d12mat101_9
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ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 6 (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 ɉɟɨɛ ɭɛɜɦɠɭɥɛ ɦɠɥɛɫɬɭɝɛ ɝɠɬɣɭ 20 ɧɞ ɣ ɬɩɟɠɫɡɣɭ 7% ɛɥɭɣɝɨɩɞɩ ɝɠɴɠɬɭɝɛ. ɋɠɜɻɨɥɮ ɝ ɝɩɢɫɛɬɭɠ ɟɩ 6 ɧɠɬɺɱɠɝ ɝɫɛɲ ɪɫɩɪɣɬɶɝɛɠɭ 0,84 ɧɞ ɛɥɭɣɝɨɩɞɩ ɝɠɴɠɬɭɝɛ ɨɛ ɥɛɡɟɶɤ ɥɣɦɩɞɫɛɧɧ ɝɠɬɛ ɝ ɬɮɭɥɣ. Ɍɥɩɦɷɥɩ ɭɛɜɦɠɭɩɥ ɸɭɩɞɩ ɦɠɥɛɫɬɭɝɛ ɬɦɠɟɮɠɭ ɟɛɭɷ ɫɠɜɻɨɥɮ ɝɠɬɩɧ 5ɥɞ ɝ ɭɠɲɠɨɣɠ ɬɮɭɩɥ?
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 6 (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 |
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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 — 160 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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2,2 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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2,2 ɫɮɜ. ɢɛ ɥȽɭ·ɲ, |
ɛ |
ɨɩɲɨɩɤ ɫɛɬɰɩɟ |
ɩɪɦɛɲɣɝɛɠɭɬɺ |
ɪɩ |
ɭɛɫɣɯɮ |
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0,6 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 |
( 4 x) |
2. |
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5 |
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ɉɭɝɠɭ: |
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B6 |
ɒɠɭɶɫɠɰɮɞɩɦɷɨɣɥ ABCD ɝɪɣɬɛɨ ɝ ɩɥɫɮɡɨɩɬɭɷ. Ɏɞɩɦ ABC ɫɛɝɠɨ 124q, |
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ɮɞɩɦCAD ɫɛɝɠɨ 76q. 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 6 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5 |
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B7 |
Ɉɛɤɟɣɭɠ ɢɨɛɲɠɨɣɠ ɝɶɫɛɡɠɨɣɺ (3142 262) : 340. |
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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 12 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: 
B9 Ƚ ɪɫɺɧɩɮɞɩɦɷɨɩɧ ɪɛɫɛɦɦɠɦɠɪɣɪɠɟɠ ABCDA1B1C1D1 ɣɢɝɠɬɭɨɩ, ɲɭɩ CC1 9, AB 2, B1C1 6. Ɉɛɤɟɣɭɠ ɟɦɣɨɮ ɟɣɛɞɩɨɛɦɣ BD1.
ɉɭɝɠɭ: 
B10 Ƚ ɬɜɩɫɨɣɥɠ ɜɣɦɠɭɩɝ ɪɩ ɯɣɢɣɥɠ ɝɬɠɞɩ 25 ɜɣɦɠɭɩɝ, ɝ 4 ɣɢ ɨɣɰ ɝɬɭɫɠɲɛɠɭɬɺ ɝɩɪɫɩɬ ɩ ɥɩɨɟɠɨɬɛɭɩɫɛɰ. Ɉɛɤɟɣɭɠ ɝɠɫɩɺɭɨɩɬɭɷ ɭɩɞɩ, ɲɭɩ ɝ ɬɦɮɲɛɤɨɩ ɝɶɜɫɛɨɨɩɧ ɨɛ ɸɥɢɛɧɠɨɠ ɜɣɦɠɭɠ ɳɥɩɦɷɨɣɥɮ ɨɠ ɟɩɬɭɛɨɠɭɬɺ ɝɩɪɫɩɬ ɩ ɥɩɨɟɠɨɬɛɭɩɫɛɰ.
