diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 33107000..d7ab001d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -762835,9 +762835,7 @@ "030471": { "id": "030471", "content": "如图所示, 正方体$ABCD-A_1B_1C_1D_1$中, $M$为$B_1C_1$边的中点, 点$P$在底面$ABCD$和侧面$CDD_1C_1$上运动并且使$\\angle MA_1C=\\angle PA_1C$, 那么点$P$的轨迹是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\def\\m{2}\n\\def\\n{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1) (A1) -- (C);\n\\draw ($(B1)!0.5!(C1)$) node [right] {$M$} coordinate (M);\n\\draw (A1) -- (M);\n\\filldraw ({1/3},0,{-1/12*(35 - 3*sqrt(97))}) node [right] {$P$} coordinate (P) circle (0.01);\n\\draw [dashed] (A1) -- (P);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{两端圆弧}{两段椭圆弧}{两段双曲线弧}{两段抛物线弧}", - "objs": [ - "KNONE" - ], + "objs": [], "tags": [ "第六单元", "空间向量" @@ -763847,9 +763845,7 @@ "030496": { "id": "030496", "content": "数列$\\{a_n\\}$是首项为$1$, 公差为$2$的等差数列, $S_n$是它前$n$项和, 若$\\dfrac{S_n}{a_n^2}\\le A$恒成立, 则$A$的最小值为\\blank{50}.", - "objs": [ - "KNONE" - ], + "objs": [], "tags": [ "第四单元", "2023届高三-赋能-赋能10" @@ -763891,9 +763887,7 @@ "030497": { "id": "030497", "content": "在正项等比数列$\\{a_n\\}$中, 已知公比为$\\dfrac 13$, 若对任意正整数$n$, $a_1+a_2+\\cdots+a_n<\\dfrac 12$恒成立, 则$a_1$的取值范围是\\blank{50}.", - "objs": [ - "KNONE" - ], + "objs": [], "tags": [ "第四单元", "2023届高三-赋能-赋能11" @@ -763977,9 +763971,7 @@ "030499": { "id": "030499", "content": "设$a_n$是$(1+x)^n$($n\\in \\mathbf{N}$, $n\\ge 2$, $x\\in \\mathbf{R}$)展开式中$x^2$项的系数, 若$a_2+a_3+\\cdots+a_n<10000$, 则$n$的最大值为\\blank{50}.", - "objs": [ - "KNONE" - ], + "objs": [], "tags": [ "第四单元", "第八单元", @@ -783858,8 +783850,7 @@ "content": "已知$a$是常数, 设函数$f(x)=(a+2)x^2+2(a+2)x-4$.\\\\\n(1) 解不等式: $f(x)>-4$;\\\\\n(2) 求实数$a$的取值范围, 使得$f(x)<0$对任意$x\\in [1,3]$恒成立.", "objs": [ "K0115001B", - "K0114001B", - "KNONE" + "K0114001B" ], "tags": [ "第一单元",