diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index cc317c1c..354ed23c 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,682 +1,547 @@ ans -13287 +13512 $2$ -13288 -$a>2$ +13513 +$x=\mu$ -13289 -$89$ +13514 +可能异面, 可能相交 -13290 -$[-1,2]$ +13515 +$\dfrac{y^2}{15}+\dfrac{x^2}{16}=1$, $x\ne 0$ -13291 -$12$ +13516 +$[1,15]$ -13292 -$\dfrac{3\sqrt{2}}{4}$ +13517 +$-\dfrac 13$ -13293 -$16$ +13518 +$\dfrac 43$ -13294 -$\arctan \dfrac{\sqrt{6}}6$ +13519 +$(-\infty,-1]\cup [3,+\infty)$ -13295 -$\dfrac 56$ - -13296 -$\dfrac{\sqrt{5}}{3}$ - -13297 -A - -13298 -B - -13299 -C - -13300 -(1) $a=4$; (2) 证明略 - -13301 -(1) $[k\pi+\dfrac\pi 3,k\pi+\dfrac{5\pi}6]$, $k\in \mathbf{Z}$; (2) $A=\dfrac\pi 3$, $b=2$, $S=2\sqrt{3}$ - -13302 -$(-\infty,0)\cup (1,+\infty)$ - -13303 -$\dfrac 32$ - -13304 -$12\pi$ - -13305 -$-\dfrac 43$ - -13306 -$\dfrac 3{16}$ - -13307 -$y=2x-\mathrm{e}$ - -13308 -$5$ - -13309 -$4\pi$ - -13310 -$-3\le a\le -1$ - -13311 -$9828$ - -13312 -C - -13313 -B - -13314 -C - -13315 -(1) 证明略; (2) $\dfrac{\sqrt{10}}5$ - -13316 -(1) $a_n=n-1$; (2) 证明略 - -13317 -$\sqrt{5}$ - -13318 -$\overrightarrow{AD}=\dfrac 23 \overrightarrow{a}+\dfrac 13 \overrightarrow{b}$ - -13319 -$\dfrac{16}{35}$ - -13320 -$[0,8)$ - -13321 -$\dfrac{25}{9}$ - -13322 -$[\dfrac 34,1]$ - -13323 -$3$ - -13324 -$0$ - -13325 -$\dfrac{\sqrt{3}}2$ - -13326 -$\dfrac 34$ - -13327 -C - -13328 -B - -13329 -B - -13330 -(1) 证明略; (2) $B_1D=\dfrac 12$ - -13331 -(1) $\dfrac{x^2}{4}+\dfrac{y^2}{3}=1$, $y\ne 0$; (2) $[12,8\sqrt{3})$; - -13332 +13520 $\sqrt{3}$ -13333 -$8$ - -13334 -$-\dfrac 12$ - -13335 -$0.14$ - -13336 -$1$ - -13337 -$-2$ - -13338 -$99.9\%$ - -13339 -$\dfrac 1{15}$ - -13340 -$4$ - -13341 -$2$ - -13342 -A - -13343 -B - -13344 -B - -13345 -(1) $\dfrac\pi 3$; (2) $\arcsin \dfrac{\sqrt{3}}3$ - -13346 -(1) $x=15$; (2) 比值为$\dfrac 12$ - -13347 -$-\dfrac 1{25}$ - -13348 -$-\dfrac{\sqrt{2}}2$ - -13349 -$6$ - -13350 -$(-1,-2)$ - -13351 -$4$ - -13352 -$0$ - -13353 -$12$ - -13354 -$1$ - -13355 -$\dfrac{\sqrt{3}}3$ - -13356 -$(0,\dfrac 14)$ - -13357 -B - -13358 -A - -13359 -D - -13360 -(1) $P(0,0)$或$P(-\dfrac 85,\dfrac 45)$; (2) 过定点$(-\dfrac 45,\dfrac 25)$ - -13361 -(1) $p=\dfrac 23$, $q=\dfrac 14$; (2) $\dfrac 16$ - -13362 -$\{5,7,9\}$ - -13363 -$a+b>2$ - -13364 -$(0,+\infty)$ - -13365 -$\dfrac 23$ - -13366 -$25$ - -13367 -$(-\infty,-8]\cup [2,+\infty)$ - -13368 -$\dfrac 52$ - -13369 -$\dfrac 23$ - -13370 -\textcircled{2}\textcircled{3} - -13371 -$9$ - -13372 -B - -13373 -D - -13374 -D - -13375 -(1) $x=1$; (2) $[\dfrac 12,+\infty)$ - -13376 -(1) $\dfrac{x^2}{4}+\dfrac{y^2}{2}=1$; (2) $y=\pm \dfrac{\sqrt{2}}2+1$ - - -13377 -$1$ - -13378 -$\dfrac{5\pi}6$ - -13379 +13521 $\pi$ -13380 -$\dfrac{\sqrt{5}-1}2$ - -13381 -$1:2\sqrt{2}$ - -13382 -$\dfrac{x^2}{18}-\dfrac{y^2}{9}=1$ - -13383 -$0.88$ - -13384 -$0.95$ - -13385 -$7$ - -13386 -$(-\infty,8)$ - -13387 -D - -13388 +13522 A -13389 -C - -13390 -(1) $y=\begin{cases}\dfrac{24x-2x^2}{15-x}, & x\in \{1,2,\cdots,9\},\\ \dfrac 53 x-\dfrac{x^3}{180},& x\in \{10,11,\cdots,20\};\end{cases}$ (2) 日进货量为$10$吨时, 日利润最大, 最大日利润是$\dfrac{100}{9}$千元 - -13391 -(1) $y=2\sin(2x+\dfrac\pi 3)-1$; (2) $[-1,1]$ - -13392 -$\{-1,2\}$ - -13393 -$8$ - -13394 -$7$ - -13395 -$0.3$ - -13396 -$0.2$ - -13397 -$1$ - -13398 -$6$ - -13399 -$\mathrm{e}-1$ - -13400 -$\dfrac{7}{25}$ - -13401 -\textcircled{1}\textcircled{2}\textcircled{3}\textcircled{5} - -13402 -C - -13403 -A - -13404 +13523 