книги / 10 класс. Математика. Диагностическая работа 1. (вар. 0201-0216) 21.05.2013г (с отв)
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Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ 0213 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) 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: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0213 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
6 |
B8 ɇɚ ɪɢɫɭɧɤɟ ɩɨɤɚɡɚɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɜɪɟɦɟɧɢ ɩɪɢ ɞɜɢɠɟɧɢɢ ɚɜɬɨɦɨɛɢɥɹ ɩɨ ɦɚɪɲɪɭɬɭ ɨɬ ɧɚɱɚɥɶɧɨɝɨ ɩɭɧɤɬɚ. ɇɚ ɨɫɢ ɚɛɫɰɢɫɫ ɨɬɤɥɚɞɵɜɚɟɬɫɹ ɜɪɟɦɹ ɜ ɱɚɫɚɯ, ɧɚ ɨɫɢ ɨɪɞɢɧɚɬ — ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ ɜ ɤɢɥɨɦɟɬɪɚɯ. ɇɚɣɞɢɬɟ ɫɪɟɞɧɸɸ ɫɤɨɪɨɫɬɶ ɚɜɬɨɦɨɛɢɥɹ ɧɚ ɷɬɨɦ ɦɚɪɲɪɭɬɟ. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɤɢɥɨɦɟɬɪɚɯ ɜ ɱɚɫ.
Ɉɬɜɟɬ: 
B9 ȼ ɩɪɚɜɢɥɶɧɨɣ |
ɱɟɬɵɪɺɯɭɝɨɥɶɧɨɣ ɩɢɪɚɦɢɞɟ SABCD ɬɨɱɤɚ O — ɰɟɧɬɪ |
ɨɫɧɨɜɚɧɢɹ, SO |
12, SB 15. ɇɚɣɞɢɬɟ ɞɥɢɧɭ ɨɬɪɟɡɤɚ AC. |
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0213 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
7 |
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B10 |
Ɇɢɲɚ, Ɉɥɟɝ, ɇɚɫɬɹ ɢ Ƚɚɥɹ ɛɪɨɫɢɥɢ ɠɪɟɛɢɣ — ɤɨɦɭ ɧɚɱɢɧɚɬɶ ɢɝɪɭ. ɇɚɣɞɢɬɟ |
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ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɧɚɱɢɧɚɬɶ ɢɝɪɭ ɞɨɥɠɧɚ ɛɭɞɟɬ Ƚɚɥɹ. |
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Ɉɬɜɟɬ: 
B11 ɇɚɣɞɢɬɟ ɩɥɨɳɚɞɶ ɩɨɜɟɪɯɧɨɫɬɢ ɦɧɨɝɨɝɪɚɧɧɢɤɚ, ɢɡɨɛɪɚɠɺɧɧɨɝɨ ɧɚ ɪɢɫɭɧɤɟ
(ɜɫɟ ɞɜɭɝɪɚɧɧɵɟ ɭɝɥɵ ɩɪɹɦɵɟ).
