2010-5-unarebi-rus
.pdf
Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɱɚɫɬɶ
ɉɪɢ ɪɚɛɨɬɟ ɧɚɞ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɱɚɫɬɶɸ ɬɟɫɬɚ ɧɭɠɧɨ ɭɱɟɫɬɶ ɫɥɟɞɭɸɳɟɟ:
xɑɟɪɬɟɠɢ, ɩɪɢɥɚɝɚɟɦɵɟ ɤ ɧɟɤɨɬɨɪɵɦ ɡɚɞɚɧɢɹɦ, ɧɟ ɫɬɪɨɹɬɫɹ ɫ ɫɨɛɥɸɞɟɧɢɟɦ ɬɨɱɧɵɯ ɪɚɡɦɟɪɨɜ, ɭɤɚɡɚɧɧɵɯ ɜ ɭɫɥɨɜɢɹɯ ɡɚɞɚɧɢɹ. ɉɨɷɬɨɦɭ ɧɟ ɫɥɟɞɭɟɬ ɞɟɥɚɬɶ ɜɵɜɨɞɵ ɨ ɞɥɢɧɟ ɨɬɪɟɡɤɨɜ ɢ ɞɪɭɝɢɯ ɜɟɥɢɱɢɧɚɯ ɧɚ ɨɫɧɨɜɚɧɢɢ ɪɚɡɦɟɪɨɜ ɱɟɪɬɟɠɚ. Ɋɭɤɨɜɨɞɫɬɜɭɣɬɟɫɶ ɥɢɲɶ ɭɫɥɨɜɢɹɦɢ ɡɚɞɚɧɢɹ.
xȿɫɥɢ ɨ ɩɪɹɦɨɣ ɥɢɧɢɢ, ɞɚɧɧɨɣ ɧɚ ɱɟɪɬɟɠɟ, ɧɢɱɟɝɨ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɧɟ ɫɤɚɡɚɧɨ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɧɢɹ, ɬɨɝɞɚ ɫɥɟɞɭɟɬ ɫɱɢɬɚɬɶ, ɱɬɨ ɷɬɚ ɥɢɧɢɹ – ɩɪɹɦɚɹ ɢɥɢ ɟɟ ɱɚɫɬɶ.
xȼ ɬɟɫɬɟ ɞɥɹ ɡɚɩɢɫɢ ɱɢɫɟɥ ɢɫɩɨɥɶɡɭɟɬɫɹ ɬɨɥɶɤɨ ɞɟɫɹɬɢɱɧɚɹ ɩɨɡɢɰɢɨɧɧɚɹ ɫɢɫɬɟɦɚ.
Ɇɚɬɟɦɚɬɢɱɟɫɤɢɟ ɨɛɨɡɧɚɱɟɧɢɹ ɢ ɮɨɪɦɭɥɵ
1.ɇɭɥɶ ɧɟ ɹɜɥɹɟɬɫɹ ɧɢ ɩɨɥɨɠɢɬɟɥɶɧɵɦ, ɧɢ ɨɬɪɢɰɚɬɟɥɶɧɵɦ ɱɢɫɥɨɦ 1 ɧɟ ɹɜɥɹɟɬɫɹ ɩɪɨɫɬɵɦ ɱɢɫɥɨɦ.
2.ɉɪɨɰɟɧɬ: k% ɨɬ ɱɢɫɥɚ a ɟɫɬɶ 
;
3.ɋɬɟɩɟɧɶ: an = a · a · a · ...· a (n-ɪɚɡ)
an · am = an + m
an : am = an – m
(an)m = an · m
4. ɉɪɨɩɨɪɰɢɹ: ɟɫɥɢ 
, ɬɨɝɞɚ ad = bc
ɪɚɫɫɬɨɹɧɢɟ
5. ɋɤɨɪɨɫɬɶ: ɫɤɨɪɨɫɬɶ
ɜɪɟɦɹ
6. ɋɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ:
ɫɭɦɦɚ ɞɚɧɧɵɯ
ɫɪɟɞɧɟɟ ɞɚɧɧɵɯ
ɤɨɥɢɱɟɫɬɜɨ ɞɚɧɧɵɯ
7. ȼɟɪɨɹɬɧɨɫɬɶ ɫɨɛɵɬɢɹ ɪɚɜɧɚ ɨɬɧɨɲɟɧɢɸ ɱɢɫɥɚ ɷɥɟɦɟɧɬɚɪɧɵɯ ɫɨɛɵɬɢɣ, ɛɥɚɝɨɩɪɢɹɬɫɬɜɭɸɳɢɯ ɞɚɧɧɨɦɭ ɫɨɛɵɬɢɸ, ɤ ɨɛɳɟɦɭ ɱɢɫɥɭ ɷɥɟɦɟɧɬɚɪɧɵɯ ɫɨɛɵɬɢɣ ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɜɫɟ ɷɥɟɦɟɧɬɚɪɧɵɟ ɫɨɛɵɬɢɹ ɪɚɜɧɨɜɟɪɨɹɬɧɵ.
