книги / 10 класс. Математика. Диагностическая работа 1. (вар. 0201-0216) 21.05.2013г (с отв)
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Ɇɚɬɟɦɚɬɢɤɚ. 10 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ Ɇ 0208 (ɡɚɩɚɞ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
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B6 ȼ ɬɪɟɭɝɨɥɶɧɢɤɟ ABC ɭɝɨɥ A ɪɚɜɟɧ 21q, ɚ ɭɝɥɵ B ɢ C ɨɫɬɪɵɟ, ɜɵɫɨɬɵ BD ɢ CEɩɟɪɟɫɟɤɚɸɬɫɹ ɜ ɬɨɱɤɟ O. ɇɚɣɞɢɬɟ ɭɝɨɥ DOE. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɝɪɚɞɭɫɚɯ.
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Ɉɬɜɟɬ: |
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B7 |
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11cos77q |
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ɇɚɣɞɢɬɟ ɡɧɚɱɟɧɢɟ ɜɵɪɚɠɟɧɢɹ |
sin13q |
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Ɉɬɜɟɬ: |
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B8 |
ɇɚ ɪɢɫɭɧɤɟ ɩɨɤɚɡɚɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɜɪɟɦɟɧɢ ɩɪɢ ɞɜɢɠɟɧɢɢ |
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ɬɟɩɥɨɯɨɞɚ ɩɨ ɦɚɪɲɪɭɬɭ ɨɬ ɧɚɱɚɥɶɧɨɝɨ ɩɭɧɤɬɚ. ɇɚ ɨɫɢ ɚɛɫɰɢɫɫ ɨɬɤɥɚɞɵɜɚɟɬɫɹ |
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ɜɪɟɦɹ ɜ ɱɚɫɚɯ, ɧɚ ɨɫɢ ɨɪɞɢɧɚɬ — ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ ɜ ɤɢɥɨɦɟɬɪɚɯ. |
ɇɚɣɞɢɬɟ |
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ɫɪɟɞɧɸɸ ɫɤɨɪɨɫɬɶ ɬɟɩɥɨɯɨɞɚ ɧɚ ɷɬɨɦ ɦɚɪɲɪɭɬɟ. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɤɢɥɨɦɟɬɪɚɯ ɜ ɱɚɫ.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ.
Ɇɚɬɟɦɚɬɢɤɚ. 10 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ Ɇ 0208 (ɡɚɩɚɞ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
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B9 ȼ ɩɪɚɜɢɥɶɧɨɣ ɬɪɟɭɝɨɥɶɧɨɣ ɩɢɪɚɦɢɞɟ |
SABC ɬɨɱɤɚ P — ɫɟɪɟɞɢɧɚ ɪɟɛɪɚ |
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AB, S — ɜɟɪɲɢɧɚ. ɂɡɜɟɫɬɧɨ, ɱɬɨ SP=4, |
ɚ ɩɥɨɳɚɞɶ ɛɨɤɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɜɧɚ |
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24. ɇɚɣɞɢɬɟ ɞɥɢɧɭ ɨɬɪɟɡɤɚ BC.
Ɉɬɜɟɬ:
B10 |
ɇɚ ɤɥɚɜɢɚɬɭɪɟ ɬɟɥɟɮɨɧɚ 10 ɰɢɮɪ: ɨɬ 0 ɞɨ 9. Ʉɚɤɨɜɚ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ |
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ɫɥɭɱɚɣɧɨ ɧɚɠɚɬɚɹ ɰɢɮɪɚ ɛɭɞɟɬ ɛɨɥɶɲɟ 6? |
Ɉɬɜɟɬ: 
B11 ɇɚɣɞɢɬɟ ɨɛɴɺɦ ɦɧɨɝɨɝɪɚɧɧɢɤɚ, ɢɡɨɛɪɚɠɺɧɧɨɝɨ ɧɚ ɪɢɫɭɧɤɟ (ɜɫɟ ɞɜɭɝɪɚɧɧɵɟ
ɭɝɥɵ ɩɪɹɦɵɟ).
Ɉɬɜɟɬ:
© ɋɬɚɬȽɪɚɞ 2013 ɝ.
Ɇɚɬɟɦɚɬɢɤɚ. 10 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ Ɇ |
0208 (ɡɚɩɚɞ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
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7 |
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B12 |
Ɂɚɜɢɫɢɦɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪɵ (ɜ ɝɪɚɞɭɫɚɯ Ʉɟɥɶɜɢɧɚ) ɨɬ ɜɪɟɦɟɧɢ ɞɥɹ ɧɚɝɪɟɜɚɬɟɥɶ- |
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ɧɨɝɨ ɷɥɟɦɟɧɬɚ ɧɟɤɨɬɨɪɨɝɨ ɩɪɢɛɨɪɚ ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ. ɇɚ |
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ɢɫɫɥɟɞɭɟɦɨɦ |
ɢɧɬɟɪɜɚɥɟ |
ɬɟɦɩɟɪɚɬɭɪɚ |
ɜɵɱɢɫɥɹɟɬɫɹ |
ɩɨ |
ɮɨɪɦɭɥɟ |
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T(t) T0 bt at2, ɝɞɟ t — |
ɜɪɟɦɹ ɜ ɦɢɧɭɬɚɯ, T0 |
1250 Ʉ, |
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5K / ɦɢɧ2, |
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b 65K / ɦɢɧ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ ɧɚɝɪɟɜɚɬɟɥɹ ɫɜɵɲɟ 1450 K |
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ɩɪɢɛɨɪ ɦɨɠɟɬ ɢɫɩɨɪɬɢɬɶɫɹ, ɩɨɷɬɨɦɭ ɟɝɨ ɧɭɠɧɨ ɨɬɤɥɸɱɢɬɶ. Ɉɩɪɟɞɟɥɢɬɟ, ɱɟɪɟɡ |
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ɤɚɤɨɟ ɧɚɢɛɨɥɶɲɟɟ ɜɪɟɦɹ ɩɨɫɥɟ ɧɚɱɚɥɚ ɪɚɛɨɬɵ ɧɭɠɧɨ ɨɬɤɥɸɱɢɬɶ ɩɪɢɛɨɪ. Ɉɬɜɟɬ |
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ɜɵɪɚɡɢɬɟ ɜ ɦɢɧɭɬɚɯ. |
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Ɉɬɜɟɬ: |
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B13 |
ȼ ɫɨɫɭɞ, ɫɨɞɟɪɠɚɳɢɣ 8 ɥɢɬɪɨɜ 30-ɩɪɨɰɟɧɬɧɨɝɨ ɜɨɞɧɨɝɨ ɪɚɫɬɜɨɪɚ ɧɟɤɨɬɨɪɨɝɨ |
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ɜɟɳɟɫɬɜɚ, ɞɨɛɚɜɢɥɢ 7 ɥɢɬɪɨɜ ɜɨɞɵ. ɋɤɨɥɶɤɨ ɩɪɨɰɟɧɬɨɜ ɫɨɫɬɚɜɥɹɟɬ |
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ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɨɥɭɱɢɜɲɟɝɨɫɹ ɪɚɫɬɜɨɪɚ? |
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Ɉɬɜɟɬ: |
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B14 |
ɇɚɣɞɢɬɟ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ y |
log2(x2 4x 20) 7. |
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Ɉɬɜɟɬ: |
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ɑɚɫɬɶ 2
Ⱦɥɹ ɡɚɩɢɫɢ ɪɟɲɟɧɢɣ ɢ ɨɬɜɟɬɨɜ ɧɚ ɡɚɞɚɧɢɹ C1–C6 ɢɫɩɨɥɶɡɭɣɬɟ ɛɥɚɧɤ ɨɬɜɟɬɨɜ
ʋ 2. Ɂɚɩɢɲɢɬɟ ɫɧɚɱɚɥɚ ɧɨɦɟɪ ɜɵɩɨɥɧɹɟɦɨɝɨ ɡɚɞɚɧɢɹ (ɋ1, ɋ2 ɢ ɬ ɞ.), ɚ ɡɚɬɟɦ ɩɨɥɧɨɟ ɨɛɨɫɧɨɜɚɧɧɨɟ ɪɟɲɟɧɢɟ ɢ ɨɬɜɟɬ.
