matem2012-04-17mioo

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 1	3
	ɒɛɬɭɷ 1

1 Ɏɬɭɛɨɩɝɣɭɠ ɬɩɩɭɝɠɭɬɭɝɣɠ ɧɠɡɟɮ ɝɶɫɛɡɠɨɣɠɧ ɣ ɢɨɛɲɠɨɣɠɧ ɝɶɫɛɡɠɨɣɺ.

ȽɖɋȻɁɀɈɃɚ												ɂɈȻɒɀɈɃɚȽɖɋȻɁɀɈɃɄ
Ȼ) 18							5					1)	6
							12					2)	7,5
	2					1
ȼ)				:								3)	1,3
3							9					4)	1,75
Ƚ) 1		2					1

312

Ȼȼ Ƚ ɉɭɝɠɭ:

2Ʌɮɬɩɥ ɦɷɟɛ ɨɛɞɫɠɦɣ, ɫɛɬɪɦɛɝɣɦɣ ɣ ɪɩɦɮɲɠɨɨɮɹ ɝɩɟɮ ɨɛɞɫɠɦɣ. Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɣɢɧɠɨɠɨɣɺ ɭɠɧɪɠɫɛɭɮɫɶ ɦɷɟɛ ɣ ɝɩɟɶ. Ɍɥɩɦɷɥɩ ɧɣɨɮɭ ɝɩɟɛ ɨɛɞɫɠɝɛɦɛɬɷ ɩɭ 0 °Ɍ ɟɩ 5 °Ɍ?

ɉɭɝɠɭ:

3Ɋɦɩɴɛɟɷ ɢɛɪɩɝɠɟɨɣɥɛ ɜɶɦɛ ɮɝɠɦɣɲɠɨɛ ɬ 250 ɦ2 ɟɩ 350 ɦ2. Ɉɛ ɬɥɩɦɷɥɩ ɪɫɩɱɠɨɭɩɝ ɮɝɠɦɣɲɣɦɛɬɷ ɪɦɩɴɛɟɷ ɢɛɪɩɝɠɟɨɣɥɛ?

ɉɭɝɠɭ:

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 1

4

4Ɏɥɛɡɣɭɠ ɝɶɫɛɡɠɨɣɠ, ɫɛɝɨɩɠ 32k 1.

1) 32k 3		2) (32k)	1	3)	9k		4)	32k
					3			3 1
5 Ʌɛɥɩɧɮ	ɣɢ	ɟɛɨɨɶɰ ɝɶɫɛɡɠɨɣɤ		ɭɩɡɟɠɬɭɝɠɨɨɩ			ɫɛɝɨɩ	ɝɶɫɛɡɠɨɣɠ
(a 1)2	(a	1)(a 2)?
1) 3a 1		2) 3 a		3) 3a 1			4) a 1

6Ɇɠɬɭɨɣɱɛ ɬɩɠɟɣɨɺɠɭ ɭɩɲɥɣ Ȼ ɣ Ƚ, ɫɛɬɬɭɩɺɨɣɠ ɧɠɡɟɮ ɥɩɭɩɫɶɧɣ ɫɛɝɨɩ 25 ɧ. Ƚɶɬɩɭɛ ɥɛɡɟɩɤ ɬɭɮɪɠɨɣ ɫɛɝɨɛ 14 ɬɧ, ɛ ɟɦɣɨɛ — 48 ɬɧ. Ɉɛɤɟɣɭɠ ɝɶɬɩɭɮ Ƚ (ɝ ɧɠɭɫɛɰ), ɨɛ ɥɩɭɩɫɮɹ ɪɩɟɨɣɧɛɠɭɬɺ ɦɠɬɭɨɣɱɛ.

ɉɭɝɠɭ:

7ɉ ɲɣɬɦɛɰ a ɣ b ɣɢɝɠɬɭɨɩ, ɲɭɩ 1 a 0, 3 b 4. Ʌɛɥɣɠ ɣɢ ɬɦɠɟɮɹɴɣɰ ɨɠɫɛɝɠɨɬɭɝ ɠɝɠɫ ɶ? ɂɛɪɣɳɣɭɠ ɣɰ ɨɩɧɠɫɛ.

1) 0 a 1 2) a b 0 3) 1 1 b

ɉɭɝɠɭ:

8Ƚ ɪɺɭɣɮɞɩɦɷɨɣɥɠ ɩɟɣɨ ɮɞɩɦ ɪɫɺɧɩɤ. Ɉɛɤɟɣɭɠ ɝɠɦɣɲɣɨɮ ɩɬɭɛɦɷɨɶɰ ɠɞɩ ɮɞɦɩɝ, ɠɬɦɣ ɣɢɝɠɬɭɨɩ, ɲɭɩ ɝɬɠ ɩɨɣ ɫɛɝɨɶ ɧɠɡɟɮ ɬɩɜɩɤ.

ɉɭɝɠɭ:

© 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

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 1	5
9 ɋɠɳɣɭɠ ɮɫɛɝɨɠɨɣɠ x2 10	3x.
ɉɭɝɠɭ:

10 Ɉɛ ɥɛɥɩɧ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɠɨɩ ɧɨɩɡɠɬɭɝɩ ɫɠɳɠɨɣɤ ɬɣɬɭɠɧɶ ɨɠɫɛɝɠɨɬɭɝ
®­x2 4	0,
¯ 15 x3	0 ?
1)	2)
3)	4)

11 Ƚ ɥɩɫɩɜɥɠ 14 ɪɛɥɠɭɣɥɩɝ ɬ ɲɻɫɨɶɧ ɲɛɠɧ ɣ 6 ɪɛɥɠɭɣɥɩɝ ɬ ɢɠɦɻɨɶɧ ɲɛɠɧ. Ɋɛɝɠɦ ɨɛɮɞɛɟ ɝɶɨɣɧɛɠɭ. ɩɟɣɨ ɪɛɥɠɭɣɥ Ʌɛɥɩɝɛ ɝɠɫɩɺɭɨɩɬɭɷ, ɭɩɞɩ ɲɭɩ ɸɭɩ ɪɛɥɠɭɣɥ ɬ ɢɠɦɻɨɶɧ ɲɛɠɧ?

