ページ1:

No.
Date
105
1. log 2 = a; log. 7 = 6R lug 35 =
10x7
log 35 = log ( 1032 ) = log 10+ log 7 - log 2
+
b
a #
*
{
log A+ log Blog A.B
I log A - log B = lug ☆
⇒
僅限log底权相同
A
B
此條件才成立
2.若某細菌每30 min分裂一次(即由1→2,2-→4...),
1亇細菌經过6hr.後則會分裂成.
亇
6 hr.
12 x 30 min
* 2
→8
P
==64x
xx64
素
8 =
× 2
x 2
4096 #
3.10人平均月薪為57000,其中7人平均月薪為27000,其餘3人平均月薪=
57000×10-27000x7
381000
3
570000-189000
3.
127000 #
4. 有樂團計劃到甲、乙兩國巡迴 甲国有3个城市,乙国有4个城市
種選擇
若先到甲国完成演出後再到乙国,路線有.
31x4! 6×24
甲国路線 乙国路線
=
=144 #
Per-Duct

ページ2:

5.△ABC三頂奌A(1,2)、B(-3,-3)、C(3,-1)
求B的中線長=
A 1-1,2)
D
21-31-3)
C(3-1)
2+(-3)
2
CD=J[3-(-2)]+[1-10]²
D
25+4
~101.
社
6. 20 csc>0, tan 0 <0,
求日為第
象限角
I. T
日:ㅍ#
tan 日 < 0 => Ⅱ、IV
729
27
7. A =
1000
343
103
No.
Date
3)+(5季),則A=
=
2°
[(告]-[(六)]+[(3]*
81
+
100
8
100.
64 128
256
8.8n=1++22+3++ + (n + 21+), #² 510 =
8n=1+++2+2
810=11+2+3+
(+1)
55+
+
4
+111
+3.
7111
+10)+++++++
256+128+64+32+16+8+4+2+
1023
512
512
= 56
511
512 #
32 33 34 35 36 37 38
Per-Duc

ページ3:

No.
Date
9. f(x)=x² + ax + 1x2x+3除之餘式為本,則f(x+1)除以x-1餘式=.
fi}) \ » (?) - 20+1 = 4
>> - a + 1 = #
=>
9-69 +4 = |
=>
13-6a = 1
=>
a = 2
f(x)=x+2x+
f(1+1) = f(2)
X-1
10.已知x+1
X-
2²+2×2+1 = 4+4 +1
=
9 #
6
12
1-x
求ㄨㄚ
6.
12
T+X
X-1
(x-1)(x-1)+6(x+1)=12
X-2x+1+6x+6=12
x+4x-5=0
-5-1
7-(x-1)
A
=> (x+5)(x-1)=0
Đ 2 : -5, X
題目分母有X-1
-6
-5 +1
#
1代入不合
11. 長方形長增加3cm,寬增加4cm後可得一正方形
且正方形面積為原長方形之2倍,求原長方形面積=
x+4
X
a
不
Per-Duct
y+3
29
{4 = 8
x=9
(x+4)(y+3)= 2xY
X+4=1+3
{3X+44 +4 +12=2XY
x=Y+1
3X+4y-xy+12=0(x代換成y+1)
=> 34 +3 +44-7 (4+1) +12=0
=> - y² +64 +16=0 - (y² -64-16) = 0.
=) - (y-8) (y+2) = 0
x7+9+8
= 72 #
> Y:8,→長度必為正
21
28 29

ページ4:

IZ.
X
+
y
= 2
,
(x,y) =
9
=
4--1
2y+3x
2xy
41+6x=
4xy
47-9x=-xy
-7144-9x=-x4
15x = 5xy
y=3
13. ax² + bx + c > 0 34% -1 < x < 3
x = 2
a+c=
#
No.
Date
(x+1)(x-3) <0
X-2x-3 <0
=> -x² + 2x + 3 >0 =>
a = 4
b=2, C=3
a + C =
1+3 = 2 #
14. A (0,1) B (-3,5), C (a,b) You h±3 [AC] = 10
且能和反向,求(a,b)=
(B) (-3,5)
(C) (6-7) (D) (-6.9)
(A) (9.0)
B(-3.5)
A (0,1)
26 27 28
C (a,b)
(B)、(D)先刪掉>位置不合
(A)、(C)代入IC奌坐標計算|
{(A) ACI = √(9-0)²+ (0-1)=
M
81+1
82 1x
| (c): | AC | = √16-0)² + (-7-1)* =√36+64 = √100 = 10
4
Per-Du