ɉɭɝɠɭ: 
© 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 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, 6 ɥɣɦɩɧɠɭɫɛ, ɪɫɣɩɜɫɠɬɭɣ ɬɥɩɫɩɬɭɷ ɨɠ ɧɠɨɠɠ 120 ɥɧ/ɲ. ɉɭɝɠɭ
ɝɶɫɛɢɣɭɠ ɝ ɤɦ/ɱ2.
ɉɭɝɠɭ: 
B13 |
ɇɩɭɩɫɨɛɺ ɦɩɟɥɛ ɪɫɩɳɦɛ ɪɫɩɭɣɝ ɭɠɲɠɨɣɺ ɫɠɥɣ 96 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 14 ɥɧ/ɲ. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɧ/ɲ. |
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ɉɭɝɠɭ: 
B14 |
Ɉɛɤɟɣɭɠ ɨɛɣɜɩɦɷɳɠɠ ɢɨɛɲɠɨɣɠ ɯɮɨɥɱɣɣ y |
34 12x x2 |
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ɉɭɝɠɭ: 
© 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 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 7 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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ª 3ʌ; |
3ʌº. |
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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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(2x 1) d 2, |
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° log |
2x 1 |
4x 7 |
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® |
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x |
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x |
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° |
9 |
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6 |
4 4 d 0. |
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C4 |
Ɋɦɩɴɛɟɷ |
ɭɫɛɪɠɱɣɣ |
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ABCD ɫɛɝɨɛ |
675. |
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 7 (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 7 (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 ɞɩɫɺɲɠɤ ɝɩɟɶ (ɬɲɻɭɲɣɥ). 1 ɛɪɫɠɦɺ ɬɲɻɭɲɣɥ ɪɩɥɛɢɶɝɛɦ ɫɛɬɰɩɟ 75 ɥɮɜ.ɧ. ɝɩɟɶ, ɛ 1 ɧɛɺ — 81 ɥɮɜ.ɧ. Ʌɛɥɮɹ ɬɮɧɧɮ ɟɩɦɡɠɨ ɢɛɪɦɛɭɣɭɷ Ȼ. ɢɛ ɞɩɫɺɲɮɹ ɝɩɟɮ ɢɛ ɛɪɫɠɦɷ, ɠɬɦɣ ɱɠɨɛ ɢɛ ɩɟɣɨ ɥɮɜ.ɧ. ɞɩɫɺɲɠɤ ɝɩɟɶ ɬɩɬɭɛɝɦɺɠɭ 97 ɫ. 50 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).
Ɉɛ ɬɥɩɦɷɥɩ ɜɛɦɦɩɝ ɩɭɦɣɲɛɠɭɬɺ ɬɫɠɟɨɣɤ ɜɛɦɦ ɮɲɛɬɭɨɣɥɩɝ ɣɢ ɌɓȻ ɩɭ ɬɫɠɟɨɠɞɩ ɜɛɦɦɛ ɮɲɛɬɭɨɣɥɩɝ ɣɢ ɓɝɠɱɣɣ?
ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 7 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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 ȿɦɺ ɩɬɭɠɥɦɠɨɣɺ ɧɮɢɠɤɨɶɰ ɝɣɭɫɣɨ ɭɫɠɜɮɠɭɬɺ ɢɛɥɛɢɛɭɷ 50 ɩɟɣɨɛɥɩɝɶɰ ɬɭɠɥɩɦ ɝ ɩɟɨɩɤ ɣɢ ɭɫɠɰ ɯɣɫɧ. Ɋɦɩɴɛɟɷ ɥɛɡɟɩɞɩ ɬɭɠɥɦɛ 0,35 ɦ2. Ƚ
ɭɛɜɦɣɱɠ ɪɫɣɝɠɟɠɨɶ ɱɠɨɶ ɨɛ ɬɭɠɥɦɩ ɣ ɨɛ ɫɠɢɥɮ ɬɭɠɥɩɦ. Ɍɥɩɦɷɥɩ ɫɮɜɦɠɤ ɜɮɟɠɭ ɬɭɩɣɭɷ ɬɛɧɶɤ ɟɠɳɠɝɶɤ ɢɛɥɛɢ?