ȿɫɥɢ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɧɢɹ ɧɟ ɨɝɨɜɨɪɟɧɨ ɩɪɨɬɢɜɧɨɟ, ɜɫɟɝɞɚ ɩɨɞɪɚɡɭɦɟɜɚɟɬɫɹ, ɱɬɨ ɜɫɟ
ɷɥɟɦɟɧɬɚɪɧɵɟ ɫɨɛɵɬɢɹ ɪɚɜɧɨɜɟɪɨɹɬɧɵ.
8. ɋɨɤɪɚɳɟɧɧɵɟ ɮɨɪɦɭɥɵ ɭɦɧɨɠɟɧɢɹ:
(a+b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2
9. ɇɚ ɱɟɪɬɟɠɟ ɭɝɨɥ ɦɨɠɟɬ ɛɵɬɶ ɨɛɨɡɧɚɱɟɧ ɞɭɝɨɣ ɦɟɠɞɭ ɫɬɨɪɨɧɚɦɢ ɭɝɥɚ, ɚ ɩɪɹɦɨɣ ɭɝɨɥ - ɤɜɚɞɪɚɬɢɤɨɦ.
Ɂɚɩɢɫɶ: A ɨɛɨɡɧɚɱɚɟɬ ɜɟɥɢɱɢɧɭ ɭɝɥɚ A.
10. ɉɚɪɚɥɥɟɥɶɧɵɟ ɩɪɹɦɵɟ:
xɉɪɢ ɩɟɪɟɫɟɱɟɧɢɢ ɞɜɭɯ
ɩɚɪɚɥɥɟɥɶɧɵɯ ɩɪɹɦɵɯ ɬɪɟɬɶɟɣ ɩɪɹɦɨɣ, ɜɧɭɬɪɟɧɧɢɟ ɧɚɤɪɟɫɬ ɥɟɠɚɳɢɟ ɭɝɥɵ ɪɚɜɧɵ: Į = ȕ.
11.Ɍɪɟɭɝɨɥɶɧɢɤ:
x ɋɭɦɦɚ ɜɟɥɢɱɢɧ ɭɝɥɨɜ ɬɪɟɭɝɨɥɶɧɢɤɚ ɪɚɜɧɚ 180°
x Ɍɟɨɪɟɦɚ ɉɢɮɚɝɨɪɚ: ɤɜɚɞɪɚɬ ɞɥɢɧɵ ɝɢɩɨɬɟɧɭɡɵ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɪɚɜɟɧ ɫɭɦɦɟ ɤɜɚɞɪɚɬɨɜ
ɞɥɢɧ ɟɝɨ ɤɚɬɟɬɨɜ:
AB2 = AC2 + BC2
xɉɥɨɳɚɞɶ ɬɪɟɭɝɨɥɶɧɢɤɚ ɪɚɜɧɚ ɩɨɥɨɜɢɧɟ
ɩɪɨɢɡɜɟɞɟɧɢɹ ɞɥɢɧɵ ɫɬɨɪɨɧɵ ɬɪɟɭɝɨɥɶɧɢɤɚ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɜɵɫɨɬɵ: 
12.ɑɟɬɵɪɟɯɭɝɨɥɶɧɢɤ:
xɋɭɦɦɚ ɜɟɥɢɱɢɧ ɭɝɥɨɜ ɱɟɬɵɪɟɯɭɝɨɥɶɧɢɤɚ ɪɚɜɧɚ
360°;
xɉɥɨɳɚɞɶ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ ɪɚɜɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ ɟɝɨ ɞɥɢɧɵ ɢ ɲɢɪɢɧɵ: S = ab;
xɉɥɨɳɚɞɶ ɩɚɪɚɥɥɟɥɨɝɪɚɦɦɚ ɪɚɜɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ ɞɥɢɧɵ ɟɝɨ ɫɬɨɪɨɧɵ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɷɬɨɣ ɫɬɨɪɨɧɟ ɜɵɫɨɬɵ: S = ah.
13.Ʉɪɭɝ, ɨɤɪɭɠɧɨɫɬɶ:
x Ⱦɥɢɧɚ ɨɤɪɭɠɧɨɫɬɢ L ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ: L = 2Sr , ɝɞɟ r ɞɥɢɧɚ ɪɚɞɢɭɫɚ,
ɚɱɢɫɥɨ S ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɫɨɬɵɯ ɪɚɜɧɨ 3,14;
x ɉɥɨɳɚɞɶ ɤɪɭɝɚ ɫ ɪɚɞɢɭɫɨɦ r ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ: L = Sr2
14. ɉɪɹɦɨɭɝɨɥɶɧɵɣ ɩɚɪɚɥɥɟɥɟɩɢɩɟɞ:
x Ɉɛɴɟɦ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɩɚɪɚɥɥɟɥɟɩɢɩɟɞɚ ɪɚɜɟɧ ɩɪɨɢɡɜɟɞɟɧɢɸ ɟɝɨ ɞɥɢɧɵ, ɲɢɪɢɧɵ ɢ ɜɵɫɨɬɵ: V = abc;
x ȼ ɫɥɭɱɚɟ ɤɭɛɚ: a = b = c.
