\magnification\magstep1
\input B4.tex
\font\sc=cmcsc10 at 12truept
\parindent 0pt
\baselineskip=15pt

\newcount\prno \prno=1
\everypar{\hangindent 17truept \hangafter=0}
\def\pr{\medskip\noindent\kern-18truept\hbox to 18truept{\bf\the\prno\hfill
    }\advance\prno by 1}
\def\nl{\hfill\break}
\def\kk{\kern 4pt}
\def\m{\phantom{-}}
\let\ds=\displaystyle
\def\frac#1#2{\textstyle{#1\over#2}}

\line{{\mr �Ш|�ǵ{�ƾǬ� }\hfill{\mr �m�W\enspace}$\underline{\hskip 3truein}$}
\bigskip
\line{{\mr\bf �Ƹ� (���ճ���) 8:30--9:30, May 2, 1998}\hfill{\mr �Ǹ�\enspace}$\underline{\hskip 3truein}$}
\bigskip

\centerline{�Ф@�߱N���׼g�b�D������.
�@ {\bf 25} �D, �Ҧ����D�������, �C�D�G��, �L�˦�.}

\pr $x^2+2xy+y^2=0$ ���ϧά�
(A) �@���u\kk (B) �G���u\kk (C) �����u\kk (D) ���.
%A

\pr $9x^2+25y^2-18x+100y-116=0$ ���ϧά�
(A) �ߪ��u\kk (B) �G���u\kk (C) �����u\kk (D) ���.
%D

\pr �H�U����C������ (A) $-122$\kk (B) $-1105$\kk (C) 1230\kk (D) 124.
$$
\left|\matrix{\m3&\m27&-41\cr -1&\m11&-23\cr -5&-32&\m65}\right|
$$
%C

\pr $(1+x+x^2)^4$ �i�}���� $x^4$ ���Y�Ƭ� (A) 19\kk (B) 24\kk (C) 16\kk(D) 10.
%A

\pr �s���Y 4 ���@���w��, �u�X�{�⦸�H�Y�����v�O
(A) $\frac12$\kk (B) $\frac14$\kk (C) $\frac3{16}$\kk (D) $\frac38$.
%(D)

\pr ���y�T���Ϊ�������� 1, �Ӥ@�y�W���u�P���䦨 $30^\circ$ ��.
�ݦ����y�T���Ϊ����n����?\nl
(A) $1\over4\sqrt3$\kk (B) $\sqrt3\over4$\kk (C) $1\over2\sqrt3$\kk
(D) $\sqrt3\over9$
%(B)

\vfill
\line{\hfill
\vbox to 1.2in{\hsize 3.2in\vfill\line{�Ϥ@\hfill}\vfill}
\vbox to 1.2in{\hsize 3.2in\vfill\line{�ϤG\hfill}\vfill}
\hfill}
\vfill

\pr �p�Ϥ@, $A$, $B$, $C$, $D$ �̦�����W�|�I. $AB$, $CD$ ��� $E$,
$DA$, $CB$ ��� $F$.
�Y $60^\circ < \angle E + \angle F < 90^\circ$,\nl
�h����
(A) $\angle D<45^\circ$\kk (B) $45^\circ<\angle D<60^\circ$\kk
(C) $60^\circ< \angle D<90^\circ$\kk (D)$\angle D>90^\circ$
%(B)

\pr �p�ϤG, ��� $ABCD$ ���W�� $AD$ �������U�� $BC$ �����@�b.
�Y $E$ �b $AD$ �W, $F$ �b $BC$ �W, $AE:ED=a:b$, $BF:FC=b:a$,
�h��� $ABFE$ �����n : ��� $EFCD$ �����n��\nl
(A) $a:b$\kk (B) $1:1$\kk (C) $a+2b:2a+b$\kk (D) $2a+b:a+2b$
%(C)

\pr �� ``�A�A�_�A�A��������´'' �Q�Ӧr������|�Ӧr, �@���X�ؿ�k?\nl
(A) 57\kk (B) 210\kk (C) 15120\kk (D) �H�W�ҫD
%A

\pr �w�� $\log_{10}3=0.47712$. �� $(\frac13)\strut^{100}$
���p���I��ĴX��}�l���� $0$?\nl
(A) 46\kk (B) 47\kk (C) 48\kk (D) �H�W�ҫD
%C

\pr �Y $\cos\theta=\cos\varphi$, �h�����@��� $n$, ��\nl
(A) $\varphi=n\pi+(-1)^n\theta$\kk
(B) $\varphi=2n\pi+\theta$ �� $\varphi=2n\pi-\theta$\kk
(C) $\varphi=n\pi+\theta$\kk (D) �H�W�ҫD
%B

\pr �Y $\cos3\theta=a\cos^3\theta+b\cos\theta$ ����N�� $\theta$ ������,
�h $(a,b)$ ��\nl
(A) $(3,4)$\kk (B) $(4,3)$\kk (C) $(3,-4)$\kk (D) $(4,-3)$
%D

