d12mat101_9
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ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 14 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5 |
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B7 |
Ɉɛɤɟɣɭɠ ɢɨɛɲɠɨɣɠ ɝɶɫɛɡɠɨɣɺ (3942 262) : 420. |
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ɉɭɝɠɭ: |
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B8 |
ɇɛɭɠɫɣɛɦɷɨɛɺ ɭɩɲɥɛ M ɨɛɲɣɨɛɠɭ ɟɝɣɡɠɨɣɠ ɣɢ ɭɩɲɥɣ A ɣ ɟɝɣɡɠɭɬɺ ɪɩ |
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ɪɫɺɧɩɤ ɨɛ ɪɫɩɭɺɡɠɨɣɣ 11 ɬɠɥɮɨɟ. Ⱦɫɛɯɣɥ ɪɩɥɛɢɶɝɛɠɭ, ɥɛɥ ɧɠɨɺɦɩɬɷ |
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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: |
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B9 Ƚ |
ɪɫɺɧɩɮɞɩɦɷɨɩɧ |
ɪɛɫɛɦɦɠɦɠɪɣɪɠɟɠ |
ABCDA B C D |
ɣɢɝɠɬɭɨɩ, ɲɭɩ |
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CC1 |
4, A1B1 1, BC |
8. Ɉɛɤɟɣɭɠ ɟɦɣɨɮ ɟɣɛɞɩɨɛɦɣ DB1. |
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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 6 |
B10 Ƚ ɬɜɩɫɨɣɥɠ ɜɣɦɠɭɩɝ ɪɩ ɣɬɭɩɫɣɣ ɝɬɠɞɩ 50 ɜɣɦɠɭɩɝ, ɝ 3 ɣɢ ɨɣɰ ɝɬɭɫɠɲɛɠɭɬɺ ɝɩɪɫɩɬ ɩɜ Ȼɦɠɥɬɛɨɟɫɠ II. Ɉɛɤɟɣɭɠ ɝɠɫɩɺɭɨɩɬɭɷ ɭɩɞɩ, ɲɭɩ ɝ ɬɦɮɲɛɤɨɩ ɝɶɜɫɛɨɨɩɧ ɨɛ ɸɥɢɛɧɠɨɠ ɜɣɦɠɭɠ ɳɥɩɦɷɨɣɥɮ ɨɠ ɟɩɬɭɛɨɠɭɬɺ ɝɩɪɫɩɬɛ ɩɜ Ȼɦɠɥɬɛɨɟɫɠ II.
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
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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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1 ɥɣɦɩɧɠɭɫ, ɪɫɣɩɜɫɠɬɭɣ ɬɥɩɫɩɬɭɷ ɨɠ ɧɠɨɠɠ 130 ɥɧ/ɲ. ɉɭɝɠɭ ɝɶɫɛɢɣɭɠ ɝ |
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ɤɦ/ɱ2. |
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ɉɭɝɠɭ: |
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B13 |
ɇɩɭɩɫɨɛɺ ɦɩɟɥɛ ɪɫɩɳɦɛ ɪɫɩɭɣɝ ɭɠɲɠɨɣɺ ɫɠɥɣ 135 ɥɧ ɣ ɝɠɫɨɮɦɛɬɷ ɝ |
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ɪɮɨɥɭ ɩɭɪɫɛɝɦɠɨɣɺ, ɢɛɭɫɛɭɣɝ ɨɛ ɩɜɫɛɭɨɶɤ ɪɮɭɷ ɨɛ 6 ɲɛɬɩɝ 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 |
61 16x x2 |
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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 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 sin2x 6cosx 6 3 sinx |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
Ƚɛɫɣɛɨɭ 15 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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ª 3ʌ; |
3ʌ |
º. |
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¬ |