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ɑɠɨɛ ɬɭɠɥɦɛ |
ɋɠɢɥɛ |
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ɏɣɫɧɛ |
ɬɭɠɥɦɛ |
ȿɩɪɩɦɨɣɭɠɦɷɨɶɠ ɮɬɦɩɝɣɺ |
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(ɫɮɜ. ɢɛ |
(ɫɮɜ. ɢɛ |
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1 ɦ2) |
ɩɟɨɩ |
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ɬɭɠɥɦɩ) |
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A |
320 |
20 |
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B |
310 |
25 |
Ɋɫɣ ɢɛɥɛɢɠ ɨɛ ɬɮɧɧɮ ɜɩɦɷɳɠ |
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C |
340 |
15 |
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7000 ɫɮɜ. ɫɠɢɥɛ ɜɠɬɪɦɛɭɨɩ |
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ɉɭɝɠɭ: 
B5 Ɉɛɤɟɣɭɠ ɥɩɫɠɨɷ ɮɫɛɝɨɠɨɣɺ: log |
( 1 x) 1. |
6 |
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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 7 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) 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: |
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B7 Ɉɛɤɟɣɭɠ ɢɨɛɲɠɨɣɠ ɝɶɫɛɡɠɨɣɺ |
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ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 7 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 6 |
B8 Ɉɛ ɫɣɬɮɨɥɠ ɪɩɥɛɢɛɨɛ ɢɛɝɣɬɣɧɩɬɭɷ ɫɛɬɬɭɩɺɨɣɺ ɩɭ ɝɫɠɧɠɨɣ ɪɫɣ ɟɝɣɡɠɨɣɣ ɛɝɭɩɧɩɜɣɦɺ ɪɩ ɧɛɫɳɫɮɭɮ ɩɭ ɨɛɲɛɦɷɨɩɞɩ ɪɮɨɥɭɛ. Ɉɛ ɩɬɣ ɛɜɬɱɣɬɬ ɩɭɥɦɛɟɶɝɛɠɭɬɺ ɝɫɠɧɺ ɝ ɲɛɬɛɰ, ɨɛ ɩɬɣ ɩɫɟɣɨɛɭ – ɪɫɩɤɟɠɨɨɶɤ ɪɮɭɷ ɝ ɥɣɦɩɧɠɭɫɛɰ. Ɉɛɤɟɣɭɠ ɬɫɠɟɨɹɹ ɬɥɩɫɩɬɭɷ ɛɝɭɩɧɩɜɣɦɺ ɨɛ ɸɭɩɧ ɧɛɫɳɫɮɭɠ. ɉɭɝɠɭ ɟɛɤɭɠ ɝ ɥɣɦɩɧɠɭɫɛɰ ɝ ɲɛɬ.