C1 |
ɚ) Ɋɟɲɢɬɟ ɭɪɚɜɧɟɧɢɟ |
1 |
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cosx |
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cos |
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7ʌ |
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ɛ) ɇɚɣɞɢɬɟ ɜɫɟ ɤɨɪɧɢ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ, ɩɪɢɧɚɞɥɟɠɚɳɢɟ ɩɪɨɦɟɠɭɬɤɭ 2ʌ; |
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2 |
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C2 |
Ɉɫɧɨɜɚɧɢɟ ɩɪɹɦɨɣ ɩɪɢɡɦɵ ABCDA1B1C1D1 |
— ɪɨɦɛ ABCD ɫ ɭɝɥɨɦ A, ɪɚɜɧɵɦ |
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120q, ɢ ɫɬɨɪɨɧɨɣ, ɪɚɜɧɨɣ |
4. ɇɚɣɞɢɬɟ ɜɵɫɨɬɭ ɩɪɢɡɦɵ, ɟɫɥɢ ɭɝɨɥ ɦɟɠɞɭ |
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ɩɥɨɫɤɨɫɬɹɦɢ ADC1 ɢ ABC ɪɚɜɟɧ 60q. |
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C3 |
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log |
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6x x2 5 t 2, |
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Ɋɟɲɢɬɟ ɫɢɫɬɟɦɭ ɧɟɪɚɜɟɧɫɬɜ ® |
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¯ |
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° |
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x |
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© ɋɬɚɬȽɪɚɞ 2013 ɝ.
Ɇɚɬɟɦɚɬɢɤɚ. 10 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ Ɇ |
0208 (ɡɚɩɚɞ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
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8 |
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C4 |
Ɍɚɧɝɟɧɫ ɭɝɥɚ C ɬɪɟɭɝɨɥɶɧɢɤɚ |
ABC |
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, D |
— ɨɬɥɢɱɧɚɹ ɨɬ |
A ɬɨɱɤɚ |
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ɩɟɪɟɫɟɱɟɧɢɹ ɨɤɪɭɠɧɨɫɬɟɣ, ɩɨɫɬɪɨɟɧɧɵɯ ɧɚ4 ɫɬɨɪɨɧɚɯ |
AB ɢ AC |
ɤɚɤ ɧɚ |
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ɞɢɚɦɟɬɪɚɯ. ɂɡɜɟɫɬɧɨ, ɱɬɨ DB : DC |
9 : 16. |
ɇɚɣɞɢɬɟ ɭɝɨɥ A. |
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C5 |
ɇɚɣɞɢɬɟ |
ɜɫɟ |
ɡɧɚɱɟɧɢɹ |
, ɩɪɢ ɤɚɠɞɨɦ |
ɢɡ |
ɤɨɬɨɪɵɯ |
ɫɢɫɬɟɦɚ |
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y |
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4a(x y) |
8a |
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2a, |
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ɭɪɚɜɧɟɧɢɣ |
° x |
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ɢɦɟɟɬ ɪɨɜɧɨ ɞɜɚ ɪɟɲɟɧɢɹ. |
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y2 8a(x y) |
32a2 18a |
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¯ |
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® x |
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C6 |
ɋɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɱɟɬɵɪɺɯ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɜ |
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ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ |
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ɫɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɨɛɪɚɬɧɵɯ ɱɢɫɟɥ. ɇɚɣɞɢɬɟ ɷɬɢ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ. |
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© ɋɬɚɬȽɪɚɞ 2013 ɝ.
Ⱦɢɚɝɧɨɫɬɢɱɟɫ ɚɹ ɪɚɛɨɬɚ ʋ 1
ɩɨ ɆȺɌȿɆȺɌɂɄȿ 21 ɦɚɹ 2013 ɝɨɞɚ
ɥɚɫɫ10
ȼɚɪɢɚɧɬ ɆȺ0209 (ɜɨɫɬɨ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ)
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Ɋɚɣɨɧ Ƚɨɪɨɞ (ɧɚɫɟɥɺɧɧɵɣ ɩɭɧɤɬ)
ɒɤɨɥɚ
Ʉɥɚɫɫ
Ɏɚɦɢɥɢɹ
ɂɦɹ
Ɉɬɱɟɫɬɜɨ
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ 0209 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) 2
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ɂɧɫɬɪɭ |
ɢɹ ɩɨ ɜɵɩɨɥɧɟɧɢɸ ɪɚɛɨɬɵ |
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ɇɚ ɜɵɩɨɥɧɟɧɢɟ ɞɢɚɝɧɨɫɬɢɱɟɫɤɨɣ ɪɚɛɨɬɵ ɩɨ ɦɚɬɟɦɚɬɢɤɟ ɞɚɺɬɫɹɦɢɧɭɬ235 |
. Ɋɚɛɨɬɚ |
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ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɱɚɫɬɟɣ ɢ ɫɨɞɟɪɠɢɬ 20 ɡɚɞɚɧɢɣ. |
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ɑɚɫɬɶ14 |
1 ɫɨɞɟɪɠɢɬ |
ɡɚɞɚɧɢɣ ɫ ɤɪɚɬɤɢɦ ɨɬɜɟɬɨɦ (ȼȼ1– 14) ɛɚɡɨɜɨɝɨ ɭɪɨɜɧɹ ɩɨ |
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ɦɚɬɟɪɢɚɥɭ |
ɤɭɪɫɚ ɦɚɬɟɦɚɬɢɤɢ |
Ɂɚɞɚɧɢɹ ɱɚɫɬɢ 1 ɫɱɢɬɚɸɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦɢ, ɟɫɥɢ |
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ɷɤɡɚɦɟɧɭɟɦɵɣ ɞɚɥ ɜɟɪɧɵɣ ɨɬɜɟɬ ɜ ɜɢɞɟ ɰɟɥɨɝɨ ɱɢɫɥɚ ɢɥɢ ɤɨɧɟɱɧɨɣ ɞɟɫɹɬɢɱɧɨɣ ɞɪɨɛɢ. ɑɚɫɬɶ 2 ɫɨɞɟɪɠɢɬ 6 ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɡɚɞɚɧɢɣ (ɋɋ1– 6) ɩɨ ɦɚɬɟɪɢɚɥɭ ɤɭɪɫɚ
ɦɚɬɟɦɚɬɢɤɢ. ɉɪɢ ɢɯ ɜɵɩɨɥɧɟɧɢɢ ɧɚɞɨ ɡɚɩɢɫɚɬɶ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ ɢ ɨɬɜɟɬ.