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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C3 |
ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ |
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(4x 7) log |
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(2x 1) d 2, |
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° log |
2x 1 |
4x 7 |
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° |
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6 |
4 4 d 0. |
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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 ɟɣɛɞɩɨɛɦɺɧɣ ɭɫɛɪɠɱɣɣ ɝ |
ɋɛɤɩɨ |
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ɭɩɲɥɛɰ M ɣ N. Ɉɛɤɟɣɭɠ ɪɦɩɴɛɟɷ ɭɫɠɮɞɩɦɷɨɣɥɛ MON, ɠɬɦɣ ɩɟɨɩ ɣɢ |
Ⱦɩɫɩɟ (ɨɛɬɠɦɻɨɨɶɤ ɪɮɨɥɭ) |
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ɩɬɨɩɝɛɨɣɤ ɭɫɛɪɠɱɣɣ ɝɟɝɩɠ ɧɠɨɷɳɠ ɟɫɮɞɩɞɩ. |
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ɓɥɩɦɛ |
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C5 |
Ɋɫɣ |
ɥɛɥɣɰ a ɮɫɛɝɨɠɨɣɠ |
x2 2x 3 2a |
x a 3 ɣɧɠɠɭ |
ɫɩɝɨɩ ɭɫɣ |
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Ʌɦɛɬɬ |
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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 671. |
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Ɉɛɤɟɣɭɠ ɲɣɬɦɩ. |
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ɏɛɧɣɦɣɺ |
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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 15 (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 15 (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 ɉɟɨɛ ɭɛɜɦɠɭɥɛ ɦɠɥɛɫɬɭɝɛ ɝɠɬɣɭ 35 ɧɞ ɣ ɬɩɟɠɫɡɣɭ 8% ɛɥɭɣɝɨɩɞɩ ɝɠɴɠɬɭɝɛ. ɋɠɜɻɨɥɮ ɝ ɝɩɢɫɛɬɭɠ ɟɩ 6 ɧɠɬɺɱɠɝ ɝɫɛɲ ɪɫɩɪɣɬɶɝɛɠɭ 0,8 ɧɞ ɛɥɭɣɝɨɩɞɩ ɝɠɴɠɬɭɝɛ ɨɛ ɥɛɡɟɶɤ ɥɣɦɩɞɫɛɧɧ ɝɠɬɛ ɝ ɬɮɭɥɣ. Ɍɥɩɦɷɥɩ ɭɛɜɦɠɭɩɥ ɸɭɩɞɩ ɦɠɥɛɫɬɭɝɛ ɬɦɠɟɮɠɭ ɟɛɭɷ ɫɠɜɻɨɥɮ ɝɠɬɩɧ 7ɥɞ ɝ ɭɠɲɠɨɣɠ ɬɮɭɩɥ?
ɉɭɝɠɭ: 
B2 Ɉɛ ɟɣɛɞɫɛɧɧɠ ɪɩɥɛɢɛɨ ɬɫɠɟɨɣɤ ɜɛɦɦ ɮɲɛɬɭɨɣɥɩɝ 8 ɬɭɫɛɨ ɝ ɭɠɬɭɣɫɩɝɛɨɣɣ ɮɲɛɴɣɰɬɺ 4-ɞɩ ɥɦɛɬɬɛ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɝ 2007 ɞɩɟɮ (ɪɩ 1000ɜɛɦɦɷɨɩɤ ɳɥɛɦɠ).
Ɉɛɤɟɣɭɠ ɲɣɬɦɩ ɬɭɫɛɨ, ɝ ɥɩɭɩɫɶɰ ɬɫɠɟɨɣɤ ɜɛɦɦ ɨɠ ɧɠɨɷɳɠ, ɲɠɧ 500.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 15 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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 ȿɦɺ ɩɬɭɠɥɦɠɨɣɺ ɧɮɢɠɤɨɶɰ ɝɣɭɫɣɨ ɭɫɠɜɮɠɭɬɺ ɢɛɥɛɢɛɭɷ 40 ɩɟɣɨɛɥɩɝɶɰ ɬɭɠɥɩɦ ɝ ɩɟɨɩɤ ɣɢ ɭɫɻɰ ɯɣɫɧ. Ɋɦɩɴɛɟɷ ɥɛɡɟɩɞɩ ɬɭɠɥɦɛ 0,15 ɦ2. Ƚ
ɭɛɜɦɣɱɠ ɪɫɣɝɠɟɠɨɶ ɱɠɨɶ ɨɛ ɬɭɠɥɦɩ ɣ ɨɛ ɫɠɢɥɮ ɬɭɠɥɩɦ. Ɍɥɩɦɷɥɩ ɫɮɜɦɠɤ ɜɮɟɠɭ ɬɭɩɣɭɷ ɬɛɧɶɤ ɟɠɳɠɝɶɤ ɢɛɥɛɢ?