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Ɉɬɜɟɬ: |
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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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—1 ɦ ɦɢɧ2 |
ɢ |
b |
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ɦ ɦɢɧ |
ɩɨɫɬɨɹɧɧɵɟ, t — |
ɜɪɟɦɹ |
ɜ ɦɢɧɭɬɚɯ, |
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ɩɪɨɲɟɞɲɟɟ ɫ ɦɨɦɟɧɬɚ ɨɬɤɪɵɬɢɹ ɤɪɚɧɚ ȼ ɬɟɱɟɧɢɟ ɤɚɤɨɝɨ ɜɪɟɦɟɧɢ ɜɨɞɚ ɛɭɞɟɬ |
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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: 
B14 ɇɚɣɞɢɬɟ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ y log9(x2 6x 18) 4.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0213 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
8 |
ɑ ɫɬɶ 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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sinx |
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sin x |
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ɛ) |
ɇɚɣɞɢɬɟ |
ɜɫɟ |
ɤɨɪɧɢ |
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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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60q, |
ɢ |
ɫɬɨɪɨɧɨɣ, |
ɪɚɜɧɨɣ |
2. |
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ɇɚɣɞɢɬɟ ɜɵɫɨɬɭ ɩɪɢɡɦɵ, ɟɫɥɢ ɭɝɨɥ ɦɟɠɞɭ |
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ɩɥɨɫɤɨɫɬɹɦɢ A1BC ɢ ABC ɪɚɜɟɧ 30q. |
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C3 |
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log |
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° |
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Ɋɟɲɢɬɟ ɫɢɫɬɟɦɭ ɧɟɪɚɜɟɧɫɬɜ ® |
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C4 |
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Ɍɚɧɝɟɧɫ |
ɭɝɥɚ C ɬɪɟɭɝɨɥɶɧɢɤɚ |
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ABC |
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ɪɚɜɟɧ |
, D — ɨɬɥɢɱɧɚɹ ɨɬ |
A ɬɨɱɤɚ |
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ɩɟɪɟɫɟɱɟɧɢɹ |
ɨɤɪɭɠɧɨɫɬɟɣ, |
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ɩɨɫɬɪɨɟɧɧɵɯ |
ɧɚ 3ɫɬɨɪɨɧɚɯ AB ɢ |
AC |
ɤɚɤ |
ɧɚ |
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ɞɢɚɦɟɬɪɚɯ. ɂɡɜɟɫɬɧɨ, ɱɬɨ DB : DC |
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4 : 9. ɇɚɣɞɢɬɟ ɭɝɨɥ A. |
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C5 |
ɇɚɣɞɢɬɟ ɜɫɟ ɡɧɚɱɟɧɢɹ, ɩɪɢ ɤɚɠɞɨɦ ɢɡ ɤɨɬɨɪɵɯ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ |
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x2 |
y2 |
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8a2 |
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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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ɫɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɨɛɪɚɬɧɵɯ ɱɢɫɟɥ. ɇɚɣɞɢɬɟ ɷɬɢ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ.
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ⱦɢ ɝɧɨɫɬɢɱɟɫɤ ɹ ɪ ɨɬ ʋ 1
ɩɨ ɆȺɌȿɆȺɌɂɄȿ
21 ɦ ɹ 2013 ɝɨɞ
ɤɥ 10ɫɫ
ȼ ɪɢ ɧɬ ɆȺ0214 (ɜɨɫɬɨɤ ɟɡ ɩɪɨɢɡɜɨɞɧɵ )
.
Ɋɚɣɨɧ Ƚɨɪɨɞ (ɧɚɫɟɥɺɧɧɵɣ ɩɭɧɤɬ)
ɒɤɨɥɚ
Ʉɥɚɫɫ
Ɏɚɦɢɥɢɹ
ɂɦɹ
Ɉɬɱɟɫɬɜɨ
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ 0214 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) 2
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ɂɧɫɬɪɭɤɰɢɹ ɩɨ ɜɵɩɨɥɧɟɧɢɸ ɪ ɨɬɵ |
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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 |
0214 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
3 |
ɑ ɫɬɶ 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 |
0214 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
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 log5(5 x) 3.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0214 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
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 Ɇɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ M ɧɚɱɢɧɚɟɬ ɞɜɢɠɟɧɢɟ ɢɡ |
ɬɨɱɤɢ A |
ɢ ɞɜɢɠɟɬɫɹ ɩɨ |
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ɩɪɹɦɨɣ ɜ ɬɟɱɟɧɢɟ |
ɫɟɤɭɧɞ. Ƚɪɚɮɢɤ ɩɨɤɚɡɵɜɚɟɬ, |
ɤɚɤ ɦɟɧɹɥɨɫɶ ɪɚɫɫɬɨɹɧɢɟ ɨɬ |
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ɬɨɱɤɢ |
A ɞɨ ɬɨɱɤɢ M ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ. ɇɚ ɨɫɢ ɚɛɫɰɢɫɫ ɨɬɤɥɚɞɵɜɚɟɬɫɹ |
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ɜɪɟɦɹ t |
ɜ ɫɟɤɭɧɞɚɯ, ɧɚ ɨɫɢ ɨɪɞɢɧɪɚɫɫɬɨɹɧɢɟ— |
ɜ ɦɟɬɪɚɯs |
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Ɉɩɪɟɞɟɥɢɬɟ, ɫɤɨɥɶɤɨ ɪɚɡ ɡɚ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ M ɨɛɪɚɳɚɥɚɫɶ ɜ ɧɨɥɶ (ɧɚɱɚɥɨ ɢ ɤɨɧɟɰ ɞɜɢɠɟɧɢɹ ɧɟ ɭɱɢɬɵɜɚɣɬɟ).
