Λύσεις Παγκύπριων...

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Λύσεις παγκύπριων εξετάσεων μέχρι το 2014.

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  • 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