d12mat101_9
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ȿɣɛɞɨɩɬɭɣɲɠɬɥɛɺ ɫɛɜɩɭɛ ʌ 1
ɪɩ ɇȻɍɀɇȻɍɃɅɀ
22 ɧɛɺ 2012 ɞɩɟɛ
10 ɥɦɛɬɬ
Ƚɛɫɣɛɨɭ 9 (Ƚɩɬɭɩɥ 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 9 (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 9 (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 |
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 9 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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: 54 5x |
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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.
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 9 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5 |
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B8 Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ |
y f (x), ɩɪɫɠɟɠɦɻɨɨɩɤ ɨɛ |
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ɣɨɭɠɫɝɛɦɠ ( 4; 9). Ɉɛɤɟɣɭɠ ɥɩɦɣɲɠɬɭɝɩ ɭɩɲɠɥ, ɝ ɥɩɭɩɫɶɰ ɥɛɬɛɭɠɦɷɨɛɺ ɥ |
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ɞɫɛɯɣɥɮ ɯɮɨɥɱɣɣ ɪɛɫɛɦɦɠɦɷɨɛ ɪɫɺɧɩɤ y |
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ɉɭɝɠɭ: 
B9 Ƚ |
ɪɫɺɧɩɮɞɩɦɷɨɩɧ |
ɪɛɫɛɦɦɠɦɠɪɣɪɠɟɠ ABCDA B C D ɣɢɝɠɬɭɨɩ, ɲɭɩ |
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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 9 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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
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 60 ɥɧ/ɲ. ɉɭɝɠɭ ɝɶɫɛɢɣɭɠ
ɝ ɤɦ/ɱ2.
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 10x 32. |
ɉɭɝɠɭ:
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 9 (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 |
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3 cos2x 6sinx 6 |
3 cosx |
0. |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
Ƚɛɫɣɛɨɭ 10 (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 |
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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d 5. |
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x |
2 |
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x 3 |
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C4 |
Ɋɦɩɴɛɟɷ |
ɭɫɛɪɠɱɣɣ |
ABCD |
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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 10 (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 10 (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 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 10 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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: 32 4x |
2. |
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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
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 10 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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 |
Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ |
y f (x), ɩɪɫɠɟɠɦɻɨɨɩɤ ɨɛ |
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ɣɨɭɠɫɝɛɦɠ ( 4; 7). Ɉɛɤɟɣɭɠ ɥɩɦɣɲɠɬɭɝɩ ɭɩɲɠɥ, ɝ ɥɩɭɩɫɶɰ ɥɛɬɛɭɠɦɷɨɛɺ ɥ |
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ɞɫɛɯɣɥɮ ɯɮɨɥɱɣɣ ɪɛɫɛɦɦɠɦɷɨɛ ɪɫɺɧɩɤ y |
11. |
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ɉɭɝɠɭ: 
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 10 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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
a ɤɦ/ɱ2, ɝɶɲɣɬɦɺɠɭɬɺ ɪɩ ɯɩɫɧɮɦɠ Ȟ 2la. ɉɪɫɠɟɠɦɣɭɠ ɨɛɣɧɠɨɷɳɠɠ
ɮɬɥɩɫɠɨɣɠ, ɬ ɥɩɭɩɫɶɧ ɟɩɦɡɠɨ ɟɝɣɞɛɭɷɬɺ ɛɝɭɩɧɩɜɣɦɷ, ɲɭɩɜɶ, ɪɫɩɠɰɛɝ 1 ɥɣɦɩɧɠɭɫ, ɪɫɣɩɜɫɠɬɭɣ ɬɥɩɫɩɬɭɷ ɨɠ ɧɠɨɠɠ 130 ɥɧ/ɲ. ɉɭɝɠɭ ɝɶɫɛɢɣɭɠ ɝ
ɤɦ/ɱ2.
ɉɭɝɠɭ: 
B13 ɇɩɭɩɫɨɛɺ ɦɩɟɥɛ ɪɫɩɳɦɛ ɪɫɩɭɣɝ ɭɠɲɠɨɣɺ ɫɠɥɣ 135 ɥɧ ɣ ɝɠɫɨɮɦɛɬɷ ɝ ɪɮɨɥɭ ɩɭɪɫɛɝɦɠɨɣɺ, ɢɛɭɫɛɭɣɝ ɨɛ ɩɜɫɛɭɨɶɤ ɪɮɭɷ ɨɛ 6 ɲɛɬɩɝ 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: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 10 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) 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 |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
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ª 3ʌ; |
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3ʌ |
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 ɨɠɫɛɝɠɨɬɭɝ |
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C4 |
Ɋɦɩɴɛɟɷ |
ɭɫɛɪɠɱɣɣ |
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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 |
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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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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 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 11 (Ƚɩɬɭɩɥ 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 11 (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 11 (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 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 11 (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 ȿɦɺ ɩɬɭɠɥɦɠɨɣɺ ɧɮɢɠɤɨɶɰ ɝɣɭɫɣɨ ɭɫɠɜɮɠɭɬɺ ɢɛɥɛɢɛɭɷ 40 ɩɟɣɨɛɥɩɝɶɰ |
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ɬɭɠɥɩɦ ɝ ɩɟɨɩɤ ɣɢ ɭɫɻɰ ɯɣɫɧ. Ɋɦɩɴɛɟɷ ɥɛɡɟɩɞɩ ɬɭɠɥɦɛ 0,15 ɦ2. Ƚ |
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ɭɛɜɦɣɱɠ ɪɫɣɝɠɟɠɨɶ ɱɠɨɶ ɨɛ ɬɭɠɥɦɩ ɣ ɨɛ ɫɠɢɥɮ ɬɭɠɥɩɦ. Ɍɥɩɦɷɥɩ ɫɮɜɦɠɤ |
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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 x 26 |
7. |
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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 11 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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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: |
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B8 |
Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ |
y f c(x) ɪɫɩɣɢɝɩɟɨɩɤ ɯɮɨɥɱɣɣ f (x), |
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ɩɪɫɠɟɠɦɻɨɨɩɤ ɨɛ ɣɨɭɠɫɝɛɦɠ ( 16; 8). Ɉɛɤɟɣɭɠ ɥɩɦɣɲɠɬɭɝɩ ɭɩɲɠɥ |
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ɧɛɥɬɣɧɮɧɛ ɯɮɨɥɱɣɣ f (x), ɪɫɣɨɛɟɦɠɡɛɴɣɰ ɩɭɫɠɢɥɮ[ 13; 6]. |
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ɉɭɝɠɭ: |
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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: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 11 (Ƚɩɬɭɩɥ ɜɠɢ ɦɩɞɛɫɣɯɧɩɝ) |
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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H |
0 |
(1 cos2Į), ɞɟɠ Ȟ |
14 ɧ/ɬ — ɨɛɲɛɦɷɨɛɺ ɬɥɩɫɩɬɭɷ ɧɺɲɣɥɛ, ɛ g — |
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4g |
0 |
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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 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?
ɉɭɝɠɭ:
B14 Ɉɛɤɟɣɭɠ ɨɛɣɜɩɦɷɳɠɠ ɢɨɛɲɠɨɣɠ ɯɮɨɥɱɣɣ y 24cosx 28x 23 ɨɛ ɩɭɫɠɢɥɠ
ª«¬0; 3ʌº»¼.
2
ɉɭɝɠɭ:
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