21
Ʉɨɥɢɱɟɫɬɜɟɧɧɵɟ ɫɪɚɜɧɟɧɢɹ
ɋɪɚɜɧɢɬɟ ɦɟɠɞɭ ɫɨɛɨɣ ɜɟɥɢɱɢɧɵ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɜ ɹɱɟɣɤɚɯ ɫɬɨɥɛɰɨɜ Ⱥ ɢ ȼ.
ȿɫɥɢ ɜɟɥɢɱɢɧɚ, ɞɚɧɧɚɹ ɜ ɹɱɟɣɤɟ ɫɬɨɥɛɰɚ Ⱥ, ɛɨɥɶɲɟ ɜɟɥɢɱɢɧɵ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɹɱɟɣɤɟ ɫɬɨɥɛɰɚ ȼ, ɜɵɛɟɪɢɬɟ (ɚ);
ȿɫɥɢ ɜɟɥɢɱɢɧɚ, ɞɚɧɧɚɹ ɜ ɹɱɟɣɤɟ ɫɬɨɥɛɰɚ ȼ, ɛɨɥɶɲɟ ɜɟɥɢɱɢɧɵ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɹɱɟɣɤɟ ɫɬɨɥɛɰɚ Ⱥ, ɜɵɛɟɪɢɬɟ (ɛ);
ȿɫɥɢ ɜɟɥɢɱɢɧɵ, ɞɚɧɧɵɟ ɜ ɹɱɟɣɤɚɯ ɨɛɨɢɯ ɫɬɨɥɛɰɨɜ, ɪɚɜɧɵ, ɜɵɛɟɪɢɬɟ (ɜ); ȿɫɥɢ ɢɦɟɸɳɚɹɫɹ ɢɧɮɨɪɦɚɰɢɹ ɧɟɞɨɫɬɚɬɨɱɧɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɬɨɝɨ, ɤɚɤɚɹ ɢɡ ɜɟɥɢɱɢɧ
ɛɨɥɶɲɟ, ɜɵɛɟɪɢɬɟ (ɝ).
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A |
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a |
ɢ b ɬɚɤɢɟ ɱɢɫɥɚ, ɱɬɨ a b ! 0 . |
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(ɚ) (ɛ) (ɜ) (ɝ) |
41. |
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ɪɚɫɫɬɨɹɧɢɟ ɧɚ ɱɢɫɥɨɜɨɣ |
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ɪɚɫɫɬɨɹɧɢɟ ɧɚ ɱɢɫɥɨɜɨɣ |
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ɨɫɢ ɨɬ ɬɨɱɤɢ, |
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ɨɫɢ ɨɬ ɬɨɱɤɢ, |
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ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ a, ɞɨ |
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ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ b , ɞɨ |
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ɧɚɱɚɥɶɧɨɣ ɬɨɱɤɢ |
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ɧɚɱɚɥɶɧɨɣ ɬɨɱɤɢ |
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ȼɟɥɢɱɢɧɚ ɬɭɩɨɝɨ ɭɝɥɚ ɪɨɦɛɚ ɪɚɜɧɚ 120°.
42. |
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ɞɥɢɧɚ ɦɚɥɨɣ ɞɢɚɝɨɧɚɥɢ |
(ɚ) (ɛ) (ɜ) (ɝ) |
ɞɥɢɧɚ ɫɬɨɪɨɧɵ ɪɨɦɛɚ |
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ɪɨɦɛɚ |
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43. |
32 · 9,6 |
320 · 0,96 |
(ɚ) (ɛ) (ɜ) (ɝ) |
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Ɇɢɲɚ, Ⱥɥɢɤ, ɋɨɮɶɹ ɢ Ⱥɧɧɚ ɩɨɲɥɢ ɡɚ ɝɪɢɛɚɦɢ. Ⱥɧɧɚ ɫɨɛɪɚɥɚ ɦɟɧɶɲɟ ɜɫɟɯ ɝɪɢɛɨɜ, ɋɨɮɶɹ ɠɟ ɧɟ ɫɦɨɝɥɚ ɫɨɛɪɚɬɶ ɛɨɥɶɲɟ ɜɫɟɯ ɝɪɢɛɨɜ.
