d12mat101_9
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ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 3 (ɂɛɪɛɟ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 6
B9 Ƚ |
ɪɫɺɧɩɮɞɩɦɷɨɩɧ ɪɛɫɛɦɦɠɦɠɪɣɪɠɟɠ ABCDA B C D ɣɢɝɠɬɭɨɩ, ɲɭɩ |
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AA1 |
4, A1B1 19, B1C1 8. Ɉɛɤɟɣɭɠ ɟɦɣɨɮ ɟɣɛɞɩɨɛɦɣ BD1. |
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ɉɭɝɠɭ: 
B10 Ƚ ɬɜɩɫɨɣɥɠ ɜɣɦɠɭɩɝ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɝɬɠɞɩ 20 ɜɣɦɠɭɩɝ, ɝ 3 ɣɢ ɨɣɰ ɝɬɭɫɠɲɛɠɭɬɺ ɝɩɪɫɩɬ ɩ ɬɝɩɤɬɭɝɛɰ ɦɩɞɛɫɣɯɧɩɝ. Ɉɛɤɟɣɭɠ ɝɠɫɩɺɭɨɩɬɭɷ ɭɩɞɩ, ɲɭɩ ɝ ɬɦɮɲɛɤɨɩ ɝɶɜɫɛɨɨɩɧ ɨɛ ɸɥɢɛɧɠɨɠ ɜɣɦɠɭɠ ɳɥɩɦɷɨɣɥɮ ɟɩɬɭɛɨɠɭɬɺ ɝɩɪɫɩɬ ɩ ɬɝɩɤɬɭɝɛɰ ɦɩɞɛɫɣɯɧɩɝ.
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 3 (ɂɛɪɛɟ 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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0 |
(1 cos2Į), ɞɟɠ Ȟ |
28 ɧ/ɬ — ɨɛɲɛɦɷɨɛɺ ɬɥɩɫɩɬɭɷ ɧɺɲɣɥɛ, ɛ g — |
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4g |
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10 ɦ/ɫ2). |
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ɮɬɥɩɫɠɨɣɠ |
ɬɝɩɜɩɟɨɩɞɩ |
ɪɛɟɠɨɣɺ (ɬɲɣɭɛɤɭɠ g |
Ɋɫɣ ɥɛɥɩɧ |
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ɨɛɣɧɠɨɷɳɠɧ ɢɨɛɲɠɨɣɣ ɮɞɦɛ Į (ɝ ɞɫɛɟɮɬɛɰ) ɧɺɲɣɥ ɪɫɩɦɠɭɣɭ ɨɛɟ ɬɭɠɨɩɤ ɝɶɬɩɭɩɤ 28, 4 ɧ ɨɛ ɫɛɬɬɭɩɺɨɣɣ 1 ɧ?
ɉɭɝɠɭ: 
B13 Ƀɧɠɠɭɬɺ ɟɝɛ ɬɪɦɛɝɛ. Ɋɠɫɝɶɤ ɬɩɟɠɫɡɣɭ 5% ɨɣɥɠɦɺ, ɝɭɩɫɩɤ — 25% ɨɣɥɠɦɺ. Ƀɢ ɸɭɣɰ ɟɝɮɰ ɬɪɦɛɝɩɝ ɪɩɦɮɲɣɦɣ ɭɫɠɭɣɤ ɬɪɦɛɝ ɧɛɬɬɩɤ 150 ɥɞ, ɬɩɟɠɫɡɛɴɣɤ 20% ɨɣɥɠɦɺ. Ɉɛ ɬɥɩɦɷɥɩ ɥɣɦɩɞɫɛɧɧɩɝ ɧɛɬɬɛ ɪɠɫɝɩɞɩ ɬɪɦɛɝɛ ɧɠɨɷɳɠ ɧɛɬɬɶ ɝɭɩɫɩɞɩ?
