令和５年度 東京都立産業技術高等専門学校 入学者選抜 学力検査

数

学

正

答

<latexit sha1_base64="ovzhAXmGFo9D0NbtzA/nlILUwsw=">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</latexit>

13
6

[問1]

<latexit sha1_base64="SYUcQnaVZXEOE8+7cb92vCCtfEA=">AAACZXichVHLSsNAFD2Nr1ofrQ9EcGGxVFyVWxUVNxbcuGyrVUGlJHFaQ9MkJGmhFn9A3KoLVwoi4me48Qdc9AtE3AgKblx4kxZERb3DzJw5c8+dMzOKpWuOS9QISG3tHZ1dwe5QT29ffzgyMLjumBVbFTnV1E17U5EdoWuGyLmaq4tNyxZyWdHFhlJa9vY3qsJ2NNNYc2uW2CnLRUMraKrsMpWdoXwkRgnyI/oTJFsgtvQMP9Jm5Arb2IUJFRWUIWDAZaxDhsNtC0kQLOZ2UGfOZqT5+wIHCLG2wlmCM2RmSzwWebXVYg1eezUdX63yKTp3m5VRxOmerumF7uiGHun911p1v4bnpcaz0tQKKx8+HF19+1dV5tnF3qfqT88uCljwvWrs3fIZ7xZqU1/dP31ZXczG65N0QU/s/5wadMs3MKqv6mVGZM8Q4g9Ifn/un2B9OpGcS8xmKJaKNn8CQYxhAlP83vNIYQVp5PjcAo5wjJPAg9QnDUsjzVQp0NIM4UtI4x8XOIr/</latexit>

30

[問1]

度

<latexit sha1_base64="bgKbt/x+FXdI4ChAUYVwP/7TkNA=">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</latexit>

3<latexit sha1_base64="ZlFP1Ui6Aodt6KtQdQNd5JwfHaI=">AAACZHichVHLSsNAFD2Nr1pf1SIIghSL4qrciKi4seDGZR/WFrSUJE5rME1CkhZq8Qd0q7hwpSAifoYbf8BFf0AQN4KCGxfepgVRUe8wM2fO3HPnzIxqG7rrETUDUld3T29fsD80MDg0PBIeHdt0raqjiaxmGZaTVxVXGLopsp7uGSJvO0KpqIbIqXtrrf1cTTiubpkbXt0WhYpSNvWSrikeUym5GI5RnPyI/gRyB8RWn+FH0gpfYRs7sKChigoETHiMDShwuW1BBsFmroAGcw4j3d8XOECItVXOEpyhMLvHY5lXWx3W5HWrpuurNT7F4O6wMooZuqdreqE7uqFHev+1VsOv0fJS51lta4VdHDmcyLz9q6rw7GH3U/WnZw8lLPtedfZu+0zrFlpbX9s/fcmspGcas3RBT+z/nJp0yzcwa6/aZUqkzxDiD5C/P/dPsDkflxfjCymKJaLtn0AQk5jGHL/3EhJYRxJZPlfgCMc4CTxIg1JEGm+nSoGOJoIvIU19AI2WisM=</latexit>

[問2]

1

[問2]

4
p
3
2

<latexit sha1_base64="nr0d3a8LAx1cvyVCQT95TVtrWSA=">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</latexit><latexit sha1_base64="dpBxiDALFRtsCp3L5fTNP6mt9+Q=">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</latexit>

6ab4

[問3]

[問3]

<latexit sha1_base64="FV9AorMkjC6ECK5NraLw4B+cuFU=">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</latexit>

cm2<latexit sha1_base64="vMx6zAp9bBsf/ozGdw6USHQRIow=">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</latexit>

1

x+y
12

[問4]
<latexit sha1_base64="cZQ+QDQrSC4y7Dcm4UvEzfKq4X4=">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</latexit><latexit sha1_base64="V1QZsuxHQ10De0PraWzSnBpeF6E=">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</latexit>

3x (x + 2y)

[問5]

p

<latexit sha1_base64="2fGgd7QcQbcxgT1flS8qam/aYjE=">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</latexit><latexit sha1_base64="DvGy9a8O2yWVDBXqzEmM2t0WO1E=">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</latexit><latexit sha1_base64="eMtcMB8RFdQXhXa3Cl1/6M4xEYk=">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</latexit>[問6]<latexit sha1_base64="U4tx09Xi2+k2ANuMzaR0e6kuCgI=">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</latexit>

x= 2<latexit sha1_base64="gOCpxpkOlEQXfkfShIOFfU+05vc=">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</latexit><latexit sha1_base64="Sq+nhn8tbGqPN9Ydeue8TKownLI=">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</latexit>

, y=

1

<latexit sha1_base64="Sq+nhn8tbGqPN9Ydeue8TKownLI=">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</latexit>