ɉɭɝɠɭ:

12 Ɉɛ ɥɫɮɞɩɝɩɤ ɟɣɛɞɫɛɧɧɠ ɪɩɥɛɢɛɨɩ, ɥɛɥ ɫɛɬɪɫɠɟɠɦɺɠɭɬɺɝ ( ɪɫɩɱɠɨɭɛɰ)

ɟɦɣɭɠɦɷɨɩɬɭɷ ɭɠɦɠɯɩɨɨɶɰ ɫɛɢɞɩɝɩɫɩɝ ɬɩɭɩɝɶɰ ɛɜɩɨɠɨɭɩɝ ɥɩɧɪɛɨɣɣ ɇɩɜɣɦ« ». Ʌɛɥɩɤ ɪɫɩɱɠɨɭ ɬɩɬɭɛɝɦɺɹɭ ɫɛɢɞɩɝɩɫɶ, ɟɦɣɭɠɦɷɨɩɬɭɷ ɥɩɭɩɫɶɰ ɨɠ ɪɫɠɝɶɳɛɠɭ 15 ɧɣɨɮɭ?

ɉɭɝɠɭ:

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 1						6
13 Ƚ	ɛɫɣɯɧɠɭɣɲɠɬɥɩɤ ɪɫɩɞɫɠɬɬɣɣ		(	a	n)	ɣɢɝɠɬɭɨɶ ɟɝɛ ɪɠɫɝɶɰ ɲɦɠɨɛ:
a1	18, a2	25. Ʌɛɥɩɠ ɲɣɬɦɩ ɬɭɩɣɭ ɝ ɸɭɩɤ ɪɫɩɞɫɠɬɬɣɣ ɨɛ 51-ɧ ɧɠɬɭɠ?

ɉɭɝɠɭ:

14 Ƚ ɩɥɫɮɡɨɩɬɭɷ ɬ ɟɣɛɧɠɭɫɩɧ ȻD ɝɪɣɬɛɨ ɲɠɭɶɫɠɰɮɞɩɦɷɨɣɥ ȻȽ D. Ɉɛɤɟɣɭɠ ɝɠɦɣɲɣɨɮ ɮɞɦɛ ȻȽ , ɠɬɦɣ CAD 20 .

ɉɭɝɠɭ:

15Ɏɥɛɡɣɭɠ ɝ ɩɭɝɠɭɠ ɨɩɧɠɫɛ ɝɠɫɨɶɰ ɮɭɝɠɫɡɟɠɨɣɤ.

1)Ɍɫɠɟɨɺɺ ɦɣɨɣɺ ɭɫɠɮɞɩɦɷɨɣɥɛ ɫɛɢɜɣɝɛɠɭ ɠɞɩ ɨɛ ɟɝɛ ɭɫɠɮɞɩɦɷɨɣɥɛ.

2)ɀɬɦɣ ɝ ɪɛɫɛɦɦɠɦɩɞɫɛɧɧɠ ɟɣɛɞɩɨɛɦɣ ɫɛɝɨɶ, ɭɩ ɸɭɩɭ ɪɛɫɛɦɦɠɦɩ- ɞɫɛɧɧ – ɪɫɺɧɩɮɞɩɦɷɨɣɥ.

3)Ⱦɣɪɩɭɠɨɮɢɛ ɪɫɺɧɩɮɞɩɦɷɨɩɞɩ ɭɫɠɮɞɩɦɷɨɣɥɛ ɜɩɦɷɳɠ ɦɹɜɩɞɩ ɠɞɩ ɥɛɭɠɭɛ.

4)ɉɭɨɩɳɠɨɣɠ ɪɦɩɴɛɟɠɤ ɪɩɟɩɜɨɶɰ ɭɫɠɮɞɩɦɷɨɣɥɩɝ ɫɛɝɨɩ ɥɩɸɯɯɣɱɣɠɨɭɮ ɪɩɟɩɜɣɺ.

ɉɭɝɠɭ:

© 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

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 1		7
16 Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ y	x2 4. Ʌɛɥɣɠ ɣɢ ɟɛɨɨɶɰ
ɪɫɺɧɶɰ ɨɠ ɣɧɠɹɭ ɬ ɞɫɛɯɣɥɩɧ ɸɭɩɤ ɯɮɨɥɱɣɣ ɨɣ ɩɟɨɩɤ ɩɜɴɠɤ?		ɭɩɲɥɣ
Ɏɥɛɡɣɭɠ ɣɰ ɨɩɧɠɫɛ.
1) y = x
2) y = x + 5
3) y = 4
4) x = – 3
5) y = 10

ɉɭɝɠɭ:

ɉɭɝɠɭɶɥ ɢɛɟɛɨɣɺɧ		17	18 ɢɛɪɣɳɣɭɠɝ ɜɦɛɨɥ ʌ 2.
17 Ƀɢ ɯɩɫɧɮɦɶ l l		tl	ɝɶɫɛɢɣɭɠ t.
	0	0
18			­	5	x2	0,
	ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ ɨɠɫɛɝɠɨɬɭɝ ¯®			1	x	2.

ɒɛɬɭɷ 2

Ɋɫɣ ɝɶɪɩɦɨɠɨɣɣ ɢɛɟɛɨɣɤ 19-23 ɣɬɪɩɦɷɢɮɤɭɠ ɩɭɟɠɦɷɨɶɤ ɦɣɬɭ (ɜɦɛɨɥ). Ɍɨɛɲɛɦɛ ɮɥɛɡɣɭɠ, ɨɩɧɠɫ ɢɛɟɛɨɣɺ ɛ ɢɛɭɠɧ ɢɛɪɣɳɣɭɠ ɠɞɩ ɫɠɳɠɨɣɠ.