44. |
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ɤɨɥɢɱɟɫɬɜɨ ɝɪɢɛɨɜ, |
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ɤɨɥɢɱɟɫɬɜɨ ɝɪɢɛɨɜ, |
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ɫɨɛɪɚɧɧɵɯ ɦɚɥɶɱɢɤɚɦɢ |
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ɫɨɛɪɚɧɧɵɯ ɞɟɜɨɱɤɚɦɢ |
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Ɉɤɪɭɠɧɨɫɬɶ, ɞɥɢɧɚ ɪɚɞɢɭɫɚ ɤɨɬɨɪɨɣ 8 ɫɦ, ɥɟɠɢɬ ɜɧɭɬɪɢ |
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ɞɪɭɝɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɞɥɢɧɚ ɪɚɞɢɭɫɚ ɤɨɬɨɪɨɣ ɪɚɜɧɚ 16 ɫɦ. |
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Ɍɨɱɤɚ E ɥɟɠɢɬ ɧɚ ɨɞɧɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɚ ɬɨɱɤɚ F _ ɧɚ ɞɪɭɝɨɣ. |
(ɚ) (ɛ) (ɜ) (ɝ) |
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45. |
ɉɟɪɢɦɟɬɪ ɬɪɟɭɝɨɥɶɧɢɤɚ, ɩɨɥɭɱɟɧɧɨɝɨ |
ɫɨɟɞɢɧɟɧɢɟɦ ɷɬɢɯ |
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ɬɨɱɟɤ ɢ ɰɟɧɬɪɚ ɦɚɥɨɣ ɨɤɪɭɠɧɨɫɬɢ ɞɪɭɝ ɫ ɞɪɭɝɨɦ, ɪɚɜɟɧ p. |
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p |
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64 ɫɦ |
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ɋɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɱɢɫɟɥ x ɢ y ɪɚɜɧɨ ɫɪɟɞɧɟɦɭ |
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ɚɪɢɮɦɟɬɢɱɟɫɤɨɦɭ ɱɢɫɟɥ x, y ɢ t. |
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46. |
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(ɚ) (ɛ) (ɜ) (ɝ) |
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ɫɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ |
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t |
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ɱɢɫɟɥ x ɢ y |
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23
Ɂɚɞɚɱɢ
47. ȿɫɥɢ z 2, ɬɨ z3 6 1 3z z2
(ɚ) –42
(ɛ) –18
(ɜ) 0
(ɝ) 6
(ɞ) 22
48. Ʌɢɤɚ ɩɨɦɟɫɬɢɥɚ 71 ɤɚɪɚɧɞɚɲ ɜ ɧɟɫɤɨɥɶɤɨ ɤɨɪɨɛɨɱɟɤ: ɜ ɧɟɤɨɬɨɪɵɟ ɩɨɥɨɠɢɥɚ ɩɨ 4 ɲɬɭɤɢ, ɜ ɧɟɤɨɬɨɪɵɟ – ɩɨ 6, ɚ ɜ ɧɟɤɨɬɨɪɵɟ – ɩɨ 9. ɂɡ ɧɢɠɟ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɱɟɦɭ ɦɨɠɟɬ ɛɵɬɶ ɪɚɜɧɨ ɤɨɥɢɱɟɫɬɜɨ ɤɨɪɨɛɨɱɟɤ, ɜ ɤɨɬɨɪɵɯ ɥɟɠɚɬ 9 ɤɚɪɚɧɞɚɲɟɣ?
(a) 2
(ɛ) 4
(ɜ) 5
(ɝ) 6
(ɞ) 7
49. ȼɟɪɲɢɧɵ ɬɪɟɭɝɨɥɶɧɢɤɚ ɢ ɩɚɪɚɥɥɟɥɨɝɪɚɦɚ ɫɨɜɩɚɞɚɸɬ ɫ ɭɡɥɚɦɢ ɫɟɬɤɢ, ɢɦɟɸɳɟɣ ɪɚɜɧɵɟ ɹɱɟɣɤɢ (ɫɦ. ɱɟɪɬɟɠ). ɑɟɦɭ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɟ ɩɥɨɳɚɞɢ ɬɪɟɭɝɨɥɶɧɢɤɚ ɤ ɩɥɨɳɚɞɢ ɩɚɪɚɥɥɟɥɨɝɪɚɦɚ?
(a) 52
(ɛ) 12 (ɜ) 85
(ɝ) 2 3
(ɞ) 54
24
50. ɉɪɨɢɡɜɟɞɟɧɢɟ ɞɟɥɢɦɨɝɨ (ɤɨɬɨɪɨɟ ɹɜɥɹɟɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɵɦ ɱɢɫɥɨɦ), ɞɟɥɢɬɟɥɹ ɢ ɢɯ ɱɚɫɬɧɨɝɨ ɪɚɜɧɨ 0,64. ɑɟɦɭ ɪɚɜɧɨ ɩɪɨɢɡɜɟɞɟɧɢɟ ɞɟɥɢɬɟɥɹ ɢ ɱɚɫɬɧɨɝɨ?
(a) 0,32
(ɛ) 0,4
(ɜ) 0,48
(ɝ) 0,6
(ɞ) 0,8
51. ȼ ɚɜɬɨɛɭɫɟ ɛɵɥɨ ɧɟɫɤɨɥɶɤɨ ɩɚɫɫɚɠɢɪɨɜ. ɉɨɫɥɟ ɩɟɪɜɨɣ ɨɫɬɚɧɨɜɤɢ ɱɢɫɥɨ ɩɚɫɫɚɠɢɪɨɜ ɭɞɜɨɢɥɨɫɶ, ɧɚ ɫɥɟɞɭɸɳɟɣ ɠɟ ɨɫɬɚɧɨɜɤɟ ɭɦɟɧɶɲɢɥɨɫɶ ɧɚ 12. ɉɨɫɥɟ ɟɳɟ ɨɞɧɨɣ ɨɫɬɚɧɨɜɤɢ ɱɢɫɥɨ ɩɚɫɫɚɠɢɪɨɜ ɜ ɚɜɬɨɛɭɫɟ ɨɩɹɬɶ ɭɞɜɨɢɥɨɫɶ, ɧɚ ɫɥɟɞɭɸɳɟɣ ɠɟ – ɜɧɨɜɶ ɭɦɟɧɶɲɢɥɨɫɶ ɧɚ 12, ɩɨɫɥɟ ɱɟɝɨ ɜ ɚɜɬɨɛɭɫɟ ɧɟ ɨɫɬɚɥɨɫɶ ɧɢ ɨɞɧɨɝɨ ɩɚɫɫɚɠɢɪɚ. ɋɤɨɥɶɤɨ ɩɚɫɫɚɠɢɪɨɜ ɛɵɥɨ ɜ ɚɜɬɨɛɭɫɟ ɞɨ ɩɟɪɜɨɣ ɨɫɬɚɧɨɜɤɢ?