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ɑɠɨɛ |
ɋɠɢɥɛ ɬɭɠɥɦɛ |
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ɏɣɫɧɛ |
ɬɭɠɥɦɛ |
(ɫɮɜ. ɢɛ ɩɟɨɩ ȿɩɪɩɦɨɣɭɠɦɷɨɶɠ ɮɬɦɩɝɣɺ |
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(ɫɮɜ. ɢɛ |
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1 ɦ2) |
ɬɭɠɥɦɩ) |
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A |
300 |
12 |
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B |
290 |
14 |
Ɋɫɣ ɢɛɥɛɢɠ ɨɛ ɬɮɧɧɮ ɜɩɦɷɳɠ 2500 |
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C |
320 |
10 |
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ɫɮɜ. ɫɠɢɥɛ ɜɠɬɪɦɛɭɨɩ |
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ɉɭɝɠɭ: |
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B5 |
Ɉɛɤɟɣɭɠ ɥɩɫɠɨɷ ɮɫɛɝɨɠɨɣɺ: log |
( 5 x) 1. |
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3 |
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ɉɭɝɠɭ: |
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B6 |
Ƚ ɭɫɠɮɞɩɦɷɨɣɥɠ ABC ɮɞɩɦ A ɫɛɝɠɨ 15q, ɛ ɮɞɦɶ B ɣ C ɩɬɭɫɶɠ. BD ɣ CE – |
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ɝɶɬɩɭɶ, ɪɠɫɠɬɠɥɛɹɴɣɠɬɺ ɝ ɭɩɲɥɠ O. Ɉɛɤɟɣɭɠ ɮɞɩɦ DOE. ɉɭɝɠɭ ɟɛɤɭɠ ɝ |
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ɞɫɛɟɮɬɛɰ. |
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ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 15 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5 |
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B7 Ɉɛɤɟɣɭɠ ɢɨɛɲɠɨɣɠ ɝɶɫɛɡɠɨɣɺ |
(3 |
6 )2 |
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6 |
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ɉɭɝɠɭ: 
B8 Ɉɛ ɫɣɬɮɨɥɠ ɪɩɥɛɢɛɨɛ ɢɛɝɣɬɣɧɩɬɭɷ ɫɛɬɬɭɩɺɨɣɺ ɩɭ ɝɫɠɧɠɨɣ ɪɫɣ ɟɝɣɡɠɨɣɣ ɭɠɪɦɩɰɩɟɛ ɪɩ ɧɛɫɳɫɮɭɮ ɩɭ ɨɛɲɛɦɷɨɩɞɩ ɪɮɨɥɭɛ. Ɉɛ ɩɬɣ ɛɜɬɱɣɬɬ ɩɭɥɦɛɟɶɝɛɠɭɬɺ ɝɫɠɧɺ ɝ ɲɛɬɛɰ, ɨɛ ɩɬɣ ɩɫɟɣɨɛɭ – ɪɫɩɤɟɠɨɨɶɤ ɪɮɭɷ ɝ ɥɣɦɩɧɠɭɫɛɰ. Ɉɛɤɟɣɭɠ ɬɫɠɟɨɹɹ ɬɥɩɫɩɬɭɷ ɭɠɪɦɩɰɩɟɛ ɨɛ ɸɭɩɧ ɧɛɫɳɫɮɭɠ. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɣɦɩɧɠɭɫɛɰ ɝ ɲɛɬ.