ɉɭɝɠɭ: 
B14 Ɉɛɤɟɣɭɠ ɨɛɣɜɩɦɷɳɠɠ ɢɨɛɲɠɨɣɠ ɯɮɨɥɱɣɣ y 11cosx 12x 28 ɨɛ ɩɭɫɠɢɥɠ
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2 ¼ |
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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 cos2x 6sinx 6 3 cosx 0. |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
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C2 |
Ƚ ɪɫɛɝɣɦɷɨɩɤ ɲɠɭɶɫɻɰɮɞɩɦɷɨɩɤ ɪɣɫɛɧɣɟɠ SABCD ɝɬɠ ɫɻɜɫɛ 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 ADS. |
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© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 3 (ɂɛɪɛɟ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 8 |
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C3 |
ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ |
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5, 6x 7, 84)(x 2, 5) t 0, |
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C4 |
Ɋɦɩɴɛɟɷ |
ɭɫɛɪɠɱɣɣ |
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ABCD ɫɛɝɨɛ |
270. ȿɣɛɞɩɨɛɦɣ |
AB ɣ |
CD |
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ɪɠɫɠɬɠɥɛɹɭɬɺ ɝ ɭɩɲɥɠ O.ɉɭɫɠɢɥɣ, |
ɬɩɠɟɣɨɺɹɴɣɠ |
ɬɠɫɠɟɣɨɮ |
P |
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ɩɬɨɩɝɛɨɣɺ |
AD ɬ ɝɠɫɳɣɨɛɧɣ |
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B ɣ C, |
ɪɠɫɠɬɠɥɛɹɭɬɺ |
ɬ |
ɟɣɛɞɩɨɛɦɺɧɣ |
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ɭɫɛɪɠɱɣɣ ɝ ɭɩɲɥɛɰ M ɣ N. Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɭɫɠɮɞɩɦɷɨɣɥɛ MON, ɠɬɦɣ ɩɟɨɩ ɣɢ ɩɬɨɩɝɛɨɣɤ ɭɫɛɪɠɱɣɣ ɝɟɝɩɠ ɧɠɨɷɳɠ ɟɫɮɞɩɞɩ.
C5 Ɋɫɣ ɥɛɥɣɰ a ɮɫɛɝɨɠɨɣɠ x2 2x 3 2a x a 3 ɣɧɠɠɭ ɫɩɝɨɩ ɭɫɣ 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 4 (ɂɛɪɛɟ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ)
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 4 (ɂɛɪɛɟ 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 4 (ɂɛɪɛɟ 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 ɰɩɦɩɟɨɩɤ ɝɩɟɶ (ɬɲɻɭɲɣɥ). 1 ɨɩɺɜɫɺ ɬɲɻɭɲɣɥ ɪɩɥɛɢɶɝɛɦ ɫɛɬɰɩɟ 126 ɥɮɜ.ɧ. ɝɩɟɶ, ɛ 1 ɟɠɥɛɜɫɺ — 141 ɥɮɜ.ɧ. Ʌɛɥɮɹ ɬɮɧɧɮ ɟɩɦɡɠɨ ɢɛɪɦɛɭɣɭɷ Ȼ. ɢɛ ɰɩɦɩɟɨɮɹ ɝɩɟɮ ɢɛ ɨɩɺɜɫɷ, ɠɬɦɣ ɱɠɨɛ ɢɛ ɩɟɣɨ ɥɮɜ.ɧ. ɰɩɦɩɟɨɩɤ ɝɩɟɶ ɬɩɬɭɛɝɦɺɠɭ 23 ɫ. 60 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 ɲɣɬɦɩ ɬɭɫɛɨ, ɝ ɥɩɭɩɫɶɰ ɬɫɠɟɨɣɤ ɜɛɦɦ ɩɭɦɣɲɛɠɭɬɺ ɩɭ ɬɫɠɟɨɠɞɩ ɜɛɦɦɛ ɜɩɦɞɛɫɬɥɣɰ ɳɥɩɦɷɨɣɥɩɝ ɧɠɨɠɠ, ɲɠɧ ɨɛ 15 (ɬɛɧɮ ȼɩɦɞɛɫɣɹ ɨɠ ɬɲɣɭɛɤɭɠ).
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 4 (ɂɛɪɛɟ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 4 |
B3 Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɭɫɠɮɞɩɦɷɨɣɥɛ, ɣɢɩɜɫɛɡɠɨɨɩɞɩ 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: 70 5x 5.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 4 (ɂɛɪɛɟ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5
B6 Ƚ ɭɫɠɮɞɩɦɷɨɣɥɠ ABC ɮɞɩɦ A ɫɛɝɠɨ 84q, 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 (2082 112) : 219.
ɉɭɝɠɭ: 
B8 Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɠɨ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ |
y f (x), ɩɪɫɠɟɠɦɠɨɨɩɤ ɨɛ |
ɣɨɭɠɫɝɛɦɠ ( 8; 3). Ɉɛɤɟɣɭɠ ɥɩɦɣɲɠɬɭɝɩ ɭɩɲɠɥ, ɝ ɥɩɭɩɫɶɰ ɥɛɬɛɭɠɦɷɨɛɺ |
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ɥ ɞɫɛɯɣɥɮ ɯɮɨɥɱɣɣ ɪɛɫɛɦɦɠɦɷɨɛ ɪɫɺɧɩɤ y |
20. |
ɉɭɝɠɭ:
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 4 (ɂɛɪɛɟ 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 ɞɠɩɞɫɛɯɣɣ ɝɬɠɞɩ 25 ɜɣɦɠɭɩɝ, ɝ 14 ɣɢ ɨɣɰ ɝɬɭɫɠɲɛɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɫɠɞɣɩɨɛɧ ɋɩɬɬɣɣ. Ɉɛɤɟɣɭɠ ɝɠɫɩɺɭɨɩɬɭɷ ɭɩɞɩ, ɲɭɩ ɝ ɬɦɮɲɛɤɨɩ ɝɶɜɫɛɨɨɩɧ ɨɛ ɸɥɢɛɧɠɨɠ ɜɣɦɠɭɠ ɳɥɩɦɷɨɣɥɮ ɨɠ ɟɩɬɭɛɨɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɫɠɞɣɩɨɛɧ ɋɩɬɬɣɣ.