ɋɨɜɟɬɭɟɦ ɞɥɹ ɷɤɨɧɨɦɢɢ ɜɪɟɦɟɧɢ ɩɪɨɩɭɫɤɚɬɶ ɡɚɞɚɧɢɟ, ɤɨɬɨɪɨɟ ɧɟ ɭɞɚɺɬɫɹ ɜɵɩɨɥɧɢɬɶ ɫɪɚɡɭ, ɢ ɩɟɪɟɯɨɞɢɬɶ ɤ ɫɥɟɞɭɸɳɟɦɭ. Ʉ ɜɵɩɨɥɧɟɧɢɸ ɩɪɨɩɭɳɟɧɧɵɯ ɡɚɞɚɧɢɣ ɦɨɠɧɨ ɜɟɪɧɭɬɶɫɹ, ɟɫɥɢ ɭ ȼɚɫ ɨɫɬɚɧɟɬɫɹ ɜɪɟɦɹ.
ɀɟɥɚɟɦ ɭɫɩɟɯɚ!
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0209 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
3 |
ɑɚɫɬɶ 1
Ɉɬɜɟɬɨɦ ɧɚ ɡɚɞɚɧɢɹ ȼ1–ȼ14 ɞɨɥɠɧɨ ɛɵɬɶ ɰɟɥɨɟ ɱɢɫɥɨ ɢɥɢ ɤɨɧɟɱɧɚɹ ɞɟɫɹɬɢɱɧɚɹ ɞɪɨɛɶ. Ɉɬɜɟɬ ɫɥɟɞɭɟɬ ɡɚɩɢɫɚɬɶ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1 ɫɩɪɚɜɚ ɨɬ ɧɨɦɟɪɚ ɜɵɩɨɥɧɹɟɦɨɝɨ ɡɚɞɚɧɢɹ, ɧɚɱɢɧɚɹ ɫ ɩɟɪɜɨɣ ɤɥɟɬɨɱɤɢ. Ʉɚɠɞɭɸ ɰɢɮɪɭ, ɡɧɚɤ ɦɢɧɭɫ ɢ ɡɚɩɹɬɭɸ ɩɢɲɢɬɟ ɜ ɨɬɞɟɥɶɧɨɣ ɤɥɟɬɨɱɤɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɜɟɞɺɧɧɵɦɢ ɜ ɛɥɚɧɤɟ ɨɛɪɚɡɰɚɦɢ. ȿɞɢɧɢɰɵ ɢɡɦɟɪɟɧɢɣ ɩɢɫɚɬɶ ɧɟ ɧɭɠɧɨ.
B1 ɉɪɢ ɨɩɥɚɬɟ ɭɫɥɭɝ ɱɟɪɟɡ ɩɥɚɬɺɠɧɵɣ ɬɟɪɦɢɧɚɥ ɜɡɢɦɚɟɬɫɹ ɤɨɦɢɫɫɢɹ 8%. Ɍɟɪɦɢɧɚɥ ɩɪɢɧɢɦɚɟɬ ɫɭɦɦɵ, ɤɪɚɬɧɵɟ 10 ɪɭɛɥɹɦ. Ɇɟɫɹɱɧɚɹ ɩɥɚɬɚ ɡɚ ɢɧɬɟɪɧɟɬ ɫɨɫɬɚɜɥɹɟɬ 550 ɪɭɛɥɟɣ. Ʉɚɤɭɸ ɦɢɧɢɦɚɥɶɧɭɸ ɫɭɦɦɭ (ɜ ɪɭɛɥɹɯ) ɧɟɨɛɯɨɞɢɦɨ ɩɨɥɨɠɢɬɶ ɜ ɩɪɢɺɦɧɨɟ ɭɫɬɪɨɣɫɬɜɨ ɬɟɪɦɢɧɚɥɚ, ɱɬɨɛɵ ɧɚ ɫɱɟɬɭ ɮɢɪɦɵ, ɩɪɟɞɨɫɬɚɜɥɹɸɳɟɣ ɢɧɬɟɪɧɟɬ ɭɫɥɭɝɢ, ɨɤɚɡɚɥɚɫɶ ɫɭɦɦɚ, ɧɟ ɦɟɧɶɲɚɹ 550 ɪɭɛɥɟɣ?
Ɉɬɜɟɬ: 
B2 ɇɚ ɪɢɫɭɧɤɟ ɠɢɪɧɵɦɢ ɬɨɱɤɚɦɢ ɩɨɤɚɡɚɧ ɤɭɪɫ ɟɜɪɨ, ɭɫɬɚɧɨɜɥɟɧɧɵɣ ɟɧɬɪɨɛɚɧɤɨɦ ɊɎ, ɜɨ ɜɫɟ ɪɚɛɨɱɢɟ ɞɧɢ ɫ 1 ɮɟɜɪɚɥɹ ɩɨ 28 ɮɟɜɪɚɥɹ 2003 ɝɨɞɚ.