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 15 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) 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 |
AA1 |
4, A1B1 19, B1C1 8. Ɉɛɤɟɣɭɠ ɟɦɣɨɮ ɟɣɛɞɩɨɛɦɣ BD1. |
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ɉɭɝɠɭ: 
B10 Ƚ ɬɜɩɫɨɣɥɠ ɜɣɦɠɭɩɝ ɪɩ ɞɠɩɞɫɛɯɣɣ ɝɬɠɞɩ 30 ɜɣɦɠɭɩɝ, ɝ 12 ɣɢ ɨɣɰ ɝɬɭɫɠɲɛɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɫɠɥɛɧ ɣ ɩɢɠɫɛɧ. Ɉɛɤɟɣɭɠ ɝɠɫɩɺɭɨɩɬɭɷ ɭɩɞɩ, ɲɭɩ ɝ ɬɦɮɲɛɤɨɩ ɝɶɜɫɛɨɨɩɧ ɨɛ ɸɥɢɛɧɠɨɠ ɜɣɦɠɭɠ ɳɥɩɦɷɨɣɥɮ ɟɩɬɭɛɨɠɭɬɺ ɝɩɪɫɩɬ ɪɩ ɫɠɥɛɧ ɣ ɩɢɠɫɛɧ.
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 15 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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 Ƀɧɠɠɭɬɺ ɟɝɛ ɬɪɦɛɝɛ. Ɋɠɫɝɶɤ ɬɩɟɠɫɡɣɭ 5% ɨɣɥɠɦɺ, ɝɭɩɫɩɤ — 35% ɨɣɥɠɦɺ. Ƀɢ ɸɭɣɰ ɟɝɮɰ ɬɪɦɛɝɩɝ ɪɩɦɮɲɣɦɣ ɭɫɠɭɣɤ ɬɪɦɛɝ ɧɛɬɬɩɤ 150 ɥɞ, ɬɩɟɠɫɡɛɴɣɤ 25% ɨɣɥɠɦɺ. Ɉɛ ɬɥɩɦɷɥɩ ɥɣɦɩɞɫɛɧɧɩɝ ɧɛɬɬɛ ɪɠɫɝɩɞɩ ɬɪɦɛɝɛ ɧɠɨɷɳɠ ɧɛɬɬɶ ɝɭɩɫɩɞɩ?
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ɉɭɝɠɭ: |
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B14 |
Ɉɛɤɟɣɭɠ ɨɛɣɜɩɦɷɳɠɠ ɢɨɛɲɠɨɣɠ ɯɮɨɥɱɣɣ y |
3 4x x2 |
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4 |
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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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¬2 |
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¼ |
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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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C3 |
ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ |
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(5x 6) log |
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° log |
4x 1 |
5x 6 |
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10 9 |
d 0. |
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3 15 |
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© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 15 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 8 |
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C4 Ɋɦɩɴɛɟɷ |
ɭɫɛɪɠɱɣɣ 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 B ɣ C, |
ɪɠɫɠɬɠɥɛɹɭɬɺ |
ɬ |
ɟɣɛɞɩɨɛɦɺɧɣ |
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 16 (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 16 (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 16 (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 10 ɬɭɫɛɨ ɝ ɭɠɬɭɣ- |
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ɫɩɝɛɨɣɣ ɮɲɛɴɣɰɬɺ 8-ɞɩ ɥɦɛɬɬɛ ɪɩ ɧɛɭɠɧɛɭɣɥɠ ɝ 2007 ɞɩɟɮ (ɪɩ 1000- |
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ɜɛɦɦɷɨɩɤ 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 16 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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.