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0214 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
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 0214 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
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 |
1 |
ɦ ɦɢɧ2 |
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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 ɧɚɢɛɨɥɶɲɟɟ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ y 2 34 12x x2 5.
Ɉɬɜɟɬ: 
ɑ ɫɬɶ 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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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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Ɋɟɲɢɬɟ ɫɢɫɬɟɦɭ ɧɟɪɚɜɟɧɫɬɜ ® |
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© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
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0214 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
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8 |
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C4 |
Ɍɚɧɝɟɧɫ ɭɝɥɚ C ɬɪɟɭɝɨɥɶɧɢɤɚ |
ABC ɪɚɜɟɧ |
3 |
, 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 |
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ɡɧɚɱɟɧɢɹ |
, |
ɩɪɢ ɤɚɠɞɨɦ ɢɡ |
ɤɨɬɨɪɵɯ |
ɫɢɫɬɟɦɚ |
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y |
2 |
4a(x y) |
8a |
2 |
2a, |
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ɭɪɚɜɧɟɧɢɣ |
° |
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ɢɦɟɟɬ ɪɨɜɧɨ ɞɜɚ ɪɟɲɟɧɢɹ. |
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y2 8a(x y) |
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C6 |
ɋɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɱɟɬɵɪɺɯ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɜ |
42 |
ɪɚɡɚ ɛɨɥɶɲɟ, |
ɱɟɦ |
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ɫɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɨɛɪɚɬɧɵɯ ɱɢɫɟɥ. ɇɚɣɞɢɬɟ ɷɬɢ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ. |
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© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ⱦɢ ɝɧɨɫɬɢɱɟɫɤ ɹ ɪ ɨɬ ʋ 1
ɩɨ ɆȺɌȿɆȺɌɂɄȿ
21 ɦ ɹ 2013 ɝɨɞ
ɤɥ 10ɫɫ
ȼ ɪɢ ɧɬ ɆȺ0215 (ɜɨɫɬɨɤ ɟɡ ɩɪɨɢɡɜɨɞɧɵ )
.
Ɋɚɣɨɧ Ƚɨɪɨɞ (ɧɚɫɟɥɺɧɧɵɣ ɩɭɧɤɬ)
