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Nội dung: <blockquote data-quote="NguoiDien" data-source="post: 124107" data-attributes="member: 75">Đề thi vào 10 Sở Hà Nam năm 2012Câu 1. (1,5 điểm) Rút gọn các biểu thức sau: a)  <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-3d99280d1d489148c97f8936040e2d0f_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> b) <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-5b321f4958379d6a6547b2e85eb06cae_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> Câu 2. (2,0 điểm) a) Giải phương trình: <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-5164d60d87429b608de1c13213cd1903_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. b) Giải hệ phương trình: <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-ebe48252e9b0d9e14bd912abd66203fa_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Câu 3. (2,0 điểm) Trong mặt phẳng tọa độ <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-94753d83b0e6a284820d11bce5ae6bd3_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> cho Parabot <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-0718119daf759d1798b37e0526c48d65_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> có phương trình <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-01ece37c7314b8ecc38559e2d5968dd7_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và đường thẳng <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-f0d62ca25ed2911a08dc3cc02481684f_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> có phương trình <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-05ff1d1a88878c3f72dcd53a2ad39265_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> (<img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-e27d3310a08258c9e04d614bc493653c_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là tham số) a) Tìm tọa độ các điểm thuộc <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-0718119daf759d1798b37e0526c48d65_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> biết tung độ của chúng bằng <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-5f64fa2845ddc6ba13a326c4e8e01946_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. b) Chứng minh rằng: <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-0718119daf759d1798b37e0526c48d65_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-f0d62ca25ed2911a08dc3cc02481684f_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> cắt nhau tại hai điểm phân biệt với mọi <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-e27d3310a08258c9e04d614bc493653c_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Gọi <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-0bc00e75b9231ed482a435d385c47d24_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-7fc953eabfa272a6d4ef64c1d77c9cd0_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là tung độ các giao điểm của <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-0718119daf759d1798b37e0526c48d65_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-f0d62ca25ed2911a08dc3cc02481684f_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Tìm <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-e27d3310a08258c9e04d614bc493653c_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> để <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-ed71050aff9b5fa0a666e7d9fe718601_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Câu 4. (3,5 điểm) Cho đường tròn tâm <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-b4a4d66352df6bbc71ec487c323b17cd_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />, đường kính <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-6a055a313bbf1687dba35102d600465a_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Trên tiếp tuyến của đường tròn <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-53327c20af6801615c99a4d92824800b_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> tại <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-bea01eace268a1d33020224707ceb982_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> lấy điểm <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-bd163e35f1859eb5dca0c739d38d8bfc_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> (<img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-bd163e35f1859eb5dca0c739d38d8bfc_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> khác <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-bea01eace268a1d33020224707ceb982_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />). Từ <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-bd163e35f1859eb5dca0c739d38d8bfc_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> vẽ tiếp tuyến thứ hai <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-fbd05e975e0bdf09ec2f51ca5474e492_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> với <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-53327c20af6801615c99a4d92824800b_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> (<img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-dfb930cb54efd420e29bbe184eca5aeb_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là tiếp điểm). Kẻ <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-104656d603eb7ae67de7a076c5e82f4a_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> vuông góc với <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-6a055a313bbf1687dba35102d600465a_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> (<img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-62871d8eba9517726c823ed68260be6c_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />), <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-8bf3c42a20397c5a8335493536427178_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> cắt <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-53327c20af6801615c99a4d92824800b_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> tại điểm thứ hai là <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-21bdabafb6966e12dcc2491a772a571f_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> và cắt <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-104656d603eb7ae67de7a076c5e82f4a_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> tại <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-8a0118b4d0f84b0237acc4cfeac90587_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Chứng minh rằng: a) Tứ giác <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-9e5be67eb8f83053ac00e9f49c0b0310_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là tứ giác nội tiếp. b) <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-bcd50b6eb984d5fe918b87d0b7a64ffc_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> c) Góc <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-d7e7623c00ef8abf9bc9196e60c5ffc4_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> bằng góc <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-c73c753bf50f9d9884bce4401724f9a5_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. d) <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-8a0118b4d0f84b0237acc4cfeac90587_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> là trung điểm của <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-104656d603eb7ae67de7a076c5e82f4a_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Câu 5. (1,0 điểm) Cho ba số thực <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-94bf78bfa574ce03c29491fb44cc15d3_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> thỏa mãn: <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-ae4d99c4fe4c33379b9671338940efd1_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />; <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-f3d607e5679fb16cc6ba8898c753f4ad_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />; <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-912073bed5d397f5e85d6108b0f162f1_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Tìm giá trị lớn nhất của biểu thức:       <img src="https://toanthpt.org/wp-content/ql-cache/quicklatex.com-be3475db06333648fdd0ba60bb3eb7ee_l3.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />- – - – - – - – - – - – - – - – HẾT- – - – - – - – - – - – - – - -<a href="https://www.box.com/s/76bad42bd0b810ab909d" target="_blank">Các bạn quan tâm down đề thi và hướng dẫn giải tại đây!</a></blockquote>

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