ɉɨ ɝɨɪɢɡɨɧɬɚɥɢ ɭɤɚɡɵɜɚɸɬɫɹ ɱɢɫɥɚ ɦɟɫɹɰɚ, ɩɨ- ɜɟɪɬɢɤɚɥɢ — ɰɟɧɚ ɟɜɪɨ ɜ ɪɭɛ ɥɹɯ. Ⱦɥɹ ɧɚɝɥɹɞɧɨɫɬɢ ɠɢɪɧɵɟ ɬɨɱɤɢ ɧɚ ɪɢɫɭɧɤɟ ɫɨɟɞɢɧɟɧɵ ɥɢɧɢɟɣ. Ɉɩɪɟɞɟɥɢɬɟ ɩɨ ɪɢɫɭɧɤɭ, ɫɤɨɥɶɤɨ ɪɚɛɨɱɢɯ ɞɧɟɣ ɢɡ ɞɚɧɧɨɝɨ ɩɟɪɢɨɞɚ ɤɭɪɫ ɟɜɪɨ
ɛɵɥ ɦɟɠɞɭ 34,1 ɢ 34,4 ɪɭɛɥɹ.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0209 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
4 |
B3 ɇɚɣɞɢɬɟ ɩɥɨɳɚɞɶu ɪɨɦɛɚ, ɢɡɨɛɪɚɠɺɧɧɨɝɨ ɧɚ ɤɥɟɬɱɚɬɨɣ ɛɭɦɚɝɟ ɫ ɪɚɡɦɟɪɨɦ ɤɥɟɬɤɢɫɦ1 1 ɫɦ (ɫɦ. ɪɢɫ.). Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɤɜɚɞɪɚɬɧɵɯ ɫɚɧɬɢɦɟɬɪɚɯ.
Ɉɬɜɟɬ: 
B4 |
ɋɟɦɶɹ ɢɡ ɬɪɺɯ ɱɟɥɨɜɟɤ ɩɥɚɧɢɪɭɟɬ ɩɨɟɯɚɬɶ ɢɡ Ɇɨɫɤɜɵ ɜ ɑɟɛɨɤɫɚɪɵ. |
Ɇɨɠɧɨ |
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ɟɯɚɬɶ ɩɨɟɡɞɨɦ— , ɚ ɦɨɠɧɨ |
ɧɚ ɫɜɨɟɣ ɦɚɲɢɧɟ. Ȼɢɥɟɬ ɧɚ ɩɨɟɡɞ ɧɚ |
ɨɞɧɨɝɨ |
ɱɟɥɨɜɟɤɚ ɫɬɨɢɬ 850 ɪɭɛɥɟɣ. ɜɬɨɦɨɛɢɥɶ ɪɚɫɯɨɞɭɟɬ 15 ɥɢɬɪɨɜ ɛɟɧɡɢɧɚ ɧɚ 100 ɤɢɥɨɦɟɬɪɨɜ ɩɭɬɢ, ɪɚɫɫɬɨɹɧɢɟ ɩɨ ɲɨɫɫɟ ɪɚɜɧɨ 700 ɤɦ, ɚ ɰɟɧɚ ɛɟɧɡɢɧɚ ɪɚɜɧɚ 20 ɪɭɛɥɟɣ ɡɚ ɥɢɬɪ. ɋɤɨɥɶɤɨ ɪɭɛɥɟɣ ɩɪɢɞɺɬɫɹ ɡɚɩɥɚɬɢɬɶ ɡɚ ɧɚɢɛɨɥɟɟ ɞɟɲɺɜɭɸ ɩɨɟɡɞɤɭ ɧɚ ɬɪɨɢɯ?
Ɉɬɜɟɬ: 
B5 ɇɚɣɞɢɬɟ ɤɨɪɟɧɶ ɭɪɚɜɧɟɧɢɹ 2x 3 5.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ 0209 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) 5
B6 ɑɟɬɵɪɺɯɭɝɨɥɶɧɢɤq ABCD ɜɩɢɫɚɧ ɜ ɨɤɪɭɠɧɨɫɬɶ. ɍɝɨɥ ABC ɪɚɜɟɧ 110q, ɭɝɨɥ CAD ɪɚɜɟɧ 69 . ɇɚɣɞɢɬɟ ɭɝɨɥ ABD. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɝɪɚɞɭɫɚɯ.
Ɉɬɜɟɬ: 
ɇɚɣɞɢɬɟ ɡɧɚɱɟɧɢɟ ɜɵɪɚɠɟɧɢɹ 24sin39qcos39q.
B7 q sin78
Ɉɬɜɟɬ: 
B8 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɝɪɚɮɢɤ ɮɭɧɤɰɢɢ y f (x) ɢ ɤɚɫɚɬɟɥɶɧɚɹ ɤ ɧɟɦɭ ɜ ɬɨɱ- ɤɟ ɫ ɚɛɫɰɢɫɫɨɣ x0. ɇɚɣɞɢɬɟ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɨɞɧɨɣ ɮɭɧɤɰɢɢ f (x) ɜ ɬɨɱɤɟ x0.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0209 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
6 |
B9 ȼ ɩɪɚɜɢɥɶɧɨɣ |
ɱɟɬɵɪɺɯɭɝɨɥɶɧɨɣ ɩɢɪɚɦɢɞɟ SABCD ɬɨɱɤɚ O |
— ɰɟɧɬɪ |
ɨɫɧɨɜɚɧɢɹ, SO |
12, SB 15. ɇɚɣɞɢɬɟ ɞɥɢɧɭ ɨɬɪɟɡɤɚ AC. |
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Ɉɬɜɟɬ: 
B10 |
Ɇɢɲɚ, Ɉɥɟɝ, ɇɚɫɬɹ ɢ Ƚɚɥɹ ɛɪɨɫɢɥɢ ɠɪɟɛɢɣ — ɤɨɦɭ ɧɚɱɢɧɚɬɶ ɢɝɪɭ. ɇɚɣɞɢɬɟ |
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ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɧɚɱɢɧɚɬɶ ɢɝɪɭ ɞɨɥɠɧɚ ɛɭɞɟɬ Ƚɚɥɹ. |
Ɉɬɜɟɬ: 
B11 ɇɚɣɞɢɬɟ ɩɥɨɳɚɞɶ ɩɨɜɟɪɯɧɨɫɬɢ ɦɧɨɝɨɝɪɚɧɧɢɤɚ, ɢɡɨɛɪɚɠɺɧɧɨɝɨ ɧɚ ɪɢɫɭɧɤɟ
(ɜɫɟ ɞɜɭɝɪɚɧɧɵɟ ɭɝɥɵ ɩɪɹɦɵɟ).