ɒɤɨɥɚ
Ʉɥɚɫɫ
Ɏɚɦɢɥɢɹ
ɂɦɹ
Ɉɬɱɟɫɬɜɨ
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ 0215 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) 2
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ɂɧɫɬɪɭɤɰɢɹ ɩɨ ɜɵɩɨɥɧɟɧɢɸ ɪ ɨɬɵ |
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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 |
0215 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
3 |
ɑ ɫɬɶ 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 6%. |
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Ɍɟɪɦɢɧɚɥ ɩɪɢɧɢɦɚɟɬ ɫɭɦɦɵ, ɤɪɚɬɧɵɟ 10 ɪɭɛɥɹɦ. Ɇɟɫɹɱɧɚɹ ɩɥɚɬɚ ɡɚ ɢɧɬɟɪɧɟɬ |
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ɫɨɫɬɚɜɥɹɟɬ 500 ɪɭɛɥɟɣ. Ʉɚɤɭɸ ɦɢɧɢɦɚɥɶɧɭɸ ɫɭɦɦɭ |
(ɜ ɪɭɛɥɹɯ) ɧɟɨɛɯɨɞɢɦɨ |
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ɩɨɥɨɠɢɬɶ ɜ ɩɪɢɺɦɧɨɟ ɭɫɬɪɨɣɫɬɜɨ ɬɟɪɦɢɧɚɥɚ, ɱɬɨɛɵ ɧɚ ɫɱɟɬɭ ɮɢɪɦɵ, |
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ɩɪɟɞɨɫɬɚɜɥɹɸɳɟɣ ɢɧɬɟɪɧɟɬ ɭɫɥɭɝɢ, ɨɤɚɡɚɥɚɫɶ ɫɭɦɦɚ, |
ɧɟ ɦɟɧɶɲɚɹ 500 ɪɭɛɥɟɣ? |
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Ɉɬɜɟɬ: |
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B2 |
ɇɚ ɞɢɚɝɪɚɦɦɟ ɩɨɤɚɡɚɧɚ ɫɪɟɞɧɟɦɟɫɹɱɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡɞɭɯɚ ɜ ȿɤɚɬɟɪɢɧɛɭɪɝɟ |
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ɋɜɟɪɞɥɨɜɫɤɟ) ɡɚ ɤɚɠɞɵɣ ɦɟɫɹɰ 1973 ɝɨɞɚ. ɉɨ ɝɨɪɢɡɨɧɬɚɥɢ ɭɤɚɡɵɜɚɸɬɫɹ |
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ɦɟɫɹɰɵ, ɩɨ ɜɟɪɬɢɤɚɥɢ — ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɝɪɚɞɭɫɚɯ |
ɟɥɶɫɢɹ Ɉɩɪɟɞɟɥɢɬɟ ɩɨ |
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ɞɢɚɝɪɚɦɦɟ, ɫɤɨɥɶɤɨ ɛɵɥɨ ɦɟɫɹɰɟɜ ɫ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɫɪɟɞɧɟɦɟɫɹɱɧɨɣ
ɬɟɦɩɟɪɚɬɭɪɨɣ.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0215 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
4 |
B3 ɇɚɣɞɢɬɟ ɩɥɨɳɚɞɶu ɪɨɦɛɚ, ɢɡɨɛɪɚɠɺɧɧɨɝɨ ɧɚ ɤɥɟɬɱɚɬɨɣ ɛɭɦɚɝɟ ɫ ɪɚɡɦɟɪɨɦ ɤɥɟɬɤɢɫɦ1 1 ɫɦ (ɫɦ. ɪɢɫ.). Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɤɜɚɞɪɚɬɧɵɯ ɫɚɧɬɢɦɟɬɪɚɯ.
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Ɉɬɜɟɬ: |
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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. 950 ɪɭɛɥɟɣ |
ɜɬɨɦɨɛɢɥɶ ɪɚɫɯɨɞɭɟɬ 8 ɥɢɬɪɨɜ ɛɟɧɡɢɧɚ ɧɚ |