4[問2]<latexit sha1_base64="n7hBmEYrLILWVzQQ6k2ZJ+5h0b8=">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</latexit><latexit sha1_base64="j1xhR41NCZqdGIf3NKFlIps24ZI=">AAACcHichVHLSsNAFD2Nr1pfVTcFF1aLIiLlVuoDNxbcuKyttQUtksRRg2kSk7SgxR/wB1y4sYKI+Blu/AEXfoK4ERXcuPAmKYiKesPNnDlzz50zM4qla45LdB+SWlrb2jvCnZGu7p7evmj/wJpjVm1VFFRTN+2SIjtC1wxRcDVXFyXLFnJF0UVR2Vvy1os1YTuaaay6B5YoV+QdQ9vWVNllqpye2ojPcM5yzm1GE5QkP+I/QaoJEotP8CNrRi+xgS2YUFFFBQIGXMY6ZDj8rSMFgsVcGXXmbEaavy5whAhrq1wluEJmdo//Ozxbb7IGz72ejq9WeRed02ZlHGN0R1f0Qrd0TQ/0/muvut/D83LAoxJohbXZdxzLv/2rqvDoYvdT9adnF9uY971q7N3yGe8UaqCvHZ685BdyY/VxOqdH9t+ge7rhExi1V/ViReROEeEHSH2/7p9gbTqZmk2mVyiRiQcvgTCGMIoJvu85ZLCMLAq87z5OcIZG6FmKScPSSFAqhZqaQXwJafIDmeeN2A==</latexit>[問7]

4, 5, 6, 7

度

180

[問1]

[問3]

2+1 2
r cm2
2
p
cm
2+ 2
<latexit sha1_base64="FV9AorMkjC6ECK5NraLw4B+cuFU=">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</latexit><latexit sha1_base64="I3qlXWLrXBnVyFXpnpiyItAuPew=">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</latexit><latexit sha1_base64="rorL7MEXOK+tui33fKblpahNoQQ=">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</latexit>

36⇡

[問1]

<latexit sha1_base64="0b90DKZfHj7M8/fkfuDUW3ug+k4=">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</latexit>

cm3<latexit sha1_base64="jSpHukcLZu3J6Q0dxkOjEWsYNS8=">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</latexit>

80

[問1]

<latexit sha1_base64="mtVaVArKe8YYhW/cSTphwsN9CDo=">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</latexit>g<latexit sha1_base64="HTbmxm8TwGUqxeuNWaWiw9e81+s=">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</latexit>\SQO : \ROP<latexit sha1_base64="Ao/JYhcOUTTTtoC9BUo8+xsIvKc=">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</latexit>

[問2]

2

10

通り

5

[問2]
<latexit sha1_base64="Sq+nhn8tbGqPN9Ydeue8TKownLI=">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</latexit><latexit sha1_base64="YezzZP33uUCjIiGq+lvDZFunZiw=">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</latexit>=<latexit sha1_base64="eMtcMB8RFdQXhXa3Cl1/6M4xEYk=">AAACZHichVHLSsNAFD2Nr1ofrRZBEKRYFFflpoiKGwU3Lq3aB1SRJE41NE1CkhZq8Qd0q7hwpSAifoYbf8BFf0AQN0IFNy68TQuiRb3DzJw5c8+dMzOqbeiuR1QPSF3dPb19wf7QwODQcDgyMppxrbKjibRmGZaTUxVXGLop0p7uGSJnO0IpqYbIqsXV5n62IhxXt8wtr2qLnZKyb+oFXVM8plLJ3UicEuRHrBPIbRBffoUf61bkBtvYgwUNZZQgYMJjbECByy0PGQSbuR3UmHMY6f6+wBFCrC1zluAMhdkij/u8yrdZk9fNmq6v1vgUg7vDyhim6ZFuqUEPdEfP9PFrrZpfo+mlyrPa0gp7N3w8vvn+r6rEs4eDL9Wfnj0UsOh71dm77TPNW2gtfeXwvLG5tDFdm6EremH/l1Sne76BWXnTrlNi4wIh/gD553N3gkwyIc8n5lIUX4m1fgJBTGAKs/zeC1jBGtaR5nMFTnCKs8CTNChFpbFWqhRoa6L4FtLkJ4+WisQ=</latexit><latexit sha1_base64="hM8+Xzfgt2FAtlsfQs998ag+nYA=">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</latexit>

5

[問3]

<latexit sha1_base64="d44K55BXFXpYfGt/HRhmnWFG84Y=">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</latexit><latexit sha1_base64="GmoEf+Wgp0jwtMMOYwV8kUwPLIc=">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</latexit>

[問4]

: 3
<latexit sha1_base64="+LBW9D2+zXGCD61nEC8SbLiHkig=">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</latexit>

2

7

個

[問3]

4p
5r
5

<latexit sha1_base64="I3qlXWLrXBnVyFXpnpiyItAuPew=">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</latexit>cm

各5点×20問=100点
受検番号得点