19 Ɍɩɥɫɛɭɣɭɠ ɟɫɩɜɷ: a 16b2 4a2 2b.

a2b

20Ɋɫɩɭɣɝɩɪɩɦɩɡɨɶɠ ɮɞɦɶ ɲɠɭɶɫɻɰɮɞɩɦɷɨɣɥɛ ɪɩɪɛɫɨɩ. ɫɛɝɨɶ ȿɩɥɛɡɣɭɠ, ɲɭɩ ɩɨ ɪɛɫɛɦɦɠɦɩɞɫɛɧɧ.

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 1

8

21ɇɠɡɟɮ ɲɣɬɦɛɧɣ 2 ɣ 18 ɝɬɭɛɝɷɭɠ ɭɫɣ ɲɣɬɦɛ, ɭɛɥ ɲɭɩɜɶ ɝɧɠɬɭɠ ɬ ɟɛɨɨɶɧɣ ɩɨɣ ɩɜɫɛɢɩɝɛɦɣ ɞɠɩɧɠɭɫɣɲɠɬɥɮɹ ɪɫɩɞɫɠɬɬɣɹ.

22Ɋɩɬɭɫɩɤɭɠ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ y x2 x5 6 ɣ ɩɪɫɠɟɠɦɣɭɠ, ɪɫɣ ɥɛɥɣɰ ɢɨɛɲɠɨɣɺɰ c ɪɫɺɧɛɺ y c ɣɧɠɠɭ ɬ ɞɫɛɯɣɥɩɧ ɫɩɝɨɩ ɭɫɣ ɩɜɴɣɠ. ɭɩɲɥɣ

23Ɉɛ ɥɛɡɟɩɤ ɣɢ ɟɝɮɰ ɩɥɫɮɡɨɩɬɭɠɤ ɬ ɫɛɟɣɮɬɛɧɣ 3 ɣ 4 ɦɠɡɛɭ ɪɩ ɭɫɣ ɝɠɫɳɣɨɶ. ɫɩɧɜɛ Ɉɛɤɟɣɭɠ ɠɞɩ ɬɭɩɫɩɨɮ.

© 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

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 2	3
	ɒɛɬɭɷ 1

1 Ɏɬɭɛɨɩɝɣɭɠ ɬɩɩɭɝɠɭɬɭɝɣɠ ɧɠɡɟɮ ɝɶɫɛɡɠɨɣɠɧ ɣ ɢɨɛɲɠɨɣɠɧ ɝɶɫɛɡɠɨɣɺ.

ȽɖɋȻɁɀɈɃɚ												ɂɈȻɒɀɈɃɚȽɖɋȻɁɀɈɃɄ
Ȼ)	1							1				1)	1,25
	1
	3							12				2)	1,75
ȼ) 21								6				3)	4,5
								28
												4)	6
Ƚ)	4							2
					:

515

Ȼȼ Ƚ ɉɭɝɠɭ:

2Ʌɮɬɩɥ ɦɷɟɛ ɨɛɞɫɠɦɣ, ɫɛɬɪɦɛɝɣɦɣ ɣ ɪɩɦɮɲɠɨɨɮɹ ɝɩɟɮ ɨɛɞɫɠɦɣ. Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɣɢɧɠɨɠɨɣɺ ɭɠɧɪɠɫɛɭɮɫɶ ɦɷɟɛ ɣ ɝɩɟɶ. Ɍɥɩɦɷɥɩ ɝɫɠɧɠɨɣ ɢɛɨɺɦ ɪɫɩɱɠɬɬ ɨɛɞɫɠɝɛɨɣɺ ɦɷɟɛɌ ɩɭ –10 ° ɟɩ –5 °Ɍ?

ɉɭɝɠɭ:

3 Ɋɦɩɴɛɟɷ ɢɛɪɩɝɠɟɨɣɥɛ ɜɶɦɛ ɮɝɠɦɣɲɠɨɛ ɬ 350 ɦ2 ɟɩ 420 ɦ2. Ɉɛ ɬɥɩɦɷɥɩ ɪɫɩɱɠɨɭɩɝ ɮɝɠɦɣɲɣɦɛɬɷ ɪɦɩɴɛɟɷ ɢɛɪɩɝɠɟɨɣɥɛ?

ɉɭɝɠɭ:

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 2

4

4Ɏɥɛɡɣɭɠ ɝɶɫɛɡɠɨɣɠ, ɫɛɝɨɩɠ 33k 2.

1)	33k			2)	27k		3) 33k 9	4) (33k)	2
	3 2				9
5 Ʌɛɥɩɧɮ			ɣɢ	ɟɛɨɨɶɰ	ɝɶɫɛɡɠɨɣɤ		ɭɩɡɟɠɬɭɝɠɨɨɩ	ɫɛɝɨɩ ɝɶɫɛɡɠɨɣɠ
(a 1)2		(a		2)(a 1)?
1) 3a 1				2) a 3			3) 3a 1	4) a 3

6Ɇɠɬɭɨɣɱɛ ɬɩɠɟɣɨɺɠɭ ɭɩɲɥɣ Ȼ ɣ Ƚ, ɫɛɬɬɭɩɺɨɣɠ ɧɠɡɟɮ ɥɩɭɩɫɶɧɣ ɫɛɝɨɩ 26 ɧ. Ƚɶɬɩɭɛ ɥɛɡɟɩɤ ɬɭɮɪɠɨɣ ɫɛɝɨɛ 20 ɬɧ, ɛ ɟɦɣɨɛ — 48 ɬɧ. Ɉɛɤɟɣɭɠ ɝɶɬɩɭɮ Ƚ (ɝ ɧɠɭɫɛɰ), ɨɛ ɥɩɭɩɫɮɹ ɪɩɟɨɣɧɛɠɭɬɺ ɦɠɬɭɨɣɱɛ.