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0209 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
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7 |
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B12 |
ȼ |
ɛɨɤɨɜɨɣ |
ɫɬɟɧɤɟ ɜɵɫɨɤɨɝɨ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɛɚɤɚ ɭ ɫɚɦɨɝɨ ɞɧɚ |
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ɡɚɤɪɟɩɥɺɧ ɤɪɚɧ. |
ɉɨɫɥɟ ɟɝɨ ɨɬɤɪɵɬɢɹ ɜɨɞɚ ɧɚɱɢɧɚɟɬ ɜɵɬɟɤɚɬɶ ɢɡ ɛɚɤɚ, |
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ɩɪɢ |
ɷɬɨɦ |
ɜɵɫɨɬɚ |
ɫɬɨɥɛɚ |
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ɜɨɞɵ ɜ ɧɺɦ, ɜɵɪɚɠɟɧɧɚɹ |
ɜ ɦɟɬɪɚɯ, ɦɟɧɹɟɬɫɹ |
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ɩɨ |
ɡɚɤɨɧɭ |
H(t) |
at2 |
bt |
H0, ɝɞɟ H0 3,5 ɦ — ɧɚɱɚɥɶɧɵɣ ɭɪɨɜɟɧɶ ɜɨɞɵ, |
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a |
—1 |
ɦ ɦɢɧ2 |
ɢ |
b |
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ɦ ɦɢɧ |
ɩɨɫɬɨɹɧɧɵɟ, t — |
ɜɪɟɦɹ ɜ ɦɢɧɭɬɚɯ, |
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ȼ ɬɟɱɟɧɢɟ ɤɚɤɨɝɨ ɜɪɟɦɟɧɢ ɜɨɞɚ ɛɭɞɟɬ |
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ɩɪɨɲɟɞɲɟɟ ɫ ɦɨɦɟɧɬɚ ɨɬɤɪɵɬɢɹ ɤɪɚɧɚ |
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ɜɵɬɟɤɚɬɶ ɢɡ ɛɚɤɚ? |
Ɉɬɜɟɬ ɩɪɢɜɟɞɢɬɟ ɜ ɦɢɧɭɬɚɯ |
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Ɉɬɜɟɬ: 
B13 Ɇɨɬɨɪɧɚɹ ɥɨɞɤɚ ɩɪɨɲɥɚ ɩɪɨɬɢɜ ɬɟɱɟɧɢɹ ɪɟɤɢ 63 ɤɦ ɢ ɜɟɪɧɭɥɚɫɶ ɜ ɩɭɧɤɬ ɨɬɩɪɚɜɥɟɧɢɹ, ɡɚɬɪɚɬɢɜ ɧɚ ɨɛɪɚɬɧɵɣ ɩɭɬɶ ɧɚ 2 ɱɚɫɚ ɦɟɧɶɲɟ. ɇɚɣɞɢɬɟ ɫɤɨɪɨɫɬɶ ɬɟɱɟɧɢɹ, ɟɫɥɢ ɫɤɨɪɨɫɬɶ ɥɨɞɤɢ ɜ ɧɟɩɨɞɜɢɠɧɨɣ ɜɨɞɟ ɪɚɜɧɚ 8 ɤɦ ɱ. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɤɦ ɱ.
Ɉɬɜɟɬ: |
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B14 ɇɚɣɞɢɬɟ ɬɨɱɤɭ ɦɢɧɢɦɭɦɚ ɮɭɧɤɰɢɢ y |
x2 6x 36. |
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Ɉɬɜɟɬ: |
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ɑɚɫɬɶ 2 |
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Ⱦɥɹ ɡɚɩɢɫɢ ɪɟɲɟɧɢɣ ɢ ɨɬɜɟɬɨɜ ɧɚ ɡɚɞɚɧɢɹ C1–C6 ɢɫɩɨɥɶɡɭɣɬɟ ɛɥɚɧɤ ɨɬɜɟɬɨɜ |
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ʋ 2. |
Ɂɚɩɢɲɢɬɟ ɫɧɚɱɚɥɚ ɧɨɦɟɪ ɜɵɩɨɥɧɹɟɦɨɝɨ ɡɚɞɚɧɢɹ (ɋ1, ɋ2 ɢ ɬ ɞ.), ɚ ɡɚɬɟɦ |
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ɩɨɥɧɨɟ ɨɛɨɫɧɨɜɚɧɧɨɟ ɪɟɲɟɧɢɟ ɢ ɨɬɜɟɬ. |
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ɚ) Ɋɟɲɢɬɟ ɭɪɚɜɧɟɧɢɟ |
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sinx |
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sin x |
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ɛ) |
ɇɚɣɞɢɬɟ ɜɫɟ |
ɤɨɪɧɢ |
ɷɬɨɝɨ |
ɭɪɚɜɧɟɧɢɹ, |
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ɩɪɢɧɚɞɥɟɠɚɳɢɟ ɩɪɨɦɟɠɭɬɤɭ |
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5ʌ |
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3ʌ |
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C2 |
Ɉɫɧɨɜɚɧɢɟ ɩɪɹɦɨɣ ɩɪɢɡɦɵ ABCDA1B1C1D1 — ɪɨɦɛ ABCD ɫ ɭɝɥɨɦ A, ɪɚɜɧɵɦ |
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ɢ ɫɬɨɪɨɧɨɣ, |
ɪɚɜɧɨɣ |
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ɇɚɣɞɢɬɟ ɜɵɫɨɬɭ ɩɪɢɡɦɵ, ɟɫɥɢ ɭɝɨɥ ɦɟɠɞɭ |
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ɩɥɨɫɤɨɫɬɹɦɢ A1BC ɢ ABC ɪɚɜɟɧ 30q. |
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10)x |
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Ɋɟɲɢɬɟ ɫɢɫɬɟɦɭ ɧɟɪɚɜɟɧɫɬɜ ® |
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t 0. |
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¯ |
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© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0209 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
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8 |
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C4 |
Ɍɚɧɝɟɧɫ ɭɝɥɚ C ɬɪɟɭɝɨɥɶɧɢɤɚ |
ABC |
ɪɚɜɟɧ |
2 |
, D — ɨɬɥɢɱɧɚɹ ɨɬ |
A ɬɨɱɤɚ |
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ɩɟɪɟɫɟɱɟɧɢɹ |
ɨɤɪɭɠɧɨɫɬɟɣ, |
ɩɨɫɬɪɨɟɧɧɵɯ |
ɧɚ 3ɫɬɨɪɨɧɚɯ AB ɢ |
AC |
ɤɚɤ |
ɧɚ |
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ɞɢɚɦɟɬɪɚɯ. ɂɡɜɟɫɬɧɨ, ɱɬɨ DB : DC 4 |
: 9. ɇɚɣɞɢɬɟ ɭɝɨɥ A. |
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C5 |
ɇɚɣɞɢɬɟ ɜɫɟ ɡɧɚɱɟɧɢɹ, |
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ɩɪɢ ɤɚɠɞɨɦ ɢɡ ɤɨɬɨɪɵɯ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ |
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y |
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2a(x y) |
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° x |
2 |
2 |
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y2 |
4a(x y) |
8a2 9a |
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® x |
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ɢɦɟɟɬ ɟɞɢɧɫɬɜɟɧɧɨɟ ɪɟɲɟɧɢɟ. |
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C6 |
ɋɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ |
ɬɪɺɯ |
ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɜ |
35 |
ɪɚɡɚ |
ɛɨɥɶɲɟ, |
ɱɟɦ |
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11 |
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ɫɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɨɛɪɚɬɧɵɯ ɱɢɫɟɥ. ɇɚɣɞɢɬɟ ɷɬɢ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ. |
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© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ⱦɢɚɝɧɨɫɬɢɱɟɫ ɚɹ ɪɚɛɨɬɚ ʋ 1
ɩɨ ɆȺɌȿɆȺɌɂɄȿ 21 ɦɚɹ 2013 ɝɨɞɚ
ɥɚɫɫ10
ȼɚɪɢɚɧɬ ɆȺ0210 (ɜɨɫɬɨ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ)
.