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 4 (ɂɛɪɛɟ 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 |
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ɯɩɫɧɮɦɩɤ |
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Ȟ2 |
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H |
0 |
(1 cos2Į), ɞɟɠ Ȟ |
28 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 |
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ɝɶɬɩɭɩɤ 28, 4 ɧ ɨɛ ɫɛɬɬɭɩɺɨɣɣ 1 ɧ? |
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ɉɭɝɠɭ: |
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B13 |
ɇɩɭɩɫɨɛɺ |
ɦɩɟɥɛ ɪɫɩɳɦɛ ɪɫɩɭɣɝ |
ɭɠɲɠɨɣɺ ɫɠɥɣ 63 ɥɧ |
ɣ |
ɝɠɫɨɮɦɛɬɷ |
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ɝ 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 8 ɥɧ/ɲ. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɧ/ɲ. |
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ɉɭɝɠɭ: |
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B14 |
Ɉɛɤɟɣɭɠ ɭɩɲɥɮ ɧɣɨɣɧɮɧɛ ɯɮɨɥɱɣɣ y |
x2 6x 29. |
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ɉɭɝɠɭ: |
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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 4 (ɂɛɪɛɟ 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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3, 6x 3, 24)(x 1, 5) t 0, |
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d 5. |
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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 5 (ɂɛɪɛɟ 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 5 (ɂɛɪɛɟ 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 5 (ɂɛɪɛɟ 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 ɨɩɺɜɫɺ ɬɲɻɭɲɣɥ ɪɩɥɛɢɶɝɛɦ ɫɛɬɰɩɟ 126 ɥɮɜ.ɧ. ɝɩɟɶ, ɛ 1 ɟɠɥɛɜɫɺ — 141 ɥɮɜ.ɧ. Ʌɛɥɮɹ ɬɮɧɧɮ ɟɩɦɡɠɨ ɢɛɪɦɛɭɣɭɷ Ȼ. ɢɛ ɰɩɦɩɟɨɮɹ ɝɩɟɮ ɢɛ ɨɩɺɜɫɷ, ɠɬɦɣ ɱɠɨɛ ɢɛ ɩɟɣɨ ɥɮɜ.ɧ. ɰɩɦɩɟɨɩɤ ɝɩɟɶ ɬɩɬɭɛɝɦɺɠɭ 23 ɫ. 60 ɥɩɪ? ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɫɮɜɦɺɰ.
ɉɭɝɠɭ: 
B2 Ɉɛ ɟɣɛɞɫɛɧɧɠ ɪɩɥɛɢɛɨ ɬɫɠɟɨɣɤ ɜɛɦɦ ɮɲɛɬɭɨɣɥɩɝ 10 ɬɭɫɛɨ ɝ ɭɠɬɭɣɫɩɝɛɨɣɣ ɮɲɛɴɣɰɬɺ 4-ɞɩ ɥɦɛɬɬɛ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɝ 2007 ɞɩɟɮ (ɪɩ 1000ɜɛɦɦɷɨɩɤ ɳɥɛɦɠ).
Ɋɩ ɟɛɨɨɶɧ ɟɣɛɞɫɛɧɧɶ ɨɛɤɟɣɭɠ ɲɣɬɦɩ ɬɭɫɛɨ, ɝ ɥɩɭɩɫɶɰ ɬɫɠɟɨɣɤ ɜɛɦɦ ɨɠ ɝɶɳɠ, ɲɠɧ 520.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 5 (ɂɛɪɛɟ 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 |
ɬɛɨɭɣɧɠɭɫɛɰ. |
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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: log |
( 1 x) 2. |
4 |
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ɉɭɝɠɭ: |
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© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 5 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5
B6 ɒɠɭɶɫɻɰɮɞɩɦɷɨɣɥ ABCD ɝɪɣɬɛɨ ɝ ɩɥɫɮɡɨɩɬɭɷ. Ɏɞɩɦ ABC ɫɛɝɠɨ 124q, ɮɞɩɦCAD ɫɛɝɠɨ 36q. Ɉɛɤɟɣɭɠ ɮɞɩɦ ABD. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɞɫɛɟɮɬɛɰ.
ɉɭɝɠɭ:
B7 Ɉɛɤɟɣɭɠ ɢɨɛɲɠɨɣɠ ɝɶɫɛɡɠɨɣɺ (2082 112) : 219.
ɉɭɝɠɭ: 
B8 ɇɛɭɠɫɣɛɦɷɨɛɺ ɭɩɲɥɛ M ɨɛɲɣɨɛɠɭ ɟɝɣɡɠɨɣɠ ɣɢ ɭɩɲɥɣ A ɣ ɟɝɣɡɠɭɬɺ ɪɩ ɪɫɺɧɩɤ ɨɛ ɪɫɩɭɺɡɠɨɣɣ 10 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:
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 5 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 6
B9 Ƚ |
ɪɫɺɧɩɮɞɩɦɷɨɩɧ ɪɛɫɛɦɦɠɦɠɪɣɪɠɟɠ ABCDA B C D ɣɢɝɠɬɭɨɩ, ɲɭɩ |
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AA1 |
4, A1B1 19, B1C1 8. Ɉɛɤɟɣɭɠ ɟɦɣɨɮ ɟɣɛɞɩɨɛɦɣ BD1. |
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ɉɭɝɠɭ: 
B10 Ƚ ɬɜɩɫɨɣɥɠ ɜɣɦɠɭɩɝ ɪɩ ɞɠɩɞɫɛɯɣɣ ɝɬɠɞɩ 25 ɜɣɦɠɭɩɝ, ɝ 14 ɣɢ ɨɣɰ ɝɬɭɫɠɲɛɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɫɠɞɣɩɨɛɧ ɋɩɬɬɣɣ. Ɉɛɤɟɣɭɠ ɝɠɫɩɺɭɨɩɬɭɷ ɭɩɞɩ, ɲɭɩ ɝ ɬɦɮɲɛɤɨɩ ɝɶɜɫɛɨɨɩɧ ɨɛ ɸɥɢɛɧɠɨɠ ɜɣɦɠɭɠ ɳɥɩɦɷɨɣɥɮ ɨɠ ɟɩɬɭɛɨɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɫɠɞɣɩɨɛɧ ɋɩɬɬɣɣ.
ɉɭɝɠɭ: 
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
a ɤɦ/ɱ2, ɝɶɲɣɬɦɺɠɭɬɺ ɪɩ ɯɩɫɧɮɦɠ Ȟ 2la. ɉɪɫɠɟɠɦɣɭɠ ɨɛɣɧɠɨɷɳɠɠ ɮɬɥɩɫɠɨɣɠ, ɬ ɥɩɭɩɫɶɧ ɟɩɦɡɠɨ ɟɝɣɞɛɭɷɬɺ ɛɝɭɩɧɩɜɣɦɷ, ɲɭɩɜɶ, ɪɫɩɠɰɛɝ 0, 8 ɥɣɦɩɧɠɭɫɛ, ɪɫɣɩɜɫɠɬɭɣ ɬɥɩɫɩɬɭɷ ɨɠ ɧɠɨɠɠ 100 ɥɧ/ɲ. ɉɭɝɠɭ
ɝɶɫɛɢɣɭɠ ɝ ɤɦ/ɱ2.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 5 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 7 |
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B13 |
ɇɩɭɩɫɨɛɺ ɦɩɟɥɛ ɪɫɩɳɦɛ ɪɫɩɭɣɝ |
ɭɠɲɠɨɣɺ |
ɫɠɥɣ |
63 ɥɧ |
ɣ ɝɠɫɨɮɦɛɬɷ |
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ɝ 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 8 ɥɧ/ɲ. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɧ/ɲ. |
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ɉɭɝɠɭ: |
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B14 |
Ɉɛɤɟɣɭɠ ɨɛɣɜɩɦɷɳɠɠ ɢɨɛɲɠɨɣɠ ɯɮɨɥɱɣɣ y |
119 22x x2 |
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6 |
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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 cos2x 6sinx 6 3 cosx |
0. |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
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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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® |
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° |
3 |
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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, |
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 |
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x2 2x 3 |
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x a |
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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 |
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ɫɛɝɨɛ 17, ɛ ɬɮɧɧɛ ɲɠɭɶɫɠɰ ɨɛɣɜɩɦɷɳɣɰ ɠɞɩ ɟɠɦɣɭɠɦɠɤ ɫɛɝɨɛ 427. |
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Ɉɛɤɟɣɭɠ ɲɣɬɦɩ. |
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© 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 6 (ɂɛɪɛɟ 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 6 (ɂɛɪɛɟ 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.
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