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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 |
6 |
(3 x) |
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ɉɭɝɠɭ: |
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B6 |
Ƚ ɭɫɠɮɞɩɦɷɨɣɥɠ ABC ɮɞɩɦ A ɫɛɝɠɨ 15q, ɛ ɮɞɦɶ B ɣ C ɩɬɭɫɶɠ. BD ɣ CE – |
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ɝɶɬɩɭɶ, ɪɠɫɠɬɠɥɛɹɴɣɠɬɺ ɝ ɭɩɲɥɠ O. Ɉɛɤɟɣɭɠ ɮɞɩɦ DOE. ɉɭɝɠɭ ɟɛɤɭɠ ɝ |
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ɞɫɛɟɮɬɛɰ. |
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ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 16 (Ƚɩɬɭɩɥ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5 |
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B7 |
Ɉɛɤɟɣɭɠ ɢɨɛɲɠɨɣɠ ɝɶɫɛɡɠɨɣɺ (1812 112) : 192. |
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ɉɭɝɠɭ: |
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B8 |
ɇɛɭɠɫɣɛɦɷɨɛɺ ɭɩɲɥɛ M ɨɛɲɣɨɛɠɭ ɟɝɣɡɠɨɣɠ ɣɢ ɭɩɲɥɣ A ɣ ɟɝɣɡɠɭɬɺ ɪɩ |
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ɪɫɺɧɩɤ ɨɛ ɪɫɩɭɺɡɠɨɣɣ 11 ɬɠɥɮɨɟ. Ⱦɫɛɯɣɥ ɪɩɥɛɢɶɝɛɠɭ, ɥɛɥ ɧɠɨɺɦɩɬɷ |
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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: |
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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 16 (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 Ɉɠɜɩɦɷɳɩɤ ɧɺɲɣɥ ɜɫɩɬɛɹɭ ɪɩɟ ɩɬɭɫɶɧ ɮɞɦɩɧ Į ɥ ɪɦɩɬɥɩɤ
ɞɩɫɣɢɩɨɭɛɦɷɨɩɤ ɪɩɝɠɫɰɨɩɬɭɣ ɢɠɧɦɣ. ɇɛɥɬɣɧɛɦɷɨɛɺ ɝɶɬɩɭɛ ɪɩɦɻɭɛ ɧɺɲɣɥɛ, ɝɶɫɛɡɠɨɨɛɺ ɝ ɧɠɭɫɛɰ, ɩɪɫɠɟɠɦɺɠɭɬɺ ɯɩɫɧɮɦɩɤ
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Ȟ2 |
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0 |
(1 cos2Į), ɞɟɠ Ȟ |
14 ɧ/ɬ — ɨɛɲɛɦɷɨɛɺ ɬɥɩɫɩɬɭɷ ɧɺɲɣɥɛ, ɛ g — |
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4g |
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ɪɛɟɠɨɣɺ (ɬɲɣɭɛɤɭɠ g 10 ɦ/ɫ2). Ɋɫɣ ɥɛɥɩɧ |
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ɮɬɥɩɫɠɨɣɠ ɬɝɩɜɩɟɨɩɞɩ |
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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 |
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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 |
61 16x x2 |
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Ɉɛɤɟɣɭɠ ɨɛɣɜɩɦɷɳɠɠ ɢɨɛɲɠɨɣɠ ɯɮɨɥɱɣɣ y 3 |
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ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 16 (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 sin2x 6cosx 6 3 sinx 0. |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
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ª 3ʌ; |
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º. |
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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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C3 |
ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ |
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(4x 7) log |
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° log |
2x 1 |
4x 7 |
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9 |
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4 4 d 0. |
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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 ɭɩɲɥɠO. ɉɭɫɠɢɥɣ, ɬɩɠɟɣɨɺɹɴɣɠ ɬɠɫɠɟɣɨɮ P ɩɬɨɩɝɛɨɣɺ |
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AD ɬ |
ɝɠɫɳɣɨɛɧɣ B ɣ C , ɪɠɫɠɬɠɥɛɹɭɬɺ ɬ 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 |
x2 2x 3 2a |
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ɫɩɝɨɩ ɭɫɣ |
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ɥɩɫɨɺ?
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