Ɋɚɣɨɧ Ƚɨɪɨɞ (ɧɚɫɟɥɺɧɧɵɣ ɩɭɧɤɬ)
ɒɤɨɥɚ
Ʉɥɚɫɫ
Ɏɚɦɢɥɢɹ
ɂɦɹ
Ɉɬɱɟɫɬɜɨ
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ 0210 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) 2
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ɂɧɫɬɪɭ |
ɢɹ ɩɨ ɜɵɩɨɥɧɟɧɢɸ ɪɚɛɨɬɵ |
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ɇɚ ɜɵɩɨɥɧɟɧɢɟ ɞɢɚɝɧɨɫɬɢɱɟɫɤɨɣ ɪɚɛɨɬɵ ɩɨ ɦɚɬɟɦɚɬɢɤɟ ɞɚɺɬɫɹɦɢɧɭɬ235 |
. Ɋɚɛɨɬɚ |
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ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɱɚɫɬɟɣ ɢ ɫɨɞɟɪɠɢɬ 20 ɡɚɞɚɧɢɣ. |
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ɑɚɫɬɶ14 |
1 ɫɨɞɟɪɠɢɬ |
ɡɚɞɚɧɢɣ ɫ ɤɪɚɬɤɢɦ ɨɬɜɟɬɨɦ (ȼȼ1– 14) ɛɚɡɨɜɨɝɨ ɭɪɨɜɧɹ ɩɨ |
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ɦɚɬɟɪɢɚɥɭ |
ɤɭɪɫɚ ɦɚɬɟɦɚɬɢɤɢ |
Ɂɚɞɚɧɢɹ ɱɚɫɬɢ 1 ɫɱɢɬɚɸɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦɢ, ɟɫɥɢ |
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ɷɤɡɚɦɟɧɭɟɦɵɣ ɞɚɥ ɜɟɪɧɵɣ ɨɬɜɟɬ ɜ ɜɢɞɟ ɰɟɥɨɝɨ ɱɢɫɥɚ ɢɥɢ ɤɨɧɟɱɧɨɣ ɞɟɫɹɬɢɱɧɨɣ ɞɪɨɛɢ. ɑɚɫɬɶ 2 ɫɨɞɟɪɠɢɬ 6 ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɡɚɞɚɧɢɣ (ɋɋ1– 6) ɩɨ ɦɚɬɟɪɢɚɥɭ ɤɭɪɫɚ
ɦɚɬɟɦɚɬɢɤɢ. ɉɪɢ ɢɯ ɜɵɩɨɥɧɟɧɢɢ ɧɚɞɨ ɡɚɩɢɫɚɬɶ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ ɢ ɨɬɜɟɬ.
ɋɨɜɟɬɭɟɦ ɞɥɹ ɷɤɨɧɨɦɢɢ ɜɪɟɦɟɧɢ ɩɪɨɩɭɫɤɚɬɶ ɡɚɞɚɧɢɟ, ɤɨɬɨɪɨɟ ɧɟ ɭɞɚɺɬɫɹ ɜɵɩɨɥɧɢɬɶ ɫɪɚɡɭ, ɢ ɩɟɪɟɯɨɞɢɬɶ ɤ ɫɥɟɞɭɸɳɟɦɭ. Ʉ ɜɵɩɨɥɧɟɧɢɸ ɩɪɨɩɭɳɟɧɧɵɯ ɡɚɞɚɧɢɣ ɦɨɠɧɨ ɜɟɪɧɭɬɶɫɹ, ɟɫɥɢ ɭ ȼɚɫ ɨɫɬɚɧɟɬɫɹ ɜɪɟɦɹ.
ɀɟɥɚɟɦ ɭɫɩɟɯɚ!
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0210 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
3 |
ɑɚɫɬɶ 1
Ɉɬɜɟɬɨɦ ɧɚ ɡɚɞɚɧɢɹ ȼ1–ȼ14 ɞɨɥɠɧɨ ɛɵɬɶ ɰɟɥɨɟ ɱɢɫɥɨ ɢɥɢ ɤɨɧɟɱɧɚɹ ɞɟɫɹɬɢɱɧɚɹ ɞɪɨɛɶ. Ɉɬɜɟɬ ɫɥɟɞɭɟɬ ɡɚɩɢɫɚɬɶ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1 ɫɩɪɚɜɚ ɨɬ ɧɨɦɟɪɚ ɜɵɩɨɥɧɹɟɦɨɝɨ ɡɚɞɚɧɢɹ, ɧɚɱɢɧɚɹ ɫ ɩɟɪɜɨɣ ɤɥɟɬɨɱɤɢ. Ʉɚɠɞɭɸ ɰɢɮɪɭ, ɡɧɚɤ ɦɢɧɭɫ ɢ ɡɚɩɹɬɭɸ ɩɢɲɢɬɟ ɜ ɨɬɞɟɥɶɧɨɣ ɤɥɟɬɨɱɤɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɜɟɞɺɧɧɵɦɢ ɜ ɛɥɚɧɤɟ ɨɛɪɚɡɰɚɦɢ. ȿɞɢɧɢɰɵ ɢɡɦɟɪɟɧɢɣ ɩɢɫɚɬɶ ɧɟ ɧɭɠɧɨ.