ɉɭɝɠɭ:
7 ɉ ɲɣɬɦɛɰ a ɣ b ɣɢɝɠɬɭɨɩ, ɲɭɩ 0 a 1, 3 b				2. Ʌɛɥɣɠ ɣɢ ɬɦɠɟɮɹɴɣɰ
ɨɠɫɛɝɠɨɬɭɝ			ɠɝɠɫ ɶ? ɂɛɪɣɳɣɭɠ ɣɰ ɨɩɧɠɫɛ.
1)	1	0	2) a b 0	3) 2 b 3
	a

ɉɭɝɠɭ:

8Ƚ ɳɠɬɭɣɮɞɩɦɷɨɣɥɠ ɩɟɣɨ ɮɞɩɦ ɪɫɺɧɩɤ. Ɉɛɤɟɣɭɠ ɝɠɦɣɲɣɨɮ ɩɬɭɛɦɷɨɶɰ ɠɞɩ ɮɞɦɩɝ, ɠɬɦɣ ɣɢɝɠɬɭɨɩ, ɲɭɩ ɝɬɠ ɩɨɣ ɫɛɝɨɶ ɧɠɡɟɮ. ɬɩɜɩɤ

ɉɭɝɠɭ:

© 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

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 2

5

9ɋɠɳɣɭɠ ɮɫɛɝɨɠɨɣɠ x2 4x 12.

ɉɭɝɠɭ:

10 Ɉɛ ɥɛɥɩɧ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɠɨɩ ɧɨɩɡɠɬɭɝɩ ɫɠɳɠɨɣɤ ɬɣɬɭɠɧɶ ɨɠɫɛɝɠɨɬɭɝ
®­x2 4	0,
¯ 15 x3	0 ?
1)	2)
3)	4)

11 Ƚ ɥɩɫɩɜɥɠ 18 ɪɛɥɠɭɣɥɩɝ ɬ ɲɻɫɨɶɧ ɲɛɠɧ ɣ 7 ɪɛɥɠɭɣɥɩɝ ɬ ɢɠɦɻɨɶɧ ɲɛɠɧ. Ɋɛɝɠɦ ɨɛɮɞɛɟ ɝɶɨɣɧɛɠɭ. ɩɟɣɨ ɪɛɥɠɭɣɥ Ʌɛɥɩɝɛ ɝɠɫɩɺɭɨɩɬɭɷ, ɭɩɞɩ ɲɭɩ ɸɭɩ ɪɛɥɠɭɣɥ ɬ ɢɠɦɻɨɶɧ ɲɛɠɧ?

ɉɭɝɠɭ:

12 Ɉɛ ɥɫɮɞɩɝɩɤ ɟɣɛɞɫɛɧɧɠ ɪɩɥɛɢɛɨɩ, ɥɛɥ ɫɛɬɪɫɠɟɠɦɺɠɭɬɺɝ ( ɪɫɩɱɠɨɭɛɰ)

ɟɦɣɭɠɦɷɨɩɬɭɷ ɭɠɦɠɯɩɨɨɶɰ ɫɛɢɞɩɝɩɫɩɝ ɬɩɭɩɝɶɰ ɛɜɩɨɠɨɭɩɝ ɥɩɧɪɛɨɣɣ ɇɩɜɣɦ« ». Ʌɛɥɩɤ ɪɫɩɱɠɨɭ ɬɩɬɭɛɝɦɺɹɭ ɫɛɢɞɩɝɩɫɶ, ɟɦɣɭɠɦɷɨɩɬɭɷ ɥɩɭɩɫɶɰ ɨɠ ɧɠɨɠɠ 15 ɧɣɨɮɭ?

ɉɭɝɠɭ:

13 Ƚ	ɛɫɣɯɧɠɭɣɲɠɬɥɩɤ ɪɫɩɞɫɠɬɬɣɣ	a	n)	ɣɢɝɠɬɭɨɶ ɟɝɛ ɪɠɫɝɶɰ ɲɦɠɨɛ:
	(
a1	16, a2 24. Ʌɛɥɩɠ ɲɣɬɦɩ ɬɭɩɣɭ ɝ ɸɭɩɤ ɪɫɩɞɫɠɬɬɣɣ ɨɛ 61-ɧ ɧɠɬɭɠ?

ɉɭɝɠɭ:

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 2	6
14 Ƚ ɩɥɫɮɡɨɩɬɭɷ ɬ ɟɣɛɧɠɭɫɩɧ ȻD ɝɪɣɬɛɨ ɲɠɭɶɫɠɰɮɞɩɦɷɨɣɥ	ȻȽ D.
Ɉɛɤɟɣɭɠ ɝɠɦɣɲɣɨɮ ɮɞɦɛ ȻȽ , ɠɬɦɣ CAD 30 .

ɉɭɝɠɭ:

15Ɏɥɛɡɣɭɠ ɝ ɩɭɝɠɭɠ ɨɩɧɠɫɛ ɝɠɫɨɶɰ ɮɭɝɠɫɡɟɠɨɣɤ.

1)Ɍɫɠɟɨɺɺ ɦɣɨɣɺ ɭɫɛɪɠɱɣɣ ɫɛɢɜɣɝɛɠɭ ɠɻ ɨɛ ɟɝɛ ɭɫɠɮɞɩɦɷɨɣɥɛ.

2)ɀɬɦɣ ɝ ɪɫɺɧɩɮɞɩɦɷɨɣɥɠ ɟɣɛɞɩɨɛɦɣ ɪɠɫɪɠɨɟɣɥɮɦɺɫɨɶ, ɭɩ ɸɭɩɭ ɪɫɺɧɩɮɞɩɦɷɨɣɥ – ɥɝɛɟɫɛɭ.

3)Ʌɛɭɠɭ ɪɫɺɧɩɮɞɩɦɷɨɩɞɩ ɭɫɠɮɞɩɦɷɨɣɥɛ ɧɠɨɷɳɠ ɠɞɩ ɞɣɪɩɭɠɨɮɢɶ.

4)ɉɭɨɩɳɠɨɣɠ ɟɦɣɨ ɞɣɪɩɭɠɨɮɢ ɟɝɮɰ ɪɩɟɩɜɨɶɰ ɪɫɺɧɩɮɞɩɦɷɨɶɰ ɭɫɠɮɞɩɦɷɨɣɥɩɝ ɫɛɝɨɩ ɥɩɸɯɯɣɱɣɠɨɭɮ ɪɩɟɩɜɣɺ.

