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Λύσεις παγκύπριων εξετάσεων μέχρι το 2014.

### Transcript of Λύσεις Παγκύπριων...

• 2006

: : , 30 2006 7:30 .

1. 3cm, 5cm 2cm. V= =3 5 = 30 cm2 3

2 12000 5% 2 .

K E XT100 =

12000 5 2T T

100 = = 1200

3

3, 5, 6, 7, 9 .

535! 120

60(5 3)! 2

= = =

4 . ( ).

: 9! 302402! 3!

=

• 5 20

.

. 0 1 2 3 . 5 8 4 3

. :

: . : .

5 1P(A)20 4

= =

4+3 7P(B)=20 20

=

6 8, y, 13, 13, 20, 26, 27, 31, 31, 31. x 21, : () y , () x x.

() 8 y+13+13+20+26+27+31+31+312110

+=

200 y21 200 y=210 y=1010+ = +

() x = 31 5 6 :

20 26 46x 22 2+= = = 3

• 7 7:00

60km/h. , , , 13:00 . :

() () . () 6 A A A AS U t S 60 6 360km= = = 360 km () 4

.

B B B B B360S U t 360 U 4 U 90km /

4= = = = h

• 8 900

. ,

() () . : 360 ( 150 + 122 + 40) = 360 312 = 48

3 :

+ 3 = 48 4 = 48 = 12 3 = 36

. . = 122900 305360 =

. = 36900 90360 =

122150

40

• 9 ,

()=2 (), 1P(B)2

= 1P(A B)5

= , () P( . A B)

() = 2 () 1 () = 2 () 3() = 1 () = 13

( ) = 1 () = 1 - 1 23 3=

P(A B) P(A) P(B) P(A B) = +

1 1 1 10 15 6 19P(A B)3 2 5 30 30

+ = + = =

10 8cm h = 5 cm.

: () , () () . () ()2 = ()2 + ()2 5 2 = 42 + 2 25 = 16 + 2 2 = 9 = 3cm

() .. = 2 h 32 5 80cm

2 2 = =

() V= 3E 64 3 64cm

3 3 = =

K

M

h

• 1 2 , 3 .

, : : . : .

22 1 1P(A) 6!6 15

4!2!2

= = =

2 3 3 1 2 11 1 1 1 1 1 2 3 3 1 2 1 11P(B)

6 15 152

+ + + + = = =

2 300

. 5000 5% 5000 10%. 16% . 12000, . 5000 :

55000100 = 250

7000 :

107000100 = 700

: 300 + 250 + 700 = 1250

: 161250100 = 200

: 1250 - 200 = 1050

• 3 . ()

.

() .

() .

() .

()

() 50

() i ii

x f 100x 2f 50

= = =

()=( )2i i

i

f x x 72 36 6 1,2f 50 25 5 = = = =

. . xi fi fi ( x - xi )2 Xi fi 0 8 0 8 4 =32 1 6 6 6 1 =6 2 20 40 20 0 = 0 3 10 30 10 1 =10 4 6 24 6 4 =24 50 100 72

2468101214161820

10 2 3 4.

• 4 4

7 5 . : () .

() 3 1 . () 1 .

() 12 12! 4954 8!4!

= =

() 7 5

35 5 1753 1 = =

() 7 5 7

35 5 35 2103 1 4 + = + =

• 5 =4cm, =5cm, =8cm, =10cm, , xy. xy.

=90

.

()2 = ()2 ()2 ()2 = 102 82 ()2 = 100 64 = 6 cm = 4cm ()2 = ()2 ()2 ()2 = 25 16 = 3cm AB = 6 3 = 3 cm E = . + . + . . + . = R = 6 10 = 60 cm 2 E. = 2R = 2 6 8 = 96 cm 2 ... = cm(R+r)=(6+3) 5=45 2 E = R2 = 32 = 9 cm2 E = 60 + 96 + 45 +9 = 210 cm2 V = V.+V V

V.= 2 2(R R r r ) (36+3 6+9) 4 84

3 3+ + = = cm3

V = 2 2 3R = 6 8 288 cm =

V =2 2

3R 6 8 96 cm3 3

= = V = 84 + 288 96 =276 cm3

x

y

• 1

: : , 31 2007 7:30 .. 10:30 ..

1.

2

2

2

cm96466

==

=

2. : 60100

20300 = : 24060300 = .

3.

720!66 ==

4.

30240!2!3

!99 ==

5.

84070007840 ==

100

=

10037000840 =

%4210840

==

6.

