɶɰ ɥɩɧɪɛɨɣɤ ɝ ɬɝɩɠɧ ɫɠɞɣɩɨɠ, ɦɣɜɩ ɬɥɣɟɥɮ |
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15% ɨɛ ɢɝɩɨɥɣ ɝ ɟɫɮɞɣɠ ɫɠɞɣɩɨɶ, ɦɣɜɩ 20% ɨɛ ɮɬɦɮɞɣ ɧɩɜɣɦɷɨɩɞɩ |
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ɣɨɭɠɫɨɠɭɛ. |
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Ʌɦɣɠɨɭ ɪɩɬɧɩɭɫɠɦ ɫɛɬɪɠɲɛɭɥɮ ɬɝɩɣɰ ɢɝɩɨɥɩɝ ɣ ɝɶɺɬɨɣɦ, ɲɭɩ ɢɛ ɧɠɬɺɱ |
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ɩɨ ɪɩɭɫɛɭɣɦ 500 ɫɮɜɦɠɤ ɨɛ ɢɝɩɨɥɣ ɛɜɩɨɠɨɭɛɧ ɟɫɮɞɣɰ ɥɩɧɪɛɨɣɤ ɝ ɬɝɩɠɧ |
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ɫɠɞɣɩɨɠ, 300 ɫɮɜɦɠɤ ɨɛ ɢɝɩɨɥɣ ɝ ɟɫɮɞɣɠ ɫɠɞɣɩɨɶ ɣ 400 ɫɮɜɦɠɤ ɨɛ |
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ɧɩɜɣɦɷɨɶɤ ɣɨɭɠɫɨɠɭ. Ʌɦɣɠɨɭ ɪɫɠɟɪɩɦɛɞɛɠɭ, ɲɭɩ ɝ ɬɦɠɟɮɹɴɠɧ ɧɠɬɺɱɠ |
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ɢɛɭɫɛɭɶ ɜɮɟɮɭ ɭɛɥɣɧɣ ɡɠ, ɣ, ɣɬɰɩɟɺ ɣɢ ɸɭɩɞɩ, ɝɶɜɣɫɛɠɭ ɨɛɣɜɩɦɠɠ |
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ɝɶɞɩɟɨɮɹ ɟɦɺ ɬɠɜɺ ɬɥɣɟɥɮ. Ʌɛɥɮɹ ɬɥɣɟɥɮ ɝɶɜɫɛɦ ɥɦɣɠɨɭ? Ƚ ɩɭɝɠɭ |
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ɢɛɪɣɳɣɭɠ, ɬɥɩɦɷɥɩ ɫɮɜɦɠɤ ɬɩɬɭɛɝɣɭ ɸɭɛ ɬɥɣɟɥɛ. |
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ɉɭɝɠɭ: |
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B5 |
Ɉɛɤɟɣɭɠ ɥɩɫɠɨɷ ɮɫɛɝɨɠɨɣɺ: log |
6 |
(3 x) |
1. |
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ɉɭɝɠɭ: |
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B6 |
ɒɠɭɶɫɠɰɮɞɩɦɷɨɣɥ ABCD ɝɪɣɬɛɨ ɝ ɩɥɫɮɡɨɩɬɭɷ. Ɏɞɩɦ ABC ɫɛɝɠɨ 102q, |
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ɮɞɩɦCAD ɫɛɝɠɨ 65q. Ɉɛɤɟɣɭɠ ɮɞɩɦ ABD. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɞɫɛɟɮɬɛɰ. |
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ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