ɉɭɝɠɭ:

16Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ y x2 4. Ʌɛɥɣɠ ɣɢ ɟɛɨɨɶɰ

ɪɫɺɧɶɰ ɨɠ ɣɧɠɹɭ ɬ ɞɫɛɯɣɥɩɧ ɸɭɩɤ ɯɮɨɥɱɣɣ ɨɣ ɩɟɨɩɤ ɩɜɴɠɤ? ɭɩɲɥɣ ɂɛɪɣɳɣɭɠ ɣɰ ɨɩɧɠɫɛ.

1)X = 3

2)Y = – 4

3)Y = – 10

4)Y = – X

5)Y = X – 5

ɉɭɝɠɭ:

© 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

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 2

7

ɉɭɝɠɭɶɥ ɢɛɟɛɨɣɺɧ		17	18 ɢɛɪɣɳɣɭɠɝ ɜɦɛɨɥ ʌ 2.
17	Ƀɢ ɯɩɫɧɮɦɶ l l	(1	t) ɝɶɫɛɢɣɭɠ l		.
	0			0
			­ 3	x2	0,
18	ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ ɨɠɫɛɝɠɨɬɭɝ ®
			¯ x	4	3.

ɒɛɬɭɷ 2

Ɋɫɣ ɝɶɪɩɦɨɠɨɣɣ ɢɛɟɛɨɣɤ 19-23 ɣɬɪɩɦɷɢɮɤɭɠ ɩɭɟɠɦɷɨɶɤ ɦɣɬɭ (ɜɦɛɨɥ). Ɍɨɛɲɛɦɛ ɮɥɛɡɣɭɠ, ɨɩɧɠɫ ɢɛɟɛɨɣɺ ɛ ɢɛɭɠɧ ɢɛɪɣɳɣɭɠ ɠɞɩ ɫɠɳɠɨɣɠ.

19 Ɍɩɥɫɛɭɣɭɠ ɟɫɩɜɷ: 2a 27b2 12a2 3b.

2a 3b

20Ɋɫɩɭɣɝɩɪɩɦɩɡɨɶɠ ɬɭɩɫɩɨɶ ɲɠɭɶɫɻɰɮɞɩɦɷɨɣɥɛ ɪɩɪɛɫɨɩ. ɫɛɝɨɶ ȿɩɥɛɡɣɭɠ, ɲɭɩ ɩɨ ɪɛɫɛɦɦɠɦɩɞɫɛɧɧ.

21ɇɠɡɟɮ ɲɣɬɦɛɧɣ 2 ɣ 72 ɝɬɭɛɝɷɭɠ ɭɫɣ ɲɣɬɦɛ, ɭɛɥ ɲɭɩɜɶ ɝɧɠɬɭɠ ɬ ɟɛɨɨɶɧɣ ɩɨɣ ɩɜɫɛɢɩɝɛɦɣ ɞɠɩɧɠɭɫɣɲɠɬɥɮɹ ɪɫɩɞɫɠɬɬɣɹ.

22Ɋɩɬɭɫɩɤɭɠ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ y x2 x5 6 ɣ ɩɪɫɠɟɠɦɣɭɠ, ɪɫɣ ɥɛɥɣɰ ɢɨɛɲɠɨɣɺɰ c ɪɫɺɧɛɺ y c ɣɧɠɠɭ ɬ ɞɫɛɯɣɥɩɧ ɫɩɝɨɩ ɭɫɣ ɩɜɴɣɠ. ɭɩɲɥɣ

23Ɉɛ ɥɛɡɟɩɤ ɣɢ ɟɝɮɰ ɩɥɫɮɡɨɩɬɭɠɤ ɬ ɫɛɟɣɮɬɛɧɣ 5 ɣ 12 ɦɠɡɛɭ ɪɩ ɭɫɣ ɝɠɫɳɣɨɶ. ɫɩɧɜɛ Ɉɛɤɟɣɭɠ ɠɞɩ ɬɭɩɫɩɨɮ.

© ɇɃɉɉ 2012 ɞ. Ɋɮɜɦɣɥɛɱɣɺ ɝ Ƀɨɭɠɫɨɠɭɠ ɣɦɣ ɪɠɲɛɭɨɶɰ ɣɢɟɛɨɣɺɰ ɜɠɢ ɪɣɬɷɧɠɨɨɩɞɩ ɬɩɞɦɛɬɣɺ ɇɃɉɉ ɢɛɪɫɠɴɠɨɛ

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 3	3
	ɒɛɬɭɷ 1

1 Ɏɬɭɛɨɩɝɣɭɠ ɬɩɩɭɝɠɭɬɭɝɣɠ ɧɠɡɟɮ ɝɶɫɛɡɠɨɣɠɧ ɣ ɢɨɛɲɠɨɣɠɧ ɝɶɫɛɡɠɨɣɺ.

ȽɖɋȻɁɀɈɃɚ												ɂɈȻɒɀɈɃɚȽɖɋȻɁɀɈɃɄ
Ȼ) 18							5					1)	6
							12					2)	7,5
	2					1
ȼ)				:								3)	1,3
3							9					4)	1,75
Ƚ) 1		2					1

312

Ȼȼ Ƚ ɉɭɝɠɭ:

2Ʌɮɬɩɥ ɦɷɟɛ ɨɛɞɫɠɦɣ, ɫɛɬɪɦɛɝɣɦɣ ɣ ɪɩɦɮɲɠɨɨɮɹ ɝɩɟɮ ɨɛɞɫɠɦɣ. Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɣɢɧɠɨɠɨɣɺ ɭɠɧɪɠɫɛɭɮɫɶ ɦɷɟɛ ɣ ɝɩɟɶ. Ɍɥɩɦɷɥɩ ɝɫɠɧɠɨɣ ɢɛɨɺɦ ɪɫɩɱɠɬɬ ɨɛɞɫɠɝɛɨɣɺ ɦɷɟɛɌ ɩɭ –10 ° ɟɩ –5 °Ɍ?

