8/14/2019 Japan Sholarship Mathematic Examination
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A 1
AUndergraduate Students
I. 1. 4 6 2 5 3 x x x
x
2. 2x 3 2 2 f x x ax bx f x 1x 3
a b
3. 2 1 y x ax a a
4. 3log 52 3log 3 log 4 3
5. tan 2A sin cossin cos
A A
A A
II. 2 2: 1 1 0C x y kx k y k k1. 2. C
III. 7 7, 0 , 0, 7 , , 02 6
A B C
2 y x ax b BA
BC
1. a b 2. BA
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A 2
I.
1. 2 4 6 2 64 6 2 5 3 1 32 5 3 3 3
x x x x x x x
x x x
2.
2x
f x
2x
0f x
8 4 2 2 0 2 5 1a b a b
3 2
22 11 11 1 1
f x x ax bx a b x a x b a
x x x
1
f x
x 3 1 3 4 2a b a b
1 2 2 5 3
41
a b a
a bb
3. 2 1 y x ax 0y 2 1 0 x ax 0 2 4 0 2a a 2a
4. 3log 52 3 2log 3 log 4 3 log 4 5 2 5 7 5.
cos tan 1sin cos 2 12 1 2 2 3 2 2
sin cos cos tan 1 2 1
A AA A
A A A A
II.1.
2 2: 1 1 0C x y kx k y k k 2 2 1 1 0 x y y x y k k
2 22 2 1 11 0
1 21 0
x y y x y y
x yx y
2
0
1 2 1 2 0 1
2
y
x y xy y xy yx
0y 1x
12
x 12
y
C 1,0 1 1,2 2
2. C
2 2 2 2
2 2 1 1: 1 1 0
2 2 2 2
k k k k C x kx y k y k
8/14/2019 Japan Sholarship Mathematic Examination
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A 3
2 2 2 2 2
1 4 4 1 2 2 6 5:
2 2 4 4
k k k k k k k k C x y
2
2 22 6 5 1 2 6 54 2
k k R R k k
22 6 5 f k k k 4 6 f x k
4 0f x
3
02
f x k
2
min
3 3 9 12 6 5 9 5
2 2 2 2f
min min
1 1 1 2
2 2 2 4R f
III.1. a b
BA BC BA y ax b
7 27
2
ya
x
2 y x b 0,7B 7b
: 2 7 BA y x 22 7 x x ax b
2 2 7 0 x a x b 0 22 4 7 0 1a b BC y a x b
7 67
6
ya
x
6 y x b 0,7B 7b : 6 7 BC y x 26 7 x x ax b
2 6 7 0 x a x b 0 26 4 7 0 2a b
1 2
2
2
2 4 7 0
6 4 7 0
a b
a b
2 6 2a a a 16 28 4 0 3b b
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A 4
2, 3a b 2.
2 2 3 y x x : 2 7 BA y x
2
2
02 7 2 3S x x x dx
22 3 2
0
2 7 2 32 3 2
x x xx x
84 14 4 6
3
83
S
-1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
x
y