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100 ɤɢɥɨɦɟɬɪɨɜ ɩɭɬɢ, ɪɚɫɫɬɨɹɧɢɟ ɩɨ ɲɨɫɫɟ ɪɚɜɧɨ 700 ɤɦ, ɚ ɰɟɧɚ ɛɟɧɡɢɧɚ ɪɚɜɧɚ |
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21 ɪɭɛɥɟɣ ɡɚ ɥɢɬɪ. ɋɤɨɥɶɤɨ ɪɭɛɥɟɣ ɩɪɢɞɺɬɫɹ ɡɚɩɥɚɬɢɬɶ ɡɚ ɧɚɢɛɨɥɟɟ ɞɟɲɺɜɭɸ |
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ɩɨɟɡɞɤɭ ɧɚ ɬɪɨɢɯ? |
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Ɉɬɜɟɬ: |
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B5 |
ɇɚɣɞɢɬɟ ɤɨɪɟɧɶ ɭɪɚɜɧɟɧɢɹ log4(2 x) 4. |
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Ɉɬɜɟɬ: |
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B6 |
ɑɟɬɵɪɺɯɭɝɨɥɶɧɢɤ ABCD ɜɩɢɫɚɧ ɜ ɨɤɪɭɠɧɨɫɬɶ, |
. ɍɝɨɥ ABC ɪɚɜɟɧ 46q ɭɝɨɥ CAD |
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ɪɚɜɟɧ 37q. ɇɚɣɞɢɬɟ ɭɝɨɥ ABD. Ɉɬɜɟɬ ɞɚɣɬɟ ɜ ɝɪɚɞɭɫɚɯ. |
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Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ 0215 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) 5
12sin3qcos3q
B7 ɇɚɣɞɢɬɟ ɡɧɚɱɟɧɢɟ ɜɵɪɚɠɟɧɢɹ q . sin6
Ɉɬɜɟɬ: 
B8 Ɇɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ M ɧɚɱɢɧɚɟɬ ɞɜɢɠɟɧɢɟ ɢɡ ɬɨɱɤɢ A ɢ ɞɜɢɠɟɬɫɹ ɩɨ ɩɪɹɦɨɣ ɧɚ ɩɪɨɬɹɠɟɧɢɢ 11 ɫɟɤɭɧɞ. Ƚɪɚɮɢɤ ɩɨɤɚɡɵɜɚɟɬ, ɤɚɤ ɦɟɧɹɥɨɫɶ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɬɨɱɤɢ A ɞɨ ɬɨɱɤɢ M ɫɨ ɜɪɟɦɟɧɟɦ. ɇɚ ɨɫɢ ɚɛɫɰɢɫɫ ɨɬɤɥɚɞɵɜɚɟɬɫɹ ɜɪɟɦɹ t
,ɜ ɫɟɤɭɧɞɚɯ. ɧɚ ɨɫɢ ɨɪɞɢɧɚɬ – ɪɚɫɫɬɨɹɧɢɟ s ɜ ɦɟɬɪɚɯ
Ɉɩɪɟɞɟɥɢɬɟ, ɫɤɨɥɶɤɨ ɪɚɡ ɡɚ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ M ɨɛɪɚɳɚɥɚɫɶ ɜ ɧɨɥɶ (ɧɚɱɚɥɨ ɢ ɤɨɧɟɰ ɞɜɢɠɟɧɢɹ ɧɟ ɭɱɢɬɵɜɚɣɬɟ).
Ɉɬɜɟɬ: 
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B9 ȼ ɩɪɚɜɢɥɶɧɨɣ |
ɱɟɬɵɪɺɯɭɝɨɥɶɧɨɣ ɩɢɪɚɦɢɞɟ SABCD ɬɨɱɤɚ O — ɰɟɧɬɪ |
ɨɫɧɨɜɚɧɢɹ, SA |
13, BD 10. ɇɚɣɞɢɬɟ ɞɥɢɧɭ ɨɬɪɟɡɤɚ SO. |
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10 |
ȼɚɪɢɚɧɬ Ɇ 0215 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
6 |
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B10 |
ɋɚɲɚ, ɋɟɦɺɧ, Ɂɨɹ ɢ Ʌɟɪɚ ɛɪɨɫɢɥɢ ɠɪɟɛɢɣ — ɤɨɦɭ ɧɚɱɢɧɚɬɶ ɢɝɪɭ. ɇɚɣɞɢɬɟ |
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ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨɱɬɨ, |
ɧɚɱɢɧɚɬɶ ɢɝɪɭ ɞɨɥɠɟɧ ɛɭɞɟɬ. |
ɧɟ ɋɟɦɺɧ |
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Ɉɬɜɟɬ: 
B11 ɇɚɣɞɢɬɟ ɩɥɨɳɚɞɶ ɩɨɜɟɪɯɧɨɫɬɢ ɦɧɨɝɨɝɪɚɧɧɢɤɚ, ɢɡɨɛɪɚɠɺɧɧɨɝɨ ɧɚ ɪɢɫɭɧɤɟ
(ɜɫɟ ɞɜɭɝɪɚɧɧɵɟ ɭɝɥɵ ɩɪɹɦɵɟ).