ページ5:

TTING
AT
BOCM
A3
No.
Date
15. AB4
LACL = 3
AB DAC
則1AB+
2 AC
=
AB-2 AL
(AB+ 2 ABY ZAC x cos 60° - 12/π(1)²
=
16+ 8 x 4 x 6 x
+
36
76
LAB + 2AC = √76 #
16.过奌(1,3)且和X軸.y軸在第二象限圍出一个等腰直角△,
下列何者為L的方程式
(A)
x-1=-2
(=
1-3 =-2
ㄓ
(B) x + y = -2
=>
1+3=4
# -2
(C) 2x-2y= |
=)
2-6=-4
丈
(D) x + y = 2 =) -/+ 3 = 4 % 2
17. f(x) = (x²+3x-1)² (x³-5ײ), * f'(1) =
fix) (x²+3x-1) (x²+3x-1) (x²-5x')
f(x) = (x²+3x-1) (x²+3x-1) (x²-5׳) + (x²+3x-1) (x²+3x-1) (x²-5x)+(x+3x-1) (X+3x-1)(x-5)
= (2x+3) (x²+3x-1) (x²-5׳) + (x²+3x-1) (2x+3)(x²-5x³) + (x²+3x-1)(x+3x-1) (3x-16x)
f(1) = 5×3× (-4) + 3 × 5 × 1-4) + 3×3× (-7)
-60
-183
-60
-63
Per-Duct

ページ6:

18. 求sin(9600)
sin (-960²)
sin (1980-960)"
sin 130°
sin 60"
2
sin 60°
19.<x<兀
兀
<
< 27
求sin(x+B)=
5
4
5
No.
Date
sind = CuSB = 1/3
5
180°
270°-3-360"
I
=> B = IV
sìn (d+3) = sindcus3+cosd sins
20.
{1,3,5,7,9}選出3个相異权字形成3位权,
有可能形成
亇3位权
=>
5×4×3
60
4
12
+(+)x(3)
48
65
15
65
63
65
#
101
21.箱子中有4紅6白,連續抽出3球,抽出結果為/紅的机率=
全:C1=
1009x84
120
24×15
= 60
60
1
120
0.5 #
3 24 25 26
Per-Duct
28 29 30 31 32 33 34 35 36 37 38 39

ページ7:

7
CUTTING
MAT
45X30CM
A3
No.
Date
22.
一組权值 54,56,62,63,65 共55
請勿該組权值的母群体变異权=
平均权:54+56+65-63-65
300
E
=60
=
5
(√(60-54) + (60-56)+(60-62)² + (60-63) " + (60-65) = 1)
+(36+16+4+9+25)
X
90
= 18 #
*母群体变異权
=(母体標準差)3
23.拋物線y=ax²+4bx+4a和x軸有2交奌,且頂奌在第一象限
下列敘述何者正確
(A) a <0,
a² <b
(B) a <o, a² > b²
(C)
a>o, a² <b²
(D) 9>0, 9² > 6²
頂桌在工
a co
⇒
x
√1463-4x9x4a >0.
6166²-160²20
b²-a> o
24. 曲線y=-x²+1 在x=-1和X=2之間與x軸所圍的面積
y=-(x²-1)
x
1-21-10
y301
y
(0,1)
2
(-1,0)
(1,0)
0-3
S₁ 1-x²-1) dx - [Si (-x²-1) dx|1-21-3)
=[-x²x]+[x-x]?1
:
++
$
x=-1
X = 2
Per-Duct
(2-3)
16

ページ8:

No.
Date
25. 橢圓x²+4y²-4x-lby+a=0不與x軸相交,與y軸相切,求入=
(0,2)
ny
(2,2)
2
=
42
x² - 4 x + 1 = )² + 4 [ y² = 4y+ ({})² ]
4+16-9
(x-2)²+4(7-2)²
(x-2)²
2009
20-9=2
20-9=4
4 cy-2)²
20-9
2
==
20-9
9=16
#