ɉɭɝɠɭ:

3Ɋɦɩɴɛɟɷ ɢɛɪɩɝɠɟɨɣɥɛ ɜɶɦɛ ɮɝɠɦɣɲɠɨɛ ɬ 250 ɦ2 ɟɩ 350 ɦ2. Ɉɛ ɬɥɩɦɷɥɩ ɪɫɩɱɠɨɭɩɝ ɮɝɠɦɣɲɣɦɛɬɷ ɪɦɩɴɛɟɷ ɢɛɪɩɝɠɟɨɣɥɛ?

ɉɭɝɠɭ:

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 3

4

4Ɏɥɛɡɣɭɠ ɝɶɫɛɡɠɨɣɠ, ɫɛɝɨɩɠ 33k 2.

1)	33k			2)	27k		3) 33k 9	4) (33k)	2
	3 2				9
5 Ʌɛɥɩɧɮ			ɣɢ	ɟɛɨɨɶɰ	ɝɶɫɛɡɠɨɣɤ		ɭɩɡɟɠɬɭɝɠɨɨɩ	ɫɛɝɨɩ ɝɶɫɛɡɠɨɣɠ
(a 1)2		(a		1)(a 2)?
1)	3a 1			2) 3 a			3) 3a 1	4) a 1

6Ɇɠɬɭɨɣɱɛ ɬɩɠɟɣɨɺɠɭ ɭɩɲɥɣ Ȼ ɣ Ƚ, ɫɛɬɬɭɩɺɨɣɠ ɧɠɡɟɮ ɥɩɭɩɫɶɧɣ ɫɛɝɨɩ 26 ɧ. Ƚɶɬɩɭɛ ɥɛɡɟɩɤ ɬɭɮɪɠɨɣ ɫɛɝɨɛ 20 ɬɧ, ɛ ɟɦɣɨɛ — 48 ɬɧ. Ɉɛɤɟɣɭɠ ɝɶɬɩɭɮ Ƚ (ɝ ɧɠɭɫɛɰ), ɨɛ ɥɩɭɩɫɮɹ ɪɩɟɨɣɧɛɠɭɬɺ ɦɠɬɭɨɣɱɛ.

ɉɭɝɠɭ:

7ɉ ɲɣɬɦɛɰ a ɣ b ɣɢɝɠɬɭɨɩ, ɲɭɩ 1 a 0, 3 b 4. Ʌɛɥɣɠ ɣɢ ɬɦɠɟɮɹɴɣɰ ɨɠɫɛɝɠɨɬɭɝ ɠɝɠɫ ɶ? ɂɛɪɣɳɣɭɠ ɣɰ ɨɩɧɠɫɛ.

1) 0 a 1 2) a b 0 3) 1 1 b

ɉɭɝɠɭ:

8Ƚ ɳɠɬɭɣɮɞɩɦɷɨɣɥɠ ɩɟɣɨ ɮɞɩɦ ɪɫɺɧɩɤ. Ɉɛɤɟɣɭɠ ɝɠɦɣɲɣɨɮ ɩɬɭɛɦɷɨɶɰ ɠɞɩ ɮɞɦɩɝ, ɠɬɦɣ ɣɢɝɠɬɭɨɩ, ɲɭɩ ɝɬɠ ɩɨɣ ɫɛɝɨɶ ɧɠɡɟɮ. ɬɩɜɩɤ

ɉɭɝɠɭ:

© 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

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 3	5
9 ɋɠɳɣɭɠ ɮɫɛɝɨɠɨɣɠ x2 10	3x.
ɉɭɝɠɭ:

10 Ɉɛ ɥɛɥɩɧ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɠɨɩ ɧɨɩɡɠɬɭɝɩ ɫɠɳɠɨɣɤ ɬɣɬɭɠɧɶ ɨɠɫɛɝɠɨɬɭɝ
®­x2 4	0,
¯ 15 x3	0 ?
1)	2)
3)	4)

11 Ƚ ɥɩɫɩɜɥɠ 14 ɪɛɥɠɭɣɥɩɝ ɬ ɲɻɫɨɶɧ ɲɛɠɧ ɣ 6 ɪɛɥɠɭɣɥɩɝ ɬ ɢɠɦɻɨɶɧ ɲɛɠɧ. Ɋɛɝɠɦ ɨɛɮɞɛɟ ɝɶɨɣɧɛɠɭ. ɩɟɣɨ ɪɛɥɠɭɣɥ Ʌɛɥɩɝɛ ɝɠɫɩɺɭɨɩɬɭɷ, ɭɩɞɩ ɲɭɩ ɸɭɩ ɪɛɥɠɭɣɥ ɬ ɢɠɦɻɨɶɧ ɲɛɠɧ?

ɉɭɝɠɭ:

12 Ɉɛ ɥɫɮɞɩɝɩɤ ɟɣɛɞɫɛɧɧɠ ɪɩɥɛɢɛɨɩ, ɥɛɥ ɫɛɬɪɫɠɟɠɦɺɠɭɬɺɝ ( ɪɫɩɱɠɨɭɛɰ)

ɟɦɣɭɠɦɷɨɩɬɭɷ ɭɠɦɠɯɩɨɨɶɰ ɫɛɢɞɩɝɩɫɩɝ ɬɩɭɩɝɶɰ ɛɜɩɨɠɨɭɩɝ ɥɩɧɪɛɨɣɣ ɇɩɜɣɦ« ». Ʌɛɥɩɤ ɪɫɩɱɠɨɭ ɬɩɬɭɛɝɦɺɹɭ ɫɛɢɞɩɝɩɫɶ, ɟɦɣɭɠɦɷɨɩɬɭɷ ɥɩɭɩɫɶɰ ɨɠ ɧɠɨɠɠ 15 ɧɣɨɮɭ?