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Ɉɬɜɟɬ: |
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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 ɜɨɞɵ ɜ ɧɺɦ, ɜɵɪɚɠɟɧɧɚɹ |
ɜ ɦɟɬɪɚɯ, ɦɟɧɹɟɬɫɹ ɩɨ |
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ɡɚɤɨɧɭ |
H(t) |
at2 |
bt H0, ɝɞɟ |
H0 |
12, 25 ɦ — ɧɚɱɚɥɶɧɵɣ ɭɪɨɜɟɧɶ |
ɜɨɞɵ, |
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a |
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ɦ ɦɢɧ2 |
ɢ |
b |
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ɦ ɦɢɧ |
— ɩɨɫɬɨɹɧɧɵɟ, |
t — ɜɪɟɦɹ |
ɜ ɦɢɧɭɬɚɯ, |
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64 |
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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
Ɉɬɜɟɬ: 
B13 Теплоход прошёл против течения реки 252 км и вернулся в пункт отправления, затратив на обратный путь на 4 часа меньше. Найдите скорость течения, если скорость теплохода в неподвижной воде равна 16 км/ч. Ответ дайте в км/ч.
Ɉɬɜɟɬ: 
B14 ɇɚɣɞɢɬɟ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ y log3(x2 2x 10) 2.
Ɉɬɜɟɬ: 
© ɋɬɚɬȽɪɚɞ 2013 ɝ
Ɇɚɬɟɦɚɬɢɤɚɤɥɚɫɫ10ȼɚɪɢɚɧɬ Ɇ |
0215 (ɜɨɫɬɨɤ ɛɟɡ ɩɪɨɢɡɜɨɞɧɵɯ) |
7 |
ɑ ɫɬɶ 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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sinx |
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sin x |
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ɛ) ɇɚɣɞɢɬɟ ɜɫɟ ɤɨɪɧɢ |
ɷɬɨɝɨ |
ɭɪɚɜɧɟɧɢɹ, ɩɪɢɧɚɞɥɟɠɚɳɢɟ ɩɪɨɦɟɠɭɬɤɭ |
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5ʌ |
; |
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3ʌ |
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C2
C3
Ɉɫɧɨɜɚɧɢɟ ɩɪɹɦɨɣ ɩɪɢɡɦɵ ABCDA1B1C1D1 — ɪɨɦɛ ABCD ɫ ɭɝɥɨɦ A, ɪɚɜɧɵɦ |
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60q, ɢ ɫɬɨɪɨɧɨɣ, ɪɚɜɧɨɣ 2. |
ɇɚɣɞɢɬɟ |
ɜɵɫɨɬɭ |
ɩɪɢɡɦɵ, ɟɫɥɢ ɭɝɨɥ ɦɟɠɞɭ |
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ɩɥɨɫɤɨɫɬɹɦɢ A1BC ɢ ABC ɪɚɜɟɧ 30q. |
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d 2, |
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log |
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6x |
x2 5 |
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Ɋɟɲɢɬɟ ɫɢɫɬɟɦɭ ɧɟɪɚɜɟɧɫɬɜ ® |
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x 3 |
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t 0. |
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C4
C5
C6
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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ɇɚɣɞɢɬɟ ɜɫɟ ɡɧɚɱɟɧɢɹ, |
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ɩɪɢ ɤɚɠɞɨɦ ɢɡ ɤɨɬɨɪɵɯ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ |
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2a(x y) |
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y2 4a(x y) |
8a2 9a |
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® x2 |
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ɢɦɟɟɬ ɟɞɢɧɫɬɜɟɧɧɨɟ ɪɟɲɟɧɢɟ.
ɋɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɬɪɺɯ ɧɚɬɭɪɚɥɶɧɵɯ ɱɢɫɟɥ ɜ 35 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ
11
ɫɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɨɛɪɚɬɧɵɯ ɱɢɫɟɥ. ɇɚɣɞɢɬɟ ɷɬɢ ɧɚɬɭɪɚɥɶɧɵɟ ɱɢɫɥɚ.
© ɋɬɚɬȽɪɚɞ 2013 ɝ