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