(a) 6
(ɛ) 7
(ɜ) 8
(ɝ) 9
(ɞ) 11
25
Ⱥɧɚɥɢɡ ɞɚɧɧɵɯ
ȼ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɵ ɞɚɧɧɵɟ ɨ ɬɨɦ, ɫɤɨɥɶɤɨ ɬɵɫɹɱ ɜɡɪɨɫɥɨɝɨ ɧɚɫɟɥɟɧɢɹ ɛɵɥɨ ɬɪɭɞɨɭɫɬɪɨɟɧɨ ɜ Ɍɛɢɥɢɫɢ ɢ ɜ ɪɚɡɥɢɱɧɵɯ ɪɟɝɢɨɧɚɯ ȼɨɫɬɨɱɧɨɣ Ƚɪɭɡɢɢ ɜ 2002-2006 ɝɨɞɵ; ɩɪɢ ɷɬɨɦ, ɞɚɧɧɵɟ 2006 ɝɨɞɚ ɩɪɟɞɫɬɚɜɥɟɧɵ ɩɨɤɜɚɪɬɚɥɶɧɨ.
Ƚɨɞ ɢ ɤɜɚɪɬɚɥ |
Ɍɛɢɥɢɫɢ |
Ʉɚɯɟɬɢɹ |
Ɇɰɯɟɬɚ-Ɇɬɢɚɧɟɬɢ |
Ʉɜɟɦɨ Ʉɚɪɬɥɢ |
ɒɢɞɚ Ʉɚɪɬɥɢ |
||
2002 ɝ |
|
|
149,0 |
10,8 |
5,6 |
23,5 |
9,8 |
2003 ɝ |
|
|
189,0 |
13,6 |
6,8 |
29,4 |
13,2 |
2004 ɝ |
|
|
189,6 |
15,9 |
7,2 |
26,2 |
15,0 |
2005 ɝ |
|
|
196,0 |
14,2 |
5,5 |
28,0 |
14,8 |
2006 ɝ |
I ɤɜ. |
181,0 |
10,7 |
4,8 |
23,7 |
12,4 |
|
|
II |
ɤɜ. |
184,6 |
11,9 |
5,1 |
24,3 |
12,0 |
|
III |
ɤɜ. |
180,8 |
12,2 |
4,8 |
24,6 |
10,1 |
|
IV |
ɤɜ. |
189,0 |
11,8 |
5,0 |
24,7 |
11,3 |
ɂɫɯɨɞɹ ɢɡ ɬɚɛɥɢɰɵ, ɨɬɜɟɬɶɬɟ ɧɚ ɫɥɟɞɭɸɳɢɟ 2 ɜɨɩɪɨɫɚ:
52. ɇɚ ɫɤɨɥɶɤɨ ɛɨɥɶɲɟ ɛɵɥɨ ɤɨɥɢɱɟɫɬɜɨ ɬɪɭɞɨɭɫɬɪɨɟɧɧɵɯ ɜ Ɍɛɢɥɢɫɢ ɥɸɞɟɣ ɜ 2005 ɝɨɞɭ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɪɟɞɵɞɭɳɢɦ ɝɨɞɨɦ?
(a)ɧɚ 6000 (ɛ) ɧɚ 6400 (ɜ) ɧɚ 7000 (ɝ) ɧɚ 7600 (ɞ) ɧɚ 8000
53.Ⱦɨɩɭɫɬɢɦ, ɱɬɨ ɜ 2006 ɝɨɞɭ ɜ ɒɢɞɚ Ʉɚɪɬɥɢ ɤɨɥɢɱɟɫɬɜɨ ɜɡɪɨɫɥɨɝɨ ɧɚɫɟɥɟɧɢɹ ɫɨɫɬɚɜɥɹɥɨ
75ɬɵɫɹɱ ɱɟɥɨɜɟɤ. Ʉɚɤɨɣ ɩɪɨɰɟɧɬ ɨɬ ɤɨɥɢɱɟɫɬɜɚ ɜɡɪɨɫɥɨɝɨ ɧɚɫɟɥɟɧɢɹ ɞɚɧɧɨɝɨ ɪɟɝɢɨɧɚ ɫɨɫɬɚɜɥɹɥɢ ɬɪɭɞɨɭɫɬɪɨɟɧɧɵɟ ɥɸɞɢ ɜɨ II ɤɜɚɪɬɚɥɟ 2006 ɝɨɞɚ?