ɉɭɝɠɭ:

13 Ƚ	ɛɫɣɯɧɠɭɣɲɠɬɥɩɤ ɪɫɩɞɫɠɬɬɣɣ	a	n)	ɣɢɝɠɬɭɨɶ ɟɝɛ ɪɠɫɝɶɰ ɲɦɠɨɛ:
	(
a1	18, a2 25. Ʌɛɥɩɠ ɲɣɬɦɩ ɬɭɩɣɭ ɝ ɸɭɩɤ ɪɫɩɞɫɠɬɬɣɣ ɨɛ 51-ɧ ɧɠɬɭɠ?

ɉɭɝɠɭ:

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 3	6
14 Ƚ ɩɥɫɮɡɨɩɬɭɷ ɬ ɟɣɛɧɠɭɫɩɧ ȻD ɝɪɣɬɛɨ ɲɠɭɶɫɠɰɮɞɩɦɷɨɣɥ	ȻȽ D.
Ɉɛɤɟɣɭɠ ɝɠɦɣɲɣɨɮ ɮɞɦɛ ȻȽ , ɠɬɦɣ CAD 30 .

ɉɭɝɠɭ:

15Ɏɥɛɡɣɭɠ ɝ ɩɭɝɠɭɠ ɨɩɧɠɫɛ ɝɠɫɨɶɰ ɮɭɝɠɫɡɟɠɨɣɤ.

1)Ɍɫɠɟɨɺɺ ɦɣɨɣɺ ɭɫɠɮɞɩɦɷɨɣɥɛ ɫɛɢɜɣɝɛɠɭ ɠɞɩ ɨɛ ɟɝɛ ɭɫɠɮɞɩɦɷɨɣɥɛ.

2)ɀɬɦɣ ɝ ɪɛɫɛɦɦɠɦɩɞɫɛɧɧɠ ɟɣɛɞɩɨɛɦɣ ɫɛɝɨɶ, ɭɩ ɸɭɩɭ ɪɛɫɛɦɦɠɦɩ- ɞɫɛɧɧ – ɪɫɺɧɩɮɞɩɦɷɨɣɥ.

3)Ⱦɣɪɩɭɠɨɮɢɛ ɪɫɺɧɩɮɞɩɦɷɨɩɞɩ ɭɫɠɮɞɩɦɷɨɣɥɛ ɜɩɦɷɳɠ ɦɹɜɩɞɩ ɠɞɩ ɥɛɭɠɭɛ.

4)ɉɭɨɩɳɠɨɣɠ ɪɦɩɴɛɟɠɤ ɪɩɟɩɜɨɶɰ ɭɫɠɮɞɩɦɷɨɣɥɩɝ ɫɛɝɨɩ ɥɩɸɯɯɣɱɣɠɨɭɮ ɪɩɟɩɜɣɺ.

ɉɭɝɠɭ:

© 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

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 3

7

16Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ y x2 4. Ʌɛɥɣɠ ɣɢ ɟɛɨɨɶɰ

ɪɫɺɧɶɰ ɨɠ ɣɧɠɹɭ ɬ ɞɫɛɯɣɥɩɧ ɸɭɩɤ ɯɮɨɥɱɣɣ ɨɣ ɩɟɨɩɤ ɩɜɴɠɤ? ɭɩɲɥɣ ɂɛɪɣɳɣɭɠ ɣɰ ɨɩɧɠɫɛ.

1)x = 3

2)y = – 4

3)y = – 10

4)y = – x

5)y = x – 5

ɉɭɝɠɭ:

ɉɭɝɠɭɶɥ ɢɛɟɛɨɣɺɧ		17	18 ɢɛɪɣɳɣɭɠɝ ɜɦɛɨɥ ʌ 2.
17	Ƀɢ ɯɩɫɧɮɦɶ l l	tl	ɝɶɫɛɢɣɭɠ t.
	0	0
			­ 3	x2	0,
18	ɋɠɳɣɭɠ ɬɣɬɭɠɧɮ ɨɠɫɛɝɠɨɬɭɝ ®
			¯ x	4	3.

ɒɛɬɭɷ 2

Ɋɫɣ ɝɶɪɩɦɨɠɨɣɣ ɢɛɟɛɨɣɤ 19-23 ɣɬɪɩɦɷɢɮɤɭɠ ɩɭɟɠɦɷɨɶɤ ɦɣɬɭ (ɜɦɛɨɥ). Ɍɨɛɲɛɦɛ ɮɥɛɡɣɭɠ, ɨɩɧɠɫ ɢɛɟɛɨɣɺ ɛ ɢɛɭɠɧ ɢɛɪɣɳɣɭɠ ɠɞɩ ɫɠɳɠɨɣɠ.

19 Ɍɩɥɫɛɭɣɭɠ ɟɫɩɜɷ: a 16b2 4a2 2b.

a2b

20Ɋɫɩɭɣɝɩɪɩɦɩɡɨɶɠ ɬɭɩɫɩɨɶ ɲɠɭɶɫɻɰɮɞɩɦɷɨɣɥɛ ɪɩɪɛɫɨɩ. ɫɛɝɨɶ ȿɩɥɛɡɣɭɠ, ɲɭɩ ɩɨ ɪɛɫɛɦɦɠɦɩɞɫɛɧɧ.

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 3

8

21ɇɠɡɟɮ ɲɣɬɦɛɧɣ 2 ɣ 18 ɝɬɭɛɝɷɭɠ ɭɫɣ ɲɣɬɦɛ, ɭɛɥ ɲɭɩɜɶ ɝɧɠɬɭɠ ɬ ɟɛɨɨɶɧɣ ɩɨɣ ɩɜɫɛɢɩɝɛɦɣ ɞɠɩɧɠɭɫɣɲɠɬɥɮɹ ɪɫɩɞɫɠɬɬɣɹ.

