gifted math answer 2

7/25/2019 Gifted Math Answer 2

1/10

2550

210 .. 2550 09.30 . 12.00 .

2

()1.

9 7 70 2. 2 30 2

15 3.

4. 5.

()6.

7.

8.

9.

:

2 6

3 6

4 4

5 10

6 10

7 11

8 10

9 12

70

2

26.5085 / 70

18.9346 / 50 (70 )

57/703/70


2/10

Gifted Mathematics 2550................................................................. .......................... 2

A =

2r

360 r

n=

21 360na sin2 n

n

=

1.

250 384 2.8 0.9 (6 )1.

16 2.

28

0.8

3. =

1 16 2.8 = 2.8 16 = 44.8

1 16

0.9 = 0.9 16 = 14.4 44.8 + 14.4 = 59.2

384 59.2 = 328.4 28 1

328.4 328.428= 11.6 = 11.6 0.8 = 14.5

= 14.5 100 5.8%250

=

5.85.8

a

a

1. 2.


3/10


2. (P) (V)(T)(n)

1.

2.

3.

(Ideal Gas Law)

2.1 ()R (3 )

1. V 1P

()

2. V T ()3. V n ()

V 1P

nT V = R 1P

nT

PV = RnT PV = nRT

2.2 R 22.4 (Lit) 1(atm) 273 (K)1 (mol)(3 ) (3 )

2.1 (1 atm)(22.4 lit) = (1 mol)R(273 K)

R =( )( )

( )( )

1 atm 22.4 lit

1 mol 273 K

R =22.4 atm lit

273 mol K

R = 0.082atm lit

mol K

R 0.082 atm litmol K


4/10


2.3 2 27 380 (4 )

1. Tc Tk

Tk= Tc+ 2732. 1 760 (mmHg)3. R2.2

2.1 Tk= 27 + 273 = 300

mmHg 380760

= 0.5

(0.5)(V) = (2)(0.082)(300)

V =(2)(0.082)(300)

0.5

V = 98.4 98.4

1.

2.

3.

2.2 2.3 (2.1)

2.32.2 (


5/10


3. a, b, c d

( ) ( ) + + + =22 23 1 3 3 1 2 0x x x x

(10)

x2 3x + 1 = A A2 3A + 2 = 0

(A 2)(A 1) = 0

A = 1, 2

x2 3x + 1 = 1 x2 3x + 1 = 2x2 3x = 0 x2 3x 1 = 0

x(x 3) = 0 x = 3 9 42

+

x = 0, 3 x = 3 132

a = 0, b = 3, c = 3 132

+d = 3 13

2

(a + b + c + d)2

(a + b + c + d)2 = (0 + 3 + 3 132+ + 3 13

2 )2

= (6)2 = 36

1.

2.

() x2 3x + 1

()

ax2+ bx + c = 0 b

a

6 36


6/10


4. (Pacman Game) A

49

6 4.1 (

)(5 )

() A = r2

A = ( )222 67

A = ( )22

367

= 113.14

a =2r

360

a = 22 36 497 360

i

a = 22 0.7 = 15.4 49 113.415.4 = 97.74

4.2

7 60 (5 )

V = 34 r3

V = 34 22

(7)3 7

=4 22

3433 7

= 1,437.33 ..

60

360 1,437.33 .. 60 = 1,437.33 60

360

=1,437.33

6

= 239.55 .. 1,437.33 - 239.55= 1197.78 ..

A

B

C

1.

2. 3. ()

4.1 4.2 (1)


7/10


5. (Quadratic Equation) ax2+ bx + c = 0a, b c a 0 x

xax2+ bx + c = 0 (11)

x2+ bx + c = 0

a; 2bx c

xa a

+ + = 0

2 22 b b b cx 2 x

2a 2a 2a a

+ + + = 0

2 2

2

b b cx

2a 4a a

+ + = 0

2 2

2

b b 4acx

2a 4a

+ = 0

22 2b b 4ac

x2a 2a

+ = 0 ****

2 2b b 4ac b b 4acx x

2a 2a 2a 2a

+ + + = 0

x =2 2b b 4ac b b 4ac

, ,2a 2a 2a 2a

+

x =2b b 4ac

2a

,2b b 4ac

2a

**** 2

2

b 4ac

4a

2

bx

2a

+ =

2

2

b 4ac

4a

bx

2a+ =

2b 4ac

2a

x =2b b 4ac

2a 2a

x =2b b 4ac

2a

1. 2.

(

x =2b b 4ac

2a

0.5 (7

)


8/10


6. 1. 1 1 2.

2 1 3. 1

2 6.1

() (4 )

.............32................. (1 )6.2 (

) (2 )n(S) = 32n(E) = 6

P(E) = n(E)n(S)

=6

32=

3

16 = 0.1785

6.3

0.2 (3)

1 24= n(E)32= n(S)

P(E) = n(E)n(S)

=24

32=

6 3

8 4= = 0.75

= 0.25

...n(E)

1. 2.


9/10


7. 1,925

7.1 7 (3 )

V = r2h

1,925 =2

22 7h

7 2

7,700 = 22 7 h

h =7,700

22 7

h = 50

7.2 14 1

0.5 3 (4 )

= ()= (0.5)(180)

= 90 90

= 90 14 = 1,260

= 1,925 1,260 = 665

7.3 7.2 35

()(an ) (5 )

n= 21 360na sin2 n

n

= 665 = ( )23a sin 60 35

19 =

2 3

3a 2

a2 =19 2

3 3

; a2 =

38

3 3 =

38 3

9

a

a

1.

()2.

2


10/10


()

1.

(

Process

Product) 1 2 ()

2.

3. .3 2 30

.3()

4.

25. 2

2

6.

1

7.

8.

()

9. ()

10.

( )

gifted math answer 2

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