(a)8%
(ɛ) 12%
(ɜ) 14%
(ɝ) 15%
(ɞ) 16%
26
Ɂɚɞɚɱɢ
54. ɇɚ ɫɤɨɥɶɤɨ ɩɪɟɜɵɲɚɟɬ ɧɚɢɛɨɥɶɲɟɟ ɬɪɟɯɡɧɚɱɧɨɟ ɱɢɫɥɨ, ɫɭɦɦɚ ɰɢɮɪ ɤɨɬɨɪɨɝɨ ɪɚɜɧɚ 16, ɧɚɢɦɟɧɶɲɟɟ ɬɪɟɯɡɧɚɱɧɨɟ ɱɢɫɥɨ, ɫɭɦɦɚ ɰɢɮɪ ɤɨɬɨɪɨɝɨ ɬɚɤɠɟ ɪɚɜɧɚ 16?
(a) ɧɚ 220 (ɛ) ɧɚ 738 (ɜ) ɧɚ 801 (ɝ) ɧɚ 870 (ɞ) ɧɚ 899
55. Ʉɨɬɨɪɨɟ ɢɡ ɧɢɠɟ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɦɨɠɟɬ ɛɵɬɶ ɤɨɨɪɞɢɧɚɬɚɦɢ ɜɟɪɲɢɧ ɬɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ, ɤɨɬɨɪɵɣ ɫɢɦɦɟɬɪɢɱɟɧ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ x ɬɪɟɭɝɨɥɶɧɢɤɭ, ɢɡɨɛɪɚɠɟɧɧɨɦɭ ɧɚ ɱɟɪɬɟɠɟ?
(a) |
(4; |
3), |
(2; |
1), |
(0; 5) |
|||
(ɛ) |
(–6; –4), |
(–3; 2), |
(0; –3) |
|||||
(ɜ) |
(–4; |
3), |
(–2; |
1), |
(0; 2) |
|||
(ɝ) |
(3; |
–4), |
(2; |
–1), |
(0; |
–2) |
||
(ɞ) |
(–4; |
–3), |
(–2; |
–1), |
(0; |
–5) |
||
56. ɍ Ⱦɚɜɢɞɚ ɜ 3 ɪɚɡɚ ɦɟɧɶɲɟ ɤɧɢɝ, ɱɟɦ ɭ Ʌɢɤɢ, ɧɨ ɜ 6 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɭ Ⱥɥɟɤɫɟɹ. Ʉɨɥɢɱɟɫɬɜɨ ɤɧɢɝ, ɢɦɟɸɳɢɯɫɹ ɭ ɜɫɟɯ ɬɪɨɢɯ, ɛɨɥɶɲɟ 70, ɧɨ ɦɟɧɶɲɟ 90. ɋɤɨɥɶɤɨ ɤɧɢɝ ɭ Ⱦɚɜɢɞɚ?
(a) 12 (ɛ) 15 (ɜ) 18 (ɝ) 21 (ɞ) 24
57. ɇɚ ɛɟɪɟɝɭ ɦɨɪɹ Ɍɚɦɚɪɚ, ɇɚɬɚ, ɋɨɮɶɹ ɢ ȿɥɟɧɚ ɫɨɛɪɚɥɢ ɜɫɟɝɨ 40 ɪɚɤɭɲɟɤ. Ɉɧɢ ɩɨɞɟɥɢɥɢɫɶ ɦɟɠɞɭ ɫɨɛɨɣ ɫɜɨɢɦɢ ɪɚɤɭɲɤɚɦɢ: Ɍɚɦɚɪɚ ɞɚɥɚ ɇɚɬɟ 1 ɪɚɤɭɲɤɭ, ɇɚɬɚ ɋɨɮɶɟ _ 3 ɪɚɤɭɲɤɢ, ɋɨɮɶɹ ȿɥɟɧɟ _ 5 ɪɚɤɭɲɟɤ. ȿɥɟɧɚ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɧɟɫɤɨɥɶɤɨ ɪɚɤɭɲɟɤ ɞɚɥɚ Ɍɚɦɚɪɟ. ɉɨɫɥɟ ɷɬɨɝɨ ɭ ɜɫɟɯ ɱɟɬɜɟɪɵɯ ɨɤɚɡɚɥɨɫɶ ɪɚɜɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɪɚɤɭɲɟɤ. ɋɤɨɥɶɤɨ ɪɚɤɭɲɟɤ ɫɨɛɪɚɥɚ ɇɚɬɚ?