B1 |
Ȼɟɝɭɧ ɩɪɨɛɟɠɚɥ 250 ɦ ɡɚ 25 ɫɟɤɭɧɞ. ɇɚɣɞɢɬɟ ɫɪɟɞɧɸɸ ɫɤɨɪɨɫɬɶ ɛɟɝɭɧɚ ɧɚ |
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ɞɢɫɬɚɧɰɢɢ. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɤɢɥɨɦɟɬɪɚɯ ɜ ɱɚɫ. |
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Ɉɬɜɟɬ: |
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B2 |
ɇɚ ɞɢɚɝɪɚɦɦɟ ɩɨɤɚɡɚɧɚ ɫɪɟɞɧɟɦɟɫɹɱɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡɞɭɯɚ ɜ Ɇɢɧɫɤɟ ɡɚ |
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ɤɚɠɞɵɣ ɦɟɫɹɰ |
2003 |
ɝɨɞɚ. |
ɉɨ ɝɨɪɢɡɨɧɬɚɥɢ ɭɤɚɡɵɜɚɸɬɫɹ ɦɟɫɹɰɵ, |
ɩɨ |
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ɜɟɪɬɢɤɚɥɢ — ɬɟɦɩɟɪɚɬɭɪɚ ɜ |
ɝɪɚɞɭɫɚɯ ɟɥɶɫɢɹ Ɉɩɪɟɞɟɥɢɬɟ ɩɨ ɞɢɚɝɪɚɦɦɟ, |
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ɫɤɨɥɶɤɨ ɛɵɥɨ ɦɟɫɹɰɟɜ ɜ |
ɝɨɞɭ, ɤɨɝɞɚ ɫɪɟɞɧɟɦɟɫɹɱɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɛɵɥɚ |
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ɩɨɥɨɠɢɬɟɥɶɧɨɣ.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0210 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
4 |
B3 ɇɚɣɞɢɬɟ ɩɥɨɳɚɞɶu ɪɨɦɛɚ, ɢɡɨɛɪɚɠɺɧɧɨɝɨ ɧɚ ɤɥɟɬɱɚɬɨɣ ɛɭɦɚɝɟ ɫ ɪɚɡɦɟɪɨɦ ɤɥɟɬɤɢɫɦ1 1 ɫɦ (ɫɦ. ɪɢɫ.). Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɤɜɚɞɪɚɬɧɵɯ ɫɚɧɬɢɦɟɬɪɚɯ.
Ɉɬɜɟɬ: 
B4 |
ɋɟɦɶɹ ɢɡ ɬɪɺɯ ɱɟɥɨɜɟɤ ɩɥɚɧɢɪɭɟɬ ɩɨɟɯɚɬɶ ɢɡ Ɇɨɫɤɜɵ ɜ ɑɟɛɨɤɫɚɪɵ. |
Ɇɨɠɧɨ |
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ɟɯɚɬɶ ɩɨɟɡɞɨɦ, ɚ ɦɨɠɧɨ — ɧɚ ɫɜɨɟɣ ɦɚɲɢɧɟ. Ȼɢɥɟɬ ɧɚ ɩɨɟɡɞ ɧɚ |
ɨɞɧɨɝɨ |
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ɱɟɥɨɜɟɤɚ ɫɬɨɢɬ 810 ɪɭɛɥɟɣ. |
ɜɬɨɦɨɛɢɥɶ ɪɚɫɯɨɞɭɟɬ 14 ɥɢɬɪɨɜ ɛɟɧɡɢɧɚ ɧɚ |
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100 ɤɢɥɨɦɟɬɪɨɜ ɩɭɬɢ, ɪɚɫɫɬɨɹɧɢɟ ɩɨ ɲɨɫɫɟ ɪɚɜɧɨ 700 ɤɦ, ɚ ɰɟɧɚ ɛɟɧɡɢɧɚ ɪɚɜɧɚ 20,5 ɪɭɛɥɹ ɡɚ ɥɢɬɪ. ɋɤɨɥɶɤɨ ɪɭɛɥɟɣ ɩɪɢɞɺɬɫɹ ɡɚɩɥɚɬɢɬɶ ɡɚ ɧɚɢɛɨɥɟɟ ɞɟɲɺɜɭɸ ɩɨɟɡɞɤɭ ɧɚ ɬɪɨɢɯ?
Ɉɬɜɟɬ: 
B5 ɇɚɣɞɢɬɟ ɤɨɪɟɧɶ ɭɪɚɜɧɟɧɢɹ 3x 4 4.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0210 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
5 |
B6 ɑɟɬɵɪɺɯɭɝɨɥɶɧɢɤq ABCD ɜɩɢɫɚɧ ɜ ɨɤɪɭɠɧɨɫɬɶ. ɍɝɨɥ ABC ɪɚɜɟɧ 66q, ɭɝɨɥ CAD ɪɚɜɟɧ 47 . ɇɚɣɞɢɬɟ ɭɝɨɥ ABD. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɝɪɚɞɭɫɚɯ.
Ɉɬɜɟɬ: 
ɇɚɣɞɢɬɟ ɡɧɚɱɟɧɢɟ ɜɵɪɚɠɟɧɢɹ 10sin16qcos16q .
B7 q sin32
Ɉɬɜɟɬ: 
B8 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɝɪɚɮɢɤ ɮɭɧɤɰɢɢ y f (x) ɢ ɤɚɫɚɬɟɥɶɧɚɹ ɤ ɧɟɦɭ ɜ ɬɨɱ- ɤɟ ɫ ɚɛɫɰɢɫɫɨɣ x0. ɇɚɣɞɢɬɟ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɨɞɧɨɣ ɮɭɧɤɰɢɢ f (x) ɜ ɬɨɱɤɟ x0.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0210 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
6 |
B9 ȼ ɩɪɚɜɢɥɶɧɨɣ |
ɱɟɬɵɪɺɯɭɝɨɥɶɧɨɣ ɩɢɪɚɦɢɞɟ SABCD |
ɬɨɱɤɚ O — ɰɟɧɬɪ |
ɨɫɧɨɜɚɧɢɹ, SO |
12, SA 13. ɇɚɣɞɢɬɟ ɞɥɢɧɭ ɨɬɪɟɡɤɚ BD. |
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Ɉɬɜɟɬ: 
B10 |
Ⱦɢɦɚ, Ɇɚɪɚɬ, ɉɟɬɹ, ɇɚɞɹ ɢ ɋɜɟɬɚ ɛɪɨɫɢɥɢ ɠɪɟɛɢɣ — ɤɨɦɭ ɧɚɱɢɧɚɬɶ ɢɝɪɭ. |
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ɇɚɣɞɢɬɟ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɧɚɱɢɧɚɬɶ ɢɝɪɭ ɞɨɥɠɟɧ ɛɭɞɟɬ ɦɚɥɶɱɢɤ. |
Ɉɬɜɟɬ: 
B11 ɇɚɣɞɢɬɟ ɩɥɨɳɚɞɶ ɩɨɜɟɪɯɧɨɫɬɢ ɦɧɨɝɨɝɪɚɧɧɢɤɚ, ɢɡɨɛɪɚɠɺɧɧɨɝɨ ɧɚ ɪɢɫɭɧɤɟ
(ɜɫɟ ɞɜɭɝɪɚɧɧɵɟ ɭɝɥɵ ɩɪɹɦɵɟ).
