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Nội dung: <blockquote data-quote="lachtach" data-source="post: 70554" data-attributes="member: 46897">Đề thi học sinh giỏi môn toán TP. Hà Nội năm 2010-2011    (Đề thi vòng 1)Câu I.  1) Giải hệ phương trình  <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image001.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />  2) Tìm <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image002.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />để hệ phương trình sau có nghiệm  <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image003.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />  Câu II.  1) Cho <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image004.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />có độ dài 3 cạnh là <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image005.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />, chiều cao tương ứng là <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image006.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image007.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />là bán kính đường tròn ngoại tiếp. CMR  <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image008.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />.  2) Cho 6 số <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image009.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Có bao nhiêu số có 6 chữ số khác nhau và tổng các chữ số hàng chục, hàng trăm lớn hơn tổng 3 số còn lại 3 đơn vị.  Câu III.  1) Chứng minh có duy nhất 1 điểm thuộc đồ thị <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image010.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />của hàm số <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image011.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />mà qua điểm đó kẻ được duy nhất một tiếp tuyến tới <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image010.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />.  2) Tìm <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image012.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />để hàm số đạt GTLN, GTNN:  <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image013.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />.  Câu IV.  Cho dãy số <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image014.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Đặt <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image015.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />.  Tính <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image016.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />.  Câu V.  1) Cho đoạn thẳng <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image017.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />nằm trong mặt phẳng <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image018.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image019.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />là trung điểm của <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image017.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Chọn điểm <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image020.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />thuộc <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image021.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Về 1 phía của mặt phẳng bờ <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image017.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />dựng hình vuông <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image022.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image023.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Tìm <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image020.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />để tổng thể tích của <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image024.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />và <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image025.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />nhỏ nhất.  2) Gọi <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image026.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Tìm quĩ tích hình chiếu vuông góc của <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image027.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />lên <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image028.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />khi <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image020.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />di động trên <img src="http://file:///C:/DOCUME%7E1/TN_COM%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image029.gif" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />.  Hết</blockquote>

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