ɉɭɝɠɭ: |
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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: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 7 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 7 |
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:
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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(1 cos2Į), ɞɟɠ Ȟ |
28 ɧ/ɬ — ɨɛɲɛɦɷɨɛɺ ɬɥɩɫɩɬɭɷ ɧɺɲɣɥɛ, ɛ g — |
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ɮɬɥɩɫɠɨɣɠ ɬɝɩɜɩɟɨɩɞɩ |
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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:
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 7 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 8 |
ȿɣɛɞɨɩɬɭɣɲɠɬɥɛɺ ɫɛɜɩɭɛ ʌ 1 |
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B14 |
Ɉɛɤɟɣɭɠ ɨɛɣɜɩɦɷɳɠɠ ɢɨɛɲɠɨɣɠ ɯɮɨɥɱɣɣ y |
23 10x x2 |
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ɪɩ ɇȻɍɀɇȻɍɃɅɀ |
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ɉɭɝɠɭ: |
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22 ɧɛɺ 2012 ɞɩɟɛ |
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10 ɥɦɛɬɬ |
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ɒɛɬɭɷ 2 |
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ȿɦɺ ɢɛɪɣɬɣ ɫɠɳɠɨɣɤ ɣ ɩɭɝɠɭɩɝ ɨɛ ɢɛɟɛɨɣɺ C1–C6 ɣɬɪɩɦɷɢɮɤɭɠ |
Ƚɛɫɣɛɨɭ 8 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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ɜɦɛɨɥ ɩɭɝɠɭɩɝ ʌ 2. ɂɛɪɣɳɣɭɠ ɬɨɛɲɛɦɛ ɨɩɧɠɫ ɝɶɪɩɦɨɺɠɧɩɞɩ |
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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 |
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ɜ) Ɉɛɤɟɣɭɠ ɝɬɠ ɥɩɫɨɣ ɸɭɩɞɩ ɮɫɛɝɨɠɨɣɺ, ɪɫɣɨɛɟɦɠɡɛɴɣɠ ɪɫɩɧɠɡɮɭɥɮ |
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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 |
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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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° log |
4x 1 |
5x 6 |
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25 |
15 10 9 |
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Ⱦɩɫɩɟ (ɨɛɬɠɦɻɨɨɶɤ ɪɮɨɥɭ) |
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C4 |
Ɋɦɩɴɛɟɷ |
ɭɫɛɪɠɱɣɣ |
ABCD ɫɛɝɨɛ |
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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 |
Ʌɦɛɬɬ |
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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 |
x a 3 ɣɧɠɠɭ |
ɫɩɝɨɩ |
ɭɫɣ |
ɏɛɧɣɦɣɺ |
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ɥɩɫɨɺ? |
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Ƀɧɺ |
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C6 |
Ɍɮɧɧɛ ɪɺɭɣ ɨɛɣɧɠɨɷɳɣɰ ɨɛɭɮɫɛɦɷɨɶɰ ɟɠɦɣɭɠɦɠɤ ɨɛɭɮɫɛɦɷɨɩɞɩ ɲɣɬɦɛ |
ɉɭɲɠɬɭɝɩ |
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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 |
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ |
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ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 8 (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 8 (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 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 8 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
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 Ɍɝɩɠɧɮ ɪɩɬɭɩɺɨɨɩɧɮ ɥɦɣɠɨɭɮ ɥɩɧɪɛɨɣɺ ɬɩɭɩɝɩɤ ɬɝɺɢɣ ɫɠɳɣɦɛ ɪɫɠɟɩɬɭɛɝɣɭɷ ɨɛ ɝɶɜɩɫ ɩɟɨɮ ɣɢ ɬɥɣɟɩɥ. Ɇɣɜɩ ɬɥɣɟɥɮ 25% ɨɛ ɢɝɩɨɥɣ ɛɜɩɨɠɨɭɛɧ ɟɫɮɞɣɰ ɬɩɭɩɝɶɰ ɥɩɧɪɛɨɣɤ ɝ ɬɝɩɠɧ ɫɠɞɣɩɨɠ, ɦɣɜɩ ɬɥɣɟɥɮ 15% ɨɛ ɢɝɩɨɥɣ ɝ ɟɫɮɞɣɠ ɫɠɞɣɩɨɶ, ɦɣɜɩ 20% ɨɛ ɮɬɦɮɞɣ ɧɩɜɣɦɷɨɩɞɩ ɣɨɭɠɫɨɠɭɛ.