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10 |
ȼɚɪɢɚɧɬ Ɇ 0210 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
7 |
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B12 |
ȼ ɛɨɤɨɜɨɣ ɫɬɟɧɤɟ ɜɵɫɨɤɨɝɨ |
ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɛɚɤɚ ɭ ɫɚɦɨɝɨ ɞɧɚ ɡɚɤɪɟɩɥɺɧ |
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ɤɪɚɧ. |
ɉɨɫɥɟ ɟɝɨ ɨɬɤɪɵɬɢɹ ɜɨɞɚ ɧɚɱɢɧɚɟɬ ɜɵɬɟɤɚɬɶ ɢɡ ɛɚɤɚ, |
ɩɪɢ ɷɬɨɦ |
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ɜɵɫɨɬɚ ɫɬɨɥɛɚ ɜɨɞɵ ɜ ɧɺɦ, ɜɵɪɚɠɟɧɧɚɹ ɜ ɦɟɬɪɚɯ, ɦɟɧɹɟɬɫɹ |
ɩɨ ɡɚɤɨɧɭ |
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H(t) |
at2 bt H0, ɝɞɟ H0 |
9 ɦ — ɧɚɱɚɥɶɧɵɣ ɭɪɨɜɟɧɶ ɜɨɞɵ, a |
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ɢ b |
ɦ ɦɢɧ — ɩɨɫɬɨɹɧɧɵɟ, t — ɜɪɟɦɹ ɜ ɦɢɧɭɬɚɯ, ɩɪɨɲɟɞɲɟɟ ɫ ɦɨɦɟɧɬɚ |
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ɨɬɤɪɵɬɢɹ ɤɪɚɧɚ. ȼ ɬɟɱɟɧɢɟ ɤɚɤɨɝɨ ɜɪɟɦɟɧɢ ɜɨɞɚ ɛɭɞɟɬ ɜɵɬɟɤɚɬɶ ɢɡ ɛɚɤɚ? Ɉɬɜɟɬ ɩɪɢɜɟɞɢɬɟ ɜ ɦɢɧɭɬɚɯ.
Ɉɬɜɟɬ: 
B13 Теплоход прошёл против течения реки 143 км и вернулся в пункт отправления, затратив на обратный путь на 2 часа меньше. Найдите скорость течения, если скорость телохода в неподвижной воде равна 12 км/ч. Ответ дайте в км/ч.
Ɉɬɜɟɬ: 
B14 ɇɚɣɞɢɬɟ ɬɨɱɤɭ ɦɚɤɫɢɦɭɦɚ ɮɭɧɤɰɢɢ y |
14 8x x2. |
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ɑɚɫɬɶ 2
Ⱦɥɹ ɡɚɩɢɫɢ ɪɟɲɟɧɢɣ ɢ ɨɬɜɟɬɨɜ ɧɚ ɡɚɞɚɧɢɹ C1–C6 ɢɫɩɨɥɶɡɭɣɬɟ ɛɥɚɧɤ ɨɬɜɟɬɨɜ
ʋ 2. Ɂɚɩɢɲɢɬɟ ɫɧɚɱɚɥɚ ɧɨɦɟɪ ɜɵɩɨɥɧɹɟɦɨɝɨ ɡɚɞɚɧɢɹ (ɋ1, ɋ2 ɢ ɬ ɞ.), ɚ ɡɚɬɟɦ ɩɨɥɧɨɟ ɨɛɨɫɧɨɜɚɧɧɨɟ ɪɟɲɟɧɢɟ ɢ ɨɬɜɟɬ.
C1 |
ɚ) Ɋɟɲɢɬɟ ɭɪɚɜɧɟɧɢɟ |
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ɛ) ɇɚɣɞɢɬɟ ɜɫɟ ɤɨɪɧɢ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ, ɩɪɢɧɚɞɥɟɠɚɳɢɟ ɩɪɨɦɟɠɭɬɤɭ 2ʌ; |
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Ɉɫɧɨɜɚɧɢɟ ɩɪɹɦɨɣ ɩɪɢɡɦɵ ABCDA1B1C1D1 — ɪɨɦɛ ABCD ɫ ɭɝɥɨɦ A, ɪɚɜɧɵɦ |
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120q, ɢ ɫɬɨɪɨɧɨɣ, ɪɚɜɧɨɣ 4. ɇɚɣɞɢɬɟ ɜɵɫɨɬɭ ɩɪɢɡɦɵ, ɟɫɥɢ ɭɝɨɥ ɦɟɠɞɭ |
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ɩɥɨɫɤɨɫɬɹɦɢ ADC1 ɢ ABC ɪɚɜɟɧ 60q. |
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Ɋɟɲɢɬɟ ɫɢɫɬɟɦɭ ɧɟɪɚɜɟɧɫɬɜ ® |
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4x 2 |
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© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
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0210 (ɜɨɫɬɨɤ ɛɟɡ ɥɨɝɚɪɢɮɦɨɜ) |
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Ɍɚɧɝɟɧɫ ɭɝɥɚ C ɬɪɟɭɝɨɥɶɧɢɤɚ |
ABC ɪɚɜɟɧ |
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, D — ɨɬɥɢɱɧɚɹ |
ɨɬ |
A ɬɨɱɤɚ |
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ɩɟɪɟɫɟɱɟɧɢɹ |
ɨɤɪɭɠɧɨɫɬɟɣ, |
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ɧɚ4 ɫɬɨɪɨɧɚɯ |
AB ɢ |
AC |
ɤɚɤ |
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ɞɢɚɦɟɬɪɚɯ. ɂɡɜɟɫɬɧɨ, ɱɬɨ DB : DC |
9 : 16. |
ɇɚɣɞɢɬɟ ɭɝɨɥ A. |
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C5 |
ɇɚɣɞɢɬɟ |
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ɩɪɢ ɤɚɠɞɨɦ ɢɡ |
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4a(x y) |
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ɢɦɟɟɬ ɪɨɜɧɨ ɞɜɚ ɪɟɲɟɧɢɹ. |
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y2 8a(x y) |
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ɋɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɱɟɬɵɪɺɯ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɜ |
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ɪɚɡɚ ɛɨɥɶɲɟ, |
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ɫɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɨɛɪɚɬɧɵɯ ɱɢɫɟɥ. ɇɚɣɞɢɬɟ ɷɬɢ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ. |
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© ɋɬɚɬȽɪɚɞ 2013 ɝ