\vfill\eject
\pr �Y�Ȧ�s�ڦ~�Q�v�� $r\%$, ���C��p���@�����ƧQ�p��.
�Y�Ʊ�G�~����X���Q�M�� $a$ ��, �h���ɦs�J����������\nl
(A) $\ds{a\over1+{r\over50}}$\kk
(B) $\ds{a\over1+2r}$\kk
(C) $\ds{a\over(1+{r\over1200})^{24}}$\kk
(D) $\ds{a\over(1+{r\over12})^{24}}$
%C

\pr �Y�դG�~�Ŧ� 20 �Z, �U�Z�ѥ[�۱j���ʪ��H�Ʀp�U:
$$
30, 35, 39, 32, 32, 29, 30, 12, 16, 32, 36,
32, 36, 32, 28, 22, 15, 18, 20, 30
$$
�h�W�C�ƾڤ�����Ƭ�
(A) 29\kk (B) 30\kk (C) 32\kk (D) 35.
%B

\pr �Y�����T���Ϊ��T��������t�ƦC, ��P���� 48 ����,
�h�䭱�n��\nl
(A) 160\kk (B) 120\kk (C) 96\kk (D) 84 ���褽��.
%C

\pr �U�C��϶������� $1-x > 2(2x-1) \geq 3x-14$?\nl
(A) $-10\leq x<{1\over 5}$\kk (B) $-11 \leq x < {2\over5}$\kk
(C) $-12\leq x < {3\over5}$\kk (D) $-13\leq x<{4\over5}$.
%D

\pr $2x : 3y^2 : 4z = 1 : 2: 3$ �h $(\ds{x+z\over y})^2$ ���Ȭ�\nl
(A) ${75\over32}$\kk (B) ${76\over32}$\kk
(C) ${77\over32}$\kk (D) �H�W�ҫD.
%D

\pr �] $k$ ���@���, �B�] $f(x) = x^3+x^2+4kx-2$ �P
$g(x) = 2x^3 +x^2 +7kx -3$ ���̰����]���� $h(x)$.
�Y $h(x)$ �����z��, �h $k$ ���Ȭ�\nl
(A) 0\kk (B) 1\kk (B) $-1$\kk (D) 2.
%A

\pr ���u $L_1$: $3x+y+2=0$ �P $L_2$: $3x-y-1=0$ ���U�樤�������u��\nl
(A) $6x-y-1=0$\kk (B) $6x+1=0$\kk (C) $36x+7y+21=0$\kk
(D) $2y+3=0$.
%B

\pr �] $z^4 + z^3 + z^2 + z +1=0$ ���|�Ӯڬ� $z_k$ ($k=1,2,3,4$).
�h�U�C��̤����T?\nl
(A) �|�Ӯڦ@��\kk (B) �|�Ӯڬ��@������Τ����I\kk
(C) $z_k = \cos {2k\pi\over5} + i\sin{2k\pi\over5}$, ($k=1,2,3,4$)\nl
(D) $z_k = \cos {k\pi\over2} + i\sin{k\pi\over2}$, ($k=0,1,2,3$).
%D

\pr �b $x\geq 0$, $y\geq 0$, $3x+y\leq 3$ �M $2x+3y\leq 6$ ������U,
$x-y$ ���̤j�Ȭ�\nl
(A) 2\kk (B) 1\kk (C) 0\kk (D) $-{9\over7}$.
%B

\pr �H�U���R�D, ��̦b���z�ƶ��X��������?\nl
(A) ����Ӥ��������j�p\kk (B) �@���@����{��������\nl
(C) �@���G����{��������\kk (D) ����Ӥ��P�������������t�@����.
%C

\pr �H�U���R�D, ��̻P�������[���L��?\nl
(A) ����w�z\kk (B) �T���Τ� SAS ����\kk (C) �u�~�@�I��u�W����v\kk
(D) �⥭��u���Z��.
%B

\pr �j��þ�ƾǮa Diophantin ���ӸO�W��۳o�Ӱ��D: ���v�󦹪��H,
�䵣�~�O�L�ͩR�� $1\over6$,
���۪� ${1\over12}$ �ͩR�O�C�~�ɴ�.  �A�L�F�ͩR�� $1\over7$ �L�~���B.
�B�� 5 �~�ͦ��@�l, ���Ĥl�u���F���ˤ@�b���~��.  �b�Ĥl����L�S���F 4 �~.
�аݹL���H, ���g���F�X��?\nl
(A) 84\kk (B) 82\kk (C) 88\kk (D) 92.
%A

\pr ��N�C�{�|�ѷ��l, ���g�b�Үֿ��x���ɭ԰ݤF�o���D��:
���]�A����L�䨫�L, ��ť�차����B.  �p�G�C�H�� 6 �ǰ�, �h�ѤU 5 ��,
�p�G�C�H�� 7 �ǰ�, �S�t�F 8 ��.  �հݸ馳�X�H?\nl
(A) 83\kk (B) 64\kk (C) 16\kk (D) 13.
%D

\bye