Ʌɦɣɠɨɭ ɪɩɬɧɩɭɫɠɦ ɫɛɬɪɠɲɛɭɥɮ ɬɝɩɣɰ ɢɝɩɨɥɩɝ ɣ ɝɶɺɬɨɣɦ, ɲɭɩ ɢɛ ɧɠɬɺɱ ɩɨ ɪɩɭɫɛɭɣɦ 500 ɫɮɜɦɠɤ ɨɛ ɢɝɩɨɥɣ ɛɜɩɨɠɨɭɛɧ ɟɫɮɞɣɰ ɥɩɧɪɛɨɣɤ ɝ ɬɝɩɠɧ ɫɠɞɣɩɨɠ, 300 ɫɮɜɦɠɤ ɨɛ ɢɝɩɨɥɣ ɝ ɟɫɮɞɣɠ ɫɠɞɣɩɨɶ ɣ 400 ɫɮɜɦɠɤ ɨɛ ɧɩɜɣɦɷɨɶɤ ɣɨɭɠɫɨɠɭ. Ʌɦɣɠɨɭ ɪɫɠɟɪɩɦɛɞɛɠɭ, ɲɭɩ ɝ ɬɦɠɟɮɹɴɠɧ ɧɠɬɺɱɠ ɢɛɭɫɛɭɶ ɜɮɟɮɭ ɭɛɥɣɧɣ ɡɠ, ɣ, ɣɬɰɩɟɺ ɣɢ ɸɭɩɞɩ, ɝɶɜɣɫɛɠɭ ɨɛɣɜɩɦɠɠ ɝɶɞɩɟɨɮɹ ɟɦɺ ɬɠɜɺ ɬɥɣɟɥɮ. Ʌɛɥɮɹ ɬɥɣɟɥɮ ɝɶɜɫɛɦ ɥɦɣɠɨɭ? Ƚ ɩɭɝɠɭ ɢɛɪɣɳɣɭɠ, ɬɥɩɦɷɥɩ ɫɮɜɦɠɤ ɬɩɬɭɛɝɣɭ ɸɭɛ ɬɥɣɟɥɛ.
ɉɭɝɠɭ: 
B5 |
Ɉɛɤɟɣɭɠ ɥɩɫɠɨɷ ɮɫɛɝɨɠɨɣɺ: log |
( 4 x) 2. |
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5 |
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ɉɭɝɠɭ: |
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B6 |
Ƚ ɭɫɠɮɞɩɦɷɨɣɥɠ ABC ɮɞɩɦ A ɫɛɝɠɨ 84q, 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 8 (ɂɛɪɛɟ ɜɠɢ ɪɫɩɣɢɝɩɟɨɩɤ) |
Ƚɣɟɠɩɫɛɢɜɩɫ ɨɛ ɬɛɤɭɠ http://statgrad.cde.ru 5 |
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B7 |
Ɉɛɤɟɣɭɠ ɢɨɛɲɠɨɣɠ ɝɶɫɛɡɠɨɣɺ (2082 112) : 219. |
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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 12 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 |
1 |
1 |
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 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:
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 8 (ɂɛɪɛɟ 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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H |
0 |
(1 cos2Į), ɞɟɠ Ȟ 28 ɧ/ɬ — ɨɛɲɛɦɷɨɛɺ ɬɥɩɫɩɬɭɷ ɧɺɲɣɥɛ, ɛ g — |
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4g |
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g 10 ɦ/ɫ2). Ɋɫɣ ɥɛɥɩɧ |
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ɮɬɥɩɫɠɨɣɠ ɬɝɩɜɩɟɨɩɞɩ ɪɛɟɠɨɣɺ (ɬɲɣɭɛɤɭɠ |
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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 ɨɛɣɜɩɦɷɳɠɠ ɢɨɛɲɠɨɣɠ ɯɮɨɥɱɣɣ y |
34 12x x2 |
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9 |
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ɉɭɝɠɭ: 
© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ
ɇɛɭɠɧɛɭɣɥɛ. 10 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 8 (ɂɛɪɛɟ 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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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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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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° |
9 |
3 |
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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 |
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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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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