平成20年 日本留学考试数学真题
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⃝ 1
y = −x2 −
A
x+5
(ii) x
0
⃝ 1
y = x2 −
B
+5
⃝ 1
y=c
N
c< c= CD <c< c= G
CD CD G G <c
N= N= N= N= N=
E F H I N
6
I 1 A 6 B 9 CD 16 EFGH 2122 IJKLM 21212 II 1 ABC 210 DE 21 FGH 370 IJ 37 III AB 60 CDE 120 FG 62 HI 30 IV A 2 B 6 CD −4 E 1 F 2 G 6 H 3 I 2 J 1 JKL 150 MNO 438 PQR 253 KL 27 M 2 NOP −29 2 Q 7 R 9 NOPQ 3223 RST 264 2 UV 17 WXYZ −5−2
2009.05.17 7
M
axy
a=
NO P
x3 − (ay )3 =
R
4
III
O ABCDE 4
A
E
D
√ √ AB=BC= 6 2, CD= 2 6, DE=4 ABC √ 18 3 ABCDE AE
B O C
(1) ∠ABC = (2) AC= (3) AE= x F
AB √
Leabharlann Baidu
◦
, ∠ADC = CDE G x
◦
∠CAD =
YZ )
2
II
1 7 −3 3 1
(1)
1 2
3 DE 3
ABC
(2) a, b, c
1
a<b<c H GH (3) I J 2 K L 2
3
2
a, x, y x + ay = 1, x2 + (ay )2 = 5, xy = 9
(1) (x + ay )2 = x2 + (ay )2 + (2) x3 + (ay )3 = (3) x > 0 Q
y=
I
x2 −
JK
x+
LM
1
2 P = 6ab + 9a − 4b − 6 (1) P P =( N a− O )( P + Q )
√ √ 6 (2) a = , P = 3− 2 3 (3) P = 17 a, b (a, b) = ( 2
√
√ b=
R
− T
S
U
,
V
), (a, b) = ( WX ,
HI
◦
, ∠AED =
JKL
◦
√ x +
2
M
N
x−
O
=0
(√ AE = P Q
√ − R
)
5
IV
y = x (x − 2) + 5 x y = 4x + c y = x (x − 2) + 5 = 4x + c
1 ······⃝
N
y = x (x − 2) + 5 − 4x
y=c
x
⃝ 1 (i) x < 0
1 I
1 2 (i) x =1 (ii) −2 2 y = ax2 + bx + c (i) b=− 2 (ii) { − B a + c = −20 CD a + c = 30 A a x x=5 6 30 −20 2 :
{ −
B a + c = 30 CD a + c = −20
2 y= F x2 − FG x − H