22Ɋɩɬɭɫɩɤɭɠ ɞɫɛɯɣɥ ɯɮɨɥɱɣɣ y x2 x5 6 ɣ ɩɪɫɠɟɠɦɣɭɠ, ɪɫɣ ɥɛɥɣɰ ɢɨɛɲɠɨɣɺɰ c ɪɫɺɧɛɺ y c ɣɧɠɠɭ ɬ ɞɫɛɯɣɥɩɧ ɫɩɝɨɩ ɭɫɣ ɩɜɴɣɠ. ɭɩɲɥɣ

23Ɉɛ ɥɛɡɟɩɤ ɣɢ ɟɝɮɰ ɩɥɫɮɡɨɩɬɭɠɤ ɬ ɫɛɟɣɮɬɛɧɣ 3 ɣ 4 ɦɠɡɛɭ ɪɩ ɭɫɣ ɝɠɫɳɣɨɶ. ɫɩɧɜɛ Ɉɛɤɟɣɭɠ ɠɞɩ ɬɭɩɫɩɨɮ.

© 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

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 4	3
	ɒɛɬɭɷ 1

1 Ɏɬɭɛɨɩɝɣɭɠ ɬɩɩɭɝɠɭɬɭɝɣɠ ɧɠɡɟɮ ɝɶɫɛɡɠɨɣɠɧ ɣ ɢɨɛɲɠɨɣɠɧ ɝɶɫɛɡɠɨɣɺ.

ȽɖɋȻɁɀɈɃɚ												ɂɈȻɒɀɈɃɚȽɖɋȻɁɀɈɃɄ
Ȼ)	1							1				1)	1,25
	1
	3							12				2)	1,75
ȼ) 21								6				3)	4,5
								28
												4)	6
Ƚ)	4							2
					:

515

Ȼȼ Ƚ ɉɭɝɠɭ:

2Ʌɮɬɩɥ ɦɷɟɛ ɨɛɞɫɠɦɣ, ɫɛɬɪɦɛɝɣɦɣ ɣ ɪɩɦɮɲɠɨɨɮɹ ɝɩɟɮ ɨɛɞɫɠɦɣ. Ɉɛ ɫɣɬɮɨɥɠ ɣɢɩɜɫɛɡɻɨ ɞɫɛɯɣɥ ɣɢɧɠɨɠɨɣɺ ɭɠɧɪɠɫɛɭɮɫɶ ɦɷɟɛ ɣ ɝɩɟɶ. Ɍɥɩɦɷɥɩ ɧɣɨɮɭ ɝɩɟɛ ɨɛɞɫɠɝɛɦɛɬɷ ɩɭ 0 °Ɍ ɟɩ 5 °Ɍ?

ɉɭɝɠɭ:

3 Ɋɦɩɴɛɟɷ ɢɛɪɩɝɠɟɨɣɥɛ ɜɶɦɛ ɮɝɠɦɣɲɠɨɛ ɬ 350 ɦ2 ɟɩ 420 ɦ2. Ɉɛ ɬɥɩɦɷɥɩ ɪɫɩɱɠɨɭɩɝ ɮɝɠɦɣɲɣɦɛɬɷ ɪɦɩɴɛɟɷ ɢɛɪɩɝɠɟɨɣɥɛ?

ɉɭɝɠɭ:

ɇɛɭɠɧɛɭɣɥɛ. 9 ɥɦɛɬɬ. Ƚɛɫɣɛɨɭ 4

4

4Ɏɥɛɡɣɭɠ ɝɶɫɛɡɠɨɣɠ, ɫɛɝɨɩɠ 32k 1.

1) 32k 3		2) (32k)	1	3)	9k		4)	32k
					3			3 1
5 Ʌɛɥɩɧɮ	ɣɢ	ɟɛɨɨɶɰ ɝɶɫɛɡɠɨɣɤ		ɭɩɡɟɠɬɭɝɠɨɨɩ			ɫɛɝɨɩ	ɝɶɫɛɡɠɨɣɠ
(a 1)2	(a	2)(a 1)?
1) 3a 1		2) a 3		3) 3a 1			4) a 3

6Ɇɠɬɭɨɣɱɛ ɬɩɠɟɣɨɺɠɭ ɭɩɲɥɣ Ȼ ɣ Ƚ, ɫɛɬɬɭɩɺɨɣɠ ɧɠɡɟɮ ɥɩɭɩɫɶɧɣ ɫɛɝɨɩ 25 ɧ. Ƚɶɬɩɭɛ ɥɛɡɟɩɤ ɬɭɮɪɠɨɣ ɫɛɝɨɛ 14 ɬɧ, ɛ ɟɦɣɨɛ — 48 ɬɧ. Ɉɛɤɟɣɭɠ ɝɶɬɩɭɮ Ƚ (ɝ ɧɠɭɫɛɰ), ɨɛ ɥɩɭɩɫɮɹ ɪɩɟɨɣɧɛɠɭɬɺ ɦɠɬɭɨɣɱɛ.

ɉɭɝɠɭ:
7 ɉ ɲɣɬɦɛɰ a ɣ b ɣɢɝɠɬɭɨɩ, ɲɭɩ 0 a 1, 3 b				2. Ʌɛɥɣɠ ɣɢ ɬɦɠɟɮɹɴɣɰ
ɨɠɫɛɝɠɨɬɭɝ			ɠɝɠɫ ɶ? ɂɛɪɣɳɣɭɠ ɣɰ ɨɩɧɠɫɛ.
1)	1	0	2) a b 0	3) 2 b 3
	a

ɉɭɝɠɭ:

8Ƚ ɪɺɭɣɮɞɩɦɷɨɣɥɠ ɩɟɣɨ ɮɞɩɦ ɪɫɺɧɩɤ. Ɉɛɤɟɣɭɠ ɝɠɦɣɲɣɨɮ ɩɬɭɛɦɷɨɶɰ ɠɞɩ ɮɞɦɩɝ, ɠɬɦɣ ɣɢɝɠɬɭɨɩ, ɲɭɩ ɝɬɠ ɩɨɣ ɫɛɝɨɶ ɧɠɡɟɮ ɬɩɜɩɤ.

ɉɭɝɠɭ:

© 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