(a) 8 (ɛ) 9 (ɜ) 10 (ɝ) 11 (ɞ) 12
27
58. ȼ ɩɪɹɦɨɭɝɨɥɶɧɨɦ ɩɚɪɚɥɥɟɥɟɩɢɩɟɞɟ 12 ɨɞɢɧɚɤɨɜɵɯ ɤɭɛɨɜ ɪɚɡɦɟɳɟɧɵ ɬɚɤ, ɱɬɨ ɤɚɠɞɵɟ ɞɜɚ ɫɨɫɟɞɧɢɯ ɤɭɛɚ ɢɦɟɸɬ ɨɞɧɭ ɨɛɳɭɸ ɝɪɚɧɶ (ɫɦ. ɱɟɪɬɟɠ). ɋɤɨɥɶɤɨ ɜɫɟɝɨ ɬɚɤɢɯ ɤɭɛɨɜ ɩɨɦɟɫɬɢɬɫɹ ɜ ɷɬɨɬ ɩɪɹɦɨɭɝɨɥɶɧɵɣ ɩɚɪɚɥɥɟɥɟɩɢɩɟɞ?
(a) 46 (ɛ) 42 (ɜ) 38 (ɝ) 34 (ɞ) 30
59. ɑɢɫɥɚ a; 3a; b; 13,6 ɪɚɫɩɨɥɨɠɟɧɵ ɜ ɩɨɪɹɞɤɟ ɜɨɡɪɚɫɬɚɧɢɹ. Ɋɚɡɧɨɫɬɶ ɦɟɠɞɭ ɤɚɠɞɵɦɢ ɞɜɭɦɹ ɫɨɫɟɞɧɢɦɢ ɱɢɫɥɚɦɢ ɦɟɧɶɲɟ 4-ɟɯ. ɂɡ ɧɢɠɟ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɱɟɦɭ ɦɨɠɟɬ ɛɵɬɶ ɪɚɜɧɨ b ?
(a) 9,2 (ɛ) 9,4 (ɜ) 9,6 (ɝ) 9,8 (ɞ) 10
60. ȼ ɝɨɫɬɢɧɢɰɟ ɢɦɟɸɬɫɹ ɬɨɥɶɤɨ ɨɞɧɨ- ɢ ɞɜɭɯɦɟɫɬɧɵɟ ɧɨɦɟɪɚ. Ɇɟɧɟɞɠɟɪɭ ɫɨɨɛɳɢɥɢ, ɱɬɨ ɨɧ ɞɨɥɠɟɧ ɪɚɡɦɟɫɬɢɬɶ 11 ɫɬɭɞɟɧɬɨɤ 5 ɭɧɢɜɟɪɫɢɬɟɬɨɜ ɫ ɭɫɥɨɜɢɟɦ, ɱɬɨɛɵ ɜ ɨɞɧɨɦ ɧɨɦɟɪɟ ɧɟ ɨɤɚɡɚɥɢɫɶ ɫɬɭɞɟɧɬɤɢ ɢɡ ɪɚɡɧɵɯ ɭɧɢɜɟɪɫɢɬɟɬɨɜ. Ɇɢɧɢɦɭɦ ɫɤɨɥɶɤɨ ɫɜɨɛɨɞɧɵɯ ɧɨɦɟɪɨɜ ɞɨɥɠɧɨ ɛɵɬɶ ɜ ɝɨɫɬɢɧɢɰɟ, ɱɬɨɛɵ ɦɟɧɟɞɠɟɪ ɧɟɩɪɟɦɟɧɧɨ ɫɦɨɝ ɪɚɡɦɟɫɬɢɬɶ ɫɬɭɞɟɧɬɨɤ ɜ ɝɨɫɬɢɧɢɰɟ ɫ ɫɨɛɥɸɞɟɧɢɟɦ ɞɚɧɧɨɝɨ ɭɫɥɨɜɢɹ?
(a) 5 (ɛ) 6 (ɜ) 7 (ɝ) 8 (ɞ) 9
28
Ʉɨɥɢɱɟɫɬɜɟɧɧɵɟ ɫɪɚɜɧɟɧɢɹ
ɋɪɚɜɧɢɬɟ ɦɟɠɞɭ ɫɨɛɨɣ ɜɟɥɢɱɢɧɵ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɜ ɹɱɟɣɤɚɯ ɫɬɨɥɛɰɨɜ Ⱥ ɢ ȼ.
ȿɫɥɢ ɜɟɥɢɱɢɧɚ, ɞɚɧɧɚɹ ɜ ɹɱɟɣɤɟ ɫɬɨɥɛɰɚ Ⱥ, ɛɨɥɶɲɟ ɜɟɥɢɱɢɧɵ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɹɱɟɣɤɟ ɫɬɨɥɛɰɚ ȼ, ɜɵɛɟɪɢɬɟ (ɚ);
ȿɫɥɢ ɜɟɥɢɱɢɧɚ, ɞɚɧɧɚɹ ɜ ɹɱɟɣɤɟ ɫɬɨɥɛɰɚ ȼ, ɛɨɥɶɲɟ ɜɟɥɢɱɢɧɵ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɹɱɟɣɤɟ ɫɬɨɥɛɰɚ Ⱥ, ɜɵɛɟɪɢɬɟ (ɛ);
ȿɫɥɢ ɜɟɥɢɱɢɧɵ, ɞɚɧɧɵɟ ɜ ɹɱɟɣɤɚɯ ɨɛɨɢɯ ɫɬɨɥɛɰɨɜ, ɪɚɜɧɵ, ɜɵɛɟɪɢɬɟ (ɜ); ȿɫɥɢ ɢɦɟɸɳɚɹɫɹ ɢɧɮɨɪɦɚɰɢɹ ɧɟɞɨɫɬɚɬɨɱɧɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɬɨɝɨ, ɤɚɤɚɹ ɢɡ ɜɟɥɢɱɢɧ
ɛɨɥɶɲɟ, ɜɵɛɟɪɢɬɟ (ɝ).