11207016 == 10206815 == 10010201120 ==

• 2

7.

( ) ( )125

12711 ===

( ) ( ) ( ) ( ) += ( )

61

125

43 +=

( )21

126

123

125

129

==+=

8. )

cm123.100400

3E

V ===

) 169512)2(h 22222 =+=+=

cm13169h ==

) 22 cm36021340100

2h

E =+=+=+=

9.

: 2040036018 =oo

: 10040036090 =oo

. +100 . +100++100+20=400 2=180 =90 : 190 :90

5cm

h

=10cm

• 3

10. . V24V =

3224h416 =

m3h =

1.

20,20,18,18,18,17,17,16,16,10 )

51721817

18

,=+=

=

) 1710

10162172183202 =++++=

( ) 68,25

561072

ff

i

2ii ===

x fi fixi (xi- )2 fi (xi- )2 20 2 40 9 18 18 3 54 1 3 17 2 34 0 0 16 2 32 1 2 10 1 10 49 49 fi=10 fi (xi- )2=72

2.

) (i) 6188!12!5

!175

17 ==

(ii) 37121103557

110

47 =+=

+

) ( ) 157545352

1037

BN ==

=

( ) ( )( ) 884225

61881575

BP ===

• 4

3. ) ={ }),(),,(),,(),,( 54453663 ={ }),(),,(),,(),,(),,(),,(),,(),,(),,( 666556644655544544

) ( )( ) 91

364

)(P ===

( )( ) 41

369

)(P ===

) ( )( ) 181

362

)B(P ===

4.

: 50002000010025 =

: 25000500020000 =+

: 50002500010020 =

30000500025000 =+

.. : 45003000010015 =

: 30000+4500 = 34500

: 69050

34500 = .

• 5

5.

cm3cm6 R

==

cm5cm3cm2cm6 R .

====

( ) cm41635 222 ===

( )( )

2

22

22.....

cm108436403626526362

RRR2

=++==+++==+++=

=++==++=

( )( )

3

222

222

...

cm5652108

22663336

RR3

R

VVV

===++=

=++===

• 1

2008

: : , 7 2008 7:30 10:30

1. 2 2

3 R 5 9V = = = 75 cm3 3

2. 2524 6

100 =

3. K E X 6000 5 3

= = = 900100 100

+ = 6000 + 900 = 6900

4. () = { },,, () ()=() 2 1

() 4 2= =

5. 12, 14, 14,15, 16, 18, 18, 18 () = 18 () = 5,152

1615=

+

6.

()= 1 () = 1 - 41

43=

() = () + () () () =

43

61

41

32

=+

• 2

7.

5 6 6 :

5 6 6 180 =

8. ()

50 10000 72000

360 = =

m3

: o

o

60 72000 12000360

= m3

: o

o

90 72000 18000360

= m3

: o

o

120 72000 24000360

= m3

: o o o o o 360 (60 90 120 50 ) 40 + + + =

o

o

40 72000 8000360

= m3

)

0

4000

8000

12000

16000

20000

24000

28000

/

(m

3 )

• 3

9. () = 2 = 100 = 10cm

() = 2h

260 = 40 h h 13 cm

2

=

() h2 = 2 + 2( )2

2 = 132 52= 144

= 12cm

V= 400312100

3=

=

cm3

2

h

10. 3

. /12 V V 8 6 2 96cm = = =

V = 8 cm3

3 = 8

= 2 cm

1. () 115 x 15640100

= x = 13600

... = 15640 13600 = 2040

() : 36 13600136

=3600

() : 13600 3600 = 10000

() 80 x 15640100

= x = 19550

• 4

2. ) 15 3003

5

=

) 13 2 14304 1

=

) 13 2863

=

3. ) ix if i ix f ( )2ix x ( )

2i if x x

3 10 30 9 90 4 0 0 4 0 5 50 250 1 50 6 80 480 0 0 7 40 280 1 40 8 20 160 4 80 if 200=

i ix f 1200= ( )2i if x x 260 =

) i ii

x f 1200x 6

f 200= = =

( )2i ii

f x x 260 1,3 1,14

f 200

= = = =

) 80 2P(A)200 5

= =

60 3P(B)200 10

= =

4. K

8

8! 40320M 201602! 2

= = =

) i. 7 7! 5040= =

ii. 66! 720

3602! 2

= = =

iii. 5 44!M 5! 14402!

= =

) 5040 1P()20160 4

= =

• 5

5. .

1

1