|
A |
B |
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ȿɥɟɧɚ ɜ ɫɭɛɛɨɬɭ ɩɨɬɪɚɬɢɥɚ 40% ɨɬ ɜɫɟɣ ɢɦɟɸɳɟɣɫɹ ɭ ɧɟɟ |
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ɫɭɦɦɵ ɞɟɧɟɝ, ɚ ɜ ɜɨɫɤɪɟɫɟɧɶɟ – 60% ɨɬ ɨɫɬɚɜɲɟɣɫɹ ɫɭɦɦɵ. |
(ɚ) (ɛ) (ɜ) (ɝ) |
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61. |
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ɤɨɥɢɱɟɫɬɜɨ ɞɟɧɟɝ, |
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ɤɨɥɢɱɟɫɬɜɨ ɞɟɧɟɝ, |
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ɩɨɬɪɚɱɟɧɧɵɯ ȿɥɟɧɨɣ |
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ɩɨɬɪɚɱɟɧɧɵɯ ȿɥɟɧɨɣ ɜ |
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ɜ ɫɭɛɛɨɬɭ |
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ɜɨɫɤɪɟɫɟɧɶɟ |
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Ɉɬɧɨɲɟɧɢɟ ɩɥɨɳɚɞɢ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ |
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AMND ɤ ɩɥɨɳɚɞɢ ɤɜɚɞɪɚɬɚ ABCD |
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ɪɚɜɧɚ 1 . |
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(ɚ) (ɛ) (ɜ) (ɝ) |
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62. |
4 |
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ɨɬɧɨɲɟɧɢɟ ɩɟɪɢɦɟɬɪɚ |
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ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ AMND ɤ |
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3 |
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ɩɟɪɢɦɟɬɪɭ ɤɜɚɞɪɚɬɚ ABCD |
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5 |
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a > b, |
b > c |
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63. |
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(ɚ) (ɛ) (ɜ) (ɝ) |
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a – 4 |
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c – 3 |
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29
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ɑɬɨɛɵ ɩɪɨɧɭɦɟɪɨɜɚɬɶ ɫɬɪɚɧɢɰɵ 12-ɫɬɪɚɧɢɱɧɨɣ ɝɚɡɟɬɵ, |
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ɧɚɪɹɞɭ ɫ ɞɪɭɝɢɦɢ ɰɢɮɪɚɦɢ, ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɹɬɶ |
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64. |
ɟɞɢɧɢɰ(ɬ.ɟ. ɰɢɮɪɭ 1). |
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(ɚ) (ɛ) (ɜ) (ɝ) |
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ɤɨɥɢɱɟɫɬɜɨ ɱɟɬɜɟɪɨɤ, |
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ɤɨɥɢɱɟɫɬɜɨ ɞɜɨɟɤ, |
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ɧɟɨɛɯɨɞɢɦɵɯɞɥɹ |
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ɧɟɨɛɯɨɞɢɦɵɯɞɥɹ |
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ɧɭɦɟɪɚɰɢɢ 400- |
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ɧɭɦɟɪɚɰɢɢ 300- |
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ɫɬɪɚɧɢɱɧɨɣ ɤɧɢɝɢ |
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ɫɬɪɚɧɢɱɧɨɣ ɤɧɢɝɢ |
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ɉɨɥɨɜɢɧɚ ɡɚɪɩɥɚɬɵ Ⱥɧɚɬɨɥɢɹ ɧɚ 250 ɥɚɪɢ ɛɨɥɶɲɟ ɱɟɬɜɟɪɬɢ |
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65. |
ɡɚɪɩɥɚɬɵ ȼɚɞɢɦɚ. |
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(ɚ) (ɛ) (ɜ) (ɝ) |
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ɡɚɪɩɥɚɬɚ Ⱥɧɚɬɨɥɢɹ |
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ɡɚɪɩɥɚɬɚ ȼɚɞɢɦɚ |
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Ⱦɥɹ ɥɸɛɨɝɨ ɱɢɫɥɚ |
a ɫɢɦɜɨɥɨɦ |
a ɨɛɨɡɧɚɱɟɧɨ |
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ɧɚɢɛɨɥɶɲɟɟ ɰɟɥɨɟ ɱɢɫɥɨ, ɦɟɧɶɲɟɟ, ɱɟɦ |
a, ɫɢɦɜɨɥɨɦ ɠɟ |
a |
(ɚ) (ɛ) (ɜ) (ɝ) |
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66. |
ɨɛɨɡɧɚɱɟɧɨ ɧɚɢɦɟɧɶɲɟɟ |
ɰɟɥɨɟ ɱɢɫɥɨ, ɛɨɥɶɲɟɟ, ɱɟɦ a. |
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a 5 # |
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a# 4 |
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30