D -13405 -(1) $\dfrac{x^2}{4}+\dfrac{y^2}{2}=1$; (2) $[0,2]$ +13524 +B -13406 -(I) (1) 证明略; (2) $S_n=4-\dfrac{n+2}{2^{n-1}}$; (II) 证明略 +13525 +(1) $\dfrac{5}{12}\text{h}$; (2) 能, $v$的取值范围为$(\dfrac{9\sqrt{3}}2,\dfrac{\sqrt{559}}3]$ -13407 -$(0,1)\cup (1,2]$ +13526 +(1) 证明略; (2) $\dfrac{a_1}{a_2}\le \dfrac{a_1+a_3+\cdots+a_{2n-1}}{a_2+a_4+\cdots+a_{2n}}$, 当且仅当$n=1$或$d=0$时成立等号; (3) $2023^2$ -13408 -$-\sqrt{13}$ +13527 +$\{(0,1),(2,5)\}$ -13409 +13528 +$x>1$且$y>1$ + +13529 $\sqrt{2}$ -13410 -$0.0044$ +13530 +$(-\infty,-8]\cup [2,+\infty)$ -13411 -$20$ +13531 +$[-2,2]$ -13412 -$2$ - -13413 -$2\sqrt{2}$ - -13414 -$x=-1$ - -13415 -$\dfrac\pi 2$ - -13416 -$-1$ - -13417 -D - -13418 -D - -13419 -C - -13420 -(1) 证明略; (2) $\dfrac{\sqrt{3}}3$ - -13421 -(1) $BD=BA$; (2) 约$0.33\text{km}$ - -13422 -$\dfrac 32$ - -13423 -$(3,4)$ - -13424 -$\sqrt{7}$ - -13425 -$\dfrac{9}{4}$或$\dfrac{4}{9}$ - -13426 -$\dfrac{24}{25}$ - -13427 -$\dfrac 34$ - -13428 -$100$ - -13429 -$-\dfrac{11}{16}$ - -13430 -$30$ - -13431 -$[\dfrac 73,\dfrac{13}{3})$ - -13432 -B - -13433 -B - -13434 -A - -13435 -(1) $\dfrac{2\sqrt{6}}3$; (2) $\dfrac{\sqrt{10}}2\text{千米}$ - -13436 -(1) 证明略; (2) $\dfrac{4\sqrt{3}}7$ - - -13437 -$\{1,3,5\}$ - -13438 -$1$ - -13439 -$2m-1$ - -13440 -$8$ - -13441 -$45$ - -13442 -$\sqrt{5}$ - -13443 -$\pi-\arctan\dfrac 32$ - -13444 -$\dfrac{11}{12}$ - -13445 -$-3$ - -13446 -$[-2,6]$ - -13447 -C - -13448 -C - -13449 -D - -13450 -(1) $4\pi$; (2) $\arctan\dfrac{\sqrt{2}}2$ - -13451 -(1) 第一个数列具有性质$P$, 第二个数列不具有性质$P$; (2) $(-\infty,-2]\cup [0,+\infty)$ - - - -13452 -$\dfrac 34\pi$ - -13453 -$\sqrt{7}$ - -13454 -$4$ - -13455 -$\dfrac{24}{25}$ - -13456 -$y=\dfrac {1}{\mathrm{e}}x$ - -13457 -$\dfrac{16}{35}$ - -13458 -$[1,3]$ - -13459 -$36$ - -13460 -$30$ - -13461 -$\dfrac{2\sqrt{3}}3$ - -13462 -B - -13463 -B - -13464 -C - -13465 -(1) 证明略; (2) $\dfrac{\sqrt{5}}5$ - -13466 -(1) $[\dfrac 14,1)$; (2) 当$\theta=\dfrac{\pi}{6}$时 - -13467 -$-2$ - -13468 -$2\sqrt{2}$ - -13469 -$16$ - -13470 -$\dfrac 14$ - -13471 -$5$ - -13472 -$\dfrac{3\pi}{4}$ - -13473 -$\sqrt{10}$ - -13474 -$\dfrac{21}{16}$ - -13475 -\textcircled{1}\textcircled{2}\textcircled{3}\textcircled{4} - -13476 -$7$ - -13477 -B - -13478 -A - -13479 -C - -13480 -(1) $\dfrac 34$; (2) $\dfrac{13}{36}$ - -13481 -(1) $-1$; (2) $(0,+\infty)$ - -13482 -$1$ - -13483 -$60$ - -13484 -$\dfrac{80}{243}$ - -13485 +13532 $\dfrac 13$ -13486 -$\arccos\dfrac{\sqrt{15}}{10}$ +13533 +$\dfrac{4\pi}{3}$ -13487 -$2-\dfrac 1n$ +13534 +$20$ -13488 -$21$ +13535 +\textcircled{3}\textcircled{4} -13489 -$y=\begin{cases}x^2+\dfrac 1x, & x>0, \\ 0, & x=0, \\ -x^2+\dfrac 1x, & x<0\end{cases}$ +13536 +\textcircled{1}\textcircled{3}\textcircled{4} -13490 -$a=2$或$a\ge 2\sqrt{2}$其中的一个即可 - -13491 -$4$ - -13492 -A - -13493 -C - -13494 +13537 B -13495 -(1) $y=x-1$; (2) $(-\infty,\dfrac 32)$ - -13496 -(1) 证明略; (2) $6\sqrt{2}$ - -13497 -$6$ - -13498 -$2$ - -13499 -$1-k$ - -13500 -$4$ - -13501 -$15$ - -13502 -$(\dfrac 12,1)$ - -13503 -$0.568$ - -13504 -$1$ - -13505 -$\lambda\ge -3$ - -13506 -$\dfrac{56}3$ - -13507 -A - -13508 +13538 C -13509 +13539 D -13510 -(1) $(3,5)$; (2) $[2,\dfrac 52]$ +13540 +(1) 甲与乙的平均数分别为$7$和$7$; (2) 甲与乙的方差分别为$3$和$1.2$; (3) 两人射击水平相当, 甲的发挥更稳定 + +13541 +(1) $\dfrac 12$; (2) $\dfrac{4\sqrt{5}}5$ + + +13542 +$3.5$ + +13543 +$\dfrac{20}{11}$ + +13544 +$a=\pm 1$ + +13545 +$-17$ + +13546 +$0.7$ + +13547 +$5$ + +13548 +$6\sqrt{3}$ + +13549 +$0.6$ + +13550 +$2\pi^2+16\pi$ + +13551 +$\dfrac 83$ + +13552 +C + +13553 +C + +13554 +B + +13555 +(1) $f(x)=\begin{cases}2^x-1+\log_2 (x+1), & x\ge 0, \\ 1-2^{-x}-\log_2(-x+1), & x<0;\end{cases}$ (2) $f(x)=-2^{x-2}+1-\log_2(x-1)$, $16.635$, 有$99.9\%$的把握认为患该疾病群体与为患该疾病群体的卫生习惯有差异; (2) 证明略, $R$的估计值为$6$ + +13571 +(1) $y=2x$; (2) $(-\infty,-1)$ + +13572 +$-\dfrac 12$ + +13573 +$2\pi$ + +13574 +$\dfrac{\sqrt{6}}2a^2$ + +13575 +$3x-y-2=0$ + +13576 +$-\dfrac{3}{25}\overrightarrow{b}$ + +13577 +$-2$ + +13578 +$\dfrac{2\sqrt{5}}5$ + +13579 +$[\dfrac 54,\dfrac{3\sqrt{17}}4]$ + +13580 +$77$ + +13581 +$4$ + +13582 +A + +13583 +B + +13584 +D + +13585 +(1) $0.89$; (2) $0.0014$ + +13586 +(1) $x^2-\dfrac{y^2}{3}=1$; (2) 证明略 + +13587 +$\{1,2\}$ + +13588 +$2$ + +13589 +$6$ + +13590 +$3$ + +13591 +$5$ + +13592 +$-\sqrt{2}$ + +13593 +$\dfrac 16$ + +13594 +$-28$ + +13595 +$0.14$ + +13596 +$2$ + +13597 +$\ln 2$ + +13598 +$\dfrac{\sqrt{13}}2$ + +13599 +A + +13600 +C + +13601 +C + +13602 +B + +13603 +(1) $\dfrac\pi 6$; (2) $6+6\sqrt{3}$ + +13604 +(1) 证明略; (2) $\dfrac{\sqrt{6}}8$ + +13605 +(1) $X\sim \begin{pmatrix} 0 & 20 & 100\\ 0.2 & 0.32 & 0.48\end{pmatrix}$; (2) 应选择先回答B类问题 + +13606 +(1) $\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$; (2) $2\sqrt{2}+\sqrt{17}$; (3) 定值为$34$ + +13607 +(1) $y=x$; (2) 在$[0,+\infty)$上是严格增函数; (3) 证明略 + +13608 +$1$ + +13609 +$[\dfrac 12,1]$ + +13610 +$2\sqrt{3}$ + +13611 +$x\le \dfrac{a+b}{2}$, 等号成立当且仅当$a=b$ + + +13612 +$2x-y+1=0$ + +13613 +$\dfrac{3\pi}{4}$ + +13614 +$115$ + +13615 +$-1$ + +13616 +如$x^2+(y-2)^2=1$等(答案不唯一) + +13617 +$(0,-4)$ + +13618 +$72$ + +13619 +$\dfrac 78$ + +13620 +B + +13621 +A + +13622 +C + +13623 +C + +13624 +(1) $\dfrac 13$; (2) 证明略 + +13625 +(1) $a_n=3n-1$; (2) $S_n=\dfrac{21}{4}-\dfrac{6n+7}{4\cdot 3^{n-1}}$ + +13626 +(1) $V=x(3-2x)^2$, $x\in (0,\dfrac 32)$; (2) 当$x=\dfrac 12$时, $V$取到最大值$2$ + +13627 +(1) 最小正周期为$\pi$, 取值范围为$[-1,2]$; (2) $\sqrt{3}$ + +13628 +(1) $2$; (2) 双曲线方程为$x^2-\dfrac{y^2}{3}=1$, 过顶点$(2,0)$与$(-1,0)$ + + +13629 +$4$或$-6$ + +13630 +$(\dfrac\pi 6,\dfrac{5\pi}6)$ + +13631 +$44$ + +13632 +$41$ + +13633 +$1$ + +13634 +$24$ + +13635 +$\dfrac{7\sqrt{3}}3\pi$ + +13636 +$20$ + +13637 +$2.5$ + +13638 +$76$元 + +13639 +$p_1$,$p_4$ + +13640 +$\dfrac 34$ + +13641 +D + +13642 +B + +13643 +C + +13644 +B + +13645 +证明略 + +13646 +(1) $\dfrac\pi 3$; (2) $(6,12]$ + +13647 +(1) $0.6$; (2) $x\sim \begin{pmatrix}0 & 10 & 20 & 30\\0.16 & 0.44 & 0.34 & 0.06\end{pmatrix}$, $E[X]=13$ + +13648 +(1) $\dfrac{x^2}3+y^2=1$; (2) $\sqrt{6}$; (3) $1$ + +13649 +(1) 在$(-1,1)$上是严格增函数, 在$(1,+\infty)$上是严格减函数; (2) $(-\infty,0]$; (3) 证明略 + +13650 +$\{(0,0),(1,0),(-1,0)\}$ + +13651 +$7$ + +13652 +$-2$ + +13653 +$0$ + +13654 +$\dfrac{6\pi}{5}$ + +13655 +$0.75$ + +13656 +$(-6,2)$ + +13657 +$\dfrac{2\sqrt{3}}3$ + +13658 +$\dfrac{16}3$ + +13659 +$\dfrac\pi 6$ + +13660 +\textcircled{1}\textcircled{2}\textcircled{4} + +13661 +$12120$ + +13662 +B + +13663 +B + +13664 +D + +13665 +D + +13666 +(1) $1$; (2) $\arcsin\dfrac{\sqrt{3}}4$ + +13667 +(1) $\sqrt{7}$; (2) $-1-\dfrac{\sqrt{3}}2$ + +13668 +(1) $(x-2)^2+y^2=\dfrac{12}7$; (2) $\dfrac{3\sqrt{2}}2$或$\dfrac{\sqrt{2}}2$ + +13669 +(1) $\dfrac 25$; (2) $X\sim \begin{pmatrix} 0 & 1 & 2 \\ \dfrac{6}{25} & \dfrac{13}{25} & \dfrac{6}{25}\end{pmatrix}$; (3) 不认为人数有变化, 理由略 + +13670 +(1) $y=x-1$; (2) $(-\infty,\dfrac{3}{2}]$; (3) $(-\infty,\dfrac{\sqrt{2}}2)$ + +13671 +$1$ + +13672 +$3$ + +13673 +$\dfrac 12$ + +13674 +$(0,2)$ + +13675 +$2$ + +13676 +$0.57$ + +13677 +$\dfrac 72+\sqrt{6}$ + +13678 +$\dfrac\pi 3$或$\dfrac{2\pi}3$ + +13679 +$\sqrt{5}$ + +13680 +$\dfrac{7\sqrt{3}}3$ + +13681 +$\dfrac 83$ + +13682 +$\dfrac 32$ + +13683 +A + +13684 +C + +13685 +A + +13686 +B + +13687 +(1) 证明略; (2) $\dfrac\pi 6$ + +13688 +(1) 证明略; (2) $(\dfrac 94,\dfrac{15}4)$ + +13689 +(1) $l=\dfrac{1}{\sin \theta}+\dfrac{1}{\cos\theta}+\dfrac{1}{\sin\theta\cdot \cos\theta}$, $\theta\in (\dfrac\pi 6,\dfrac\pi 3)$; (2) $2+2\sqrt{2}$, 此时$\theta=\dfrac\pi 4$ + +13690 +(1) $\dfrac{\sqrt{2}}2$; (2) $t=\dfrac{\sqrt{6}}3b$ + +13691 +(1) $a=1$, $b=0$; (2) $3$; (3) 证明略 -13511 -(1) 约$16173$升; (2) 从第$13$个月起 diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index ece98c9b..6aa5f380 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -353899,7 +353899,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -353921,7 +353921,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$x=\\mu$", "solution": "", "duration": -1, "usages": [], @@ -353943,7 +353943,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "可能异面, 可能相交", "solution": "", "duration": -1, "usages": [], @@ -353965,7 +353965,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{y^2}{15}+\\dfrac{x^2}{16}=1$, $x\\ne 0$", "solution": "", "duration": -1, "usages": [], @@ -353987,7 +353987,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[1,15]$", "solution": "", "duration": -1, "usages": [], @@ -354009,7 +354009,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 13$", "solution": "", "duration": -1, "usages": [], @@ -354031,7 +354031,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 43$", "solution": "", "duration": -1, "usages": [], @@ -354053,7 +354053,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-1]\\cup [3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -354075,7 +354075,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -354097,7 +354097,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pi$", "solution": "", "duration": -1, "usages": [], @@ -354119,7 +354119,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -354141,7 +354141,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -354163,7 +354163,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -354185,7 +354185,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{5}{12}\\text{h}$; (2) 能, $v$的取值范围为$(\\dfrac{9\\sqrt{3}}2,\\dfrac{\\sqrt{559}}3]$", "solution": "", "duration": -1, "usages": [], @@ -354207,7 +354207,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $\\dfrac{a_1}{a_2}\\le \\dfrac{a_1+a_3+\\cdots+a_{2n-1}}{a_2+a_4+\\cdots+a_{2n}}$, 当且仅当$n=1$或$d=0$时成立等号; (3) $2023^2$", "solution": "", "duration": -1, "usages": [], @@ -354229,7 +354229,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{(0,1),(2,5)\\}$", "solution": "", "duration": -1, "usages": [], @@ -354251,7 +354251,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$x>1$且$y>1$", "solution": "", "duration": -1, "usages": [], @@ -354273,7 +354273,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -354295,7 +354295,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-8]\\cup [2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -354317,7 +354317,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-2,2]$", "solution": "", "duration": -1, "usages": [], @@ -354339,7 +354339,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 13$", "solution": "", "duration": -1, "usages": [], @@ -354361,7 +354361,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{4\\pi}{3}$", "solution": "", "duration": -1, "usages": [], @@ -354383,7 +354383,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$20$", "solution": "", "duration": -1, "usages": [], @@ -354405,7 +354405,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{3}\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -354427,7 +354427,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{3}\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -354449,7 +354449,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -354471,7 +354471,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -354493,7 +354493,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -354515,7 +354515,7 @@ "第九单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 甲与乙的平均数分别为$7$和$7$; (2) 甲与乙的方差分别为$3$和$1.2$; (3) 两人射击水平相当, 甲的发挥更稳定", "solution": "", "duration": -1, "usages": [], @@ -354537,7 +354537,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 12$; (2) $\\dfrac{4\\sqrt{5}}5$", "solution": "", "duration": -1, "usages": [], @@ -354559,7 +354559,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$3.5$", "solution": "", "duration": -1, "usages": [], @@ -354581,7 +354581,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{20}{11}$", "solution": "", "duration": -1, "usages": [], @@ -354603,7 +354603,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$a=\\pm 1$", "solution": "", "duration": -1, "usages": [], @@ -354625,7 +354625,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$-17$", "solution": "", "duration": -1, "usages": [], @@ -354647,7 +354647,7 @@ "第九单元" ], "genre": "填空题", - "ans": "", + "ans": "$0.7$", "solution": "", "duration": -1, "usages": [], @@ -354669,7 +354669,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [], @@ -354691,7 +354691,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$6\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -354713,7 +354713,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$0.6$", "solution": "", "duration": -1, "usages": [], @@ -354735,7 +354735,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\pi^2+16\\pi$", "solution": "", "duration": -1, "usages": [], @@ -354757,7 +354757,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 83$", "solution": "", "duration": -1, "usages": [], @@ -354779,7 +354779,7 @@ "第六单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -354801,7 +354801,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -354823,7 +354823,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -354845,7 +354845,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $f(x)=\\begin{cases}2^x-1+\\log_2 (x+1), & x\\ge 0, \\\\ 1-2^{-x}-\\log_2(-x+1), & x<0;\\end{cases}$ (2) $f(x)=-2^{x-2}+1-\\log_2(x-1)$, $16.635$, 有$99.9\\%$的把握认为患该疾病群体与为患该疾病群体的卫生习惯有差异; (2) 证明略, $R$的估计值为$6$", "solution": "", "duration": -1, "usages": [], @@ -355212,7 +355212,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=2x$; (2) $(-\\infty,-1)$", "solution": "", "duration": -1, "usages": [], @@ -355234,7 +355234,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 12$", "solution": "", "duration": -1, "usages": [], @@ -355256,7 +355256,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\pi$", "solution": "", "duration": -1, "usages": [], @@ -355278,7 +355278,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{6}}2a^2$", "solution": "", "duration": -1, "usages": [], @@ -355300,7 +355300,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$3x-y-2=0$", "solution": "", "duration": -1, "usages": [], @@ -355322,7 +355322,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{3}{25}\\overrightarrow{b}$", "solution": "", "duration": -1, "usages": [], @@ -355344,7 +355344,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$-2$", "solution": "", "duration": -1, "usages": [], @@ -355366,7 +355366,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2\\sqrt{5}}5$", "solution": "", "duration": -1, "usages": [], @@ -355388,7 +355388,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$[\\dfrac 54,\\dfrac{3\\sqrt{17}}4]$", "solution": "", "duration": -1, "usages": [], @@ -355410,7 +355410,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$77$", "solution": "", "duration": -1, "usages": [], @@ -355432,7 +355432,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [], @@ -355454,7 +355454,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -355477,7 +355477,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -355499,7 +355499,7 @@ "第六单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -355522,7 +355522,7 @@ "第九单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $0.89$; (2) $0.0014$", "solution": "", "duration": -1, "usages": [], @@ -355544,7 +355544,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $x^2-\\dfrac{y^2}{3}=1$; (2) 证明略", "solution": "", "duration": -1, "usages": [], @@ -355566,7 +355566,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{1,2\\}$", "solution": "", "duration": -1, "usages": [], @@ -355588,7 +355588,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -355610,7 +355610,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [], @@ -355632,7 +355632,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -355654,7 +355654,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [ @@ -355680,7 +355680,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -355702,7 +355702,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 16$", "solution": "", "duration": -1, "usages": [], @@ -355724,7 +355724,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$-28$", "solution": "", "duration": -1, "usages": [], @@ -355746,7 +355746,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$0.14$", "solution": "", "duration": -1, "usages": [], @@ -355769,7 +355769,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -355791,7 +355791,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\ln 2$", "solution": "", "duration": -1, "usages": [], @@ -355813,7 +355813,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{13}}2$", "solution": "", "duration": -1, "usages": [], @@ -355835,7 +355835,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -355857,7 +355857,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -355879,7 +355879,7 @@ "第九单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -355901,7 +355901,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -355923,7 +355923,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac\\pi 6$; (2) $6+6\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -355945,7 +355945,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $\\dfrac{\\sqrt{6}}8$", "solution": "", "duration": -1, "usages": [], @@ -355967,7 +355967,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $X\\sim \\begin{pmatrix} 0 & 20 & 100\\\\ 0.2 & 0.32 & 0.48\\end{pmatrix}$; (2) 应选择先回答B类问题", "solution": "", "duration": -1, "usages": [], @@ -355989,7 +355989,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{x^2}{25}+\\dfrac{y^2}{9}=1$; (2) $2\\sqrt{2}+\\sqrt{17}$; (3) 定值为$34$", "solution": "", "duration": -1, "usages": [], @@ -356011,7 +356011,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=x$; (2) 在$[0,+\\infty)$上是严格增函数; (3) 证明略", "solution": "", "duration": -1, "usages": [], @@ -356033,7 +356033,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -356055,7 +356055,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$[\\dfrac 12,1]$", "solution": "", "duration": -1, "usages": [], @@ -356077,7 +356077,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -356099,7 +356099,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$x\\le \\dfrac{a+b}{2}$, 等号成立当且仅当$a=b$", "solution": "", "duration": -1, "usages": [], @@ -356121,7 +356121,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$2x-y+1=0$", "solution": "", "duration": -1, "usages": [], @@ -356143,7 +356143,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{3\\pi}{4}$", "solution": "", "duration": -1, "usages": [], @@ -356165,7 +356165,7 @@ "第九单元" ], "genre": "填空题", - "ans": "", + "ans": "$115$", "solution": "", "duration": -1, "usages": [], @@ -356187,7 +356187,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [], @@ -356209,7 +356209,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "如$x^2+(y-2)^2=1$等(答案不唯一)", "solution": "", "duration": -1, "usages": [], @@ -356231,7 +356231,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$(0,-4)$", "solution": "", "duration": -1, "usages": [], @@ -356253,7 +356253,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$72$", "solution": "", "duration": -1, "usages": [], @@ -356275,7 +356275,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 78$", "solution": "", "duration": -1, "usages": [], @@ -356297,7 +356297,7 @@ "第八单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -356319,7 +356319,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -356341,7 +356341,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -356363,7 +356363,7 @@ "第八单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -356385,7 +356385,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 13$; (2) 证明略", "solution": "", "duration": -1, "usages": [], @@ -356407,7 +356407,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a_n=3n-1$; (2) $S_n=\\dfrac{21}{4}-\\dfrac{6n+7}{4\\cdot 3^{n-1}}$", "solution": "", "duration": -1, "usages": [], @@ -356429,7 +356429,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $V=x(3-2x)^2$, $x\\in (0,\\dfrac 32)$; (2) 当$x=\\dfrac 12$时, $V$取到最大值$2$", "solution": "", "duration": -1, "usages": [], @@ -356451,7 +356451,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 最小正周期为$\\pi$, 取值范围为$[-1,2]$; (2) $\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -356473,7 +356473,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2$; (2) 双曲线方程为$x^2-\\dfrac{y^2}{3}=1$, 过顶点$(2,0)$与$(-1,0)$", "solution": "", "duration": -1, "usages": [], @@ -356495,7 +356495,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$或$-6$", "solution": "", "duration": -1, "usages": [], @@ -356517,7 +356517,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac\\pi 6,\\dfrac{5\\pi}6)$", "solution": "", "duration": -1, "usages": [], @@ -356539,7 +356539,7 @@ "第九单元" ], "genre": "填空题", - "ans": "", + "ans": "$44$", "solution": "", "duration": -1, "usages": [], @@ -356561,7 +356561,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$41$", "solution": "", "duration": -1, "usages": [], @@ -356617,7 +356617,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$24$", "solution": "", "duration": -1, "usages": [], @@ -356639,7 +356639,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{7\\sqrt{3}}3\\pi$", "solution": "", "duration": -1, "usages": [], @@ -356661,7 +356661,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$20$", "solution": "", "duration": -1, "usages": [], @@ -356683,7 +356683,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2.5$", "solution": "", "duration": -1, "usages": [], @@ -356705,7 +356705,7 @@ "第九单元" ], "genre": "填空题", - "ans": "", + "ans": "$76$元", "solution": "", "duration": -1, "usages": [], @@ -356727,7 +356727,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$p_1$,$p_4$", "solution": "", "duration": -1, "usages": [], @@ -356749,7 +356749,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 34$", "solution": "", "duration": -1, "usages": [], @@ -356771,7 +356771,7 @@ "第六单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -356793,7 +356793,7 @@ "第六单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -356815,7 +356815,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -356837,7 +356837,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -356859,7 +356859,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -356881,7 +356881,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac\\pi 3$; (2) $(6,12]$", "solution": "", "duration": -1, "usages": [], @@ -356903,7 +356903,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $0.6$; (2) $x\\sim \\begin{pmatrix}0 & 10 & 20 & 30\\\\0.16 & 0.44 & 0.34 & 0.06\\end{pmatrix}$, $E[X]=13$", "solution": "", "duration": -1, "usages": [], @@ -356925,7 +356925,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{x^2}3+y^2=1$; (2) $\\sqrt{6}$; (3) $1$", "solution": "", "duration": -1, "usages": [], @@ -356948,7 +356948,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 在$(-1,1)$上是严格增函数, 在$(1,+\\infty)$上是严格减函数; (2) $(-\\infty,0]$; (3) 证明略", "solution": "", "duration": -1, "usages": [], @@ -356970,7 +356970,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{(0,0),(1,0),(-1,0)\\}$", "solution": "", "duration": -1, "usages": [], @@ -356992,7 +356992,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$7$", "solution": "", "duration": -1, "usages": [], @@ -357014,7 +357014,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-2$", "solution": "", "duration": -1, "usages": [], @@ -357036,7 +357036,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [], @@ -357058,7 +357058,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{6\\pi}{5}$", "solution": "", "duration": -1, "usages": [], @@ -357080,7 +357080,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$0.75$", "solution": "", "duration": -1, "usages": [], @@ -357102,7 +357102,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-6,2)$", "solution": "", "duration": -1, "usages": [], @@ -357124,7 +357124,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2\\sqrt{3}}3$", "solution": "", "duration": -1, "usages": [], @@ -357146,7 +357146,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{16}3$", "solution": "", "duration": -1, "usages": [], @@ -357168,7 +357168,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi 6$", "solution": "", "duration": -1, "usages": [], @@ -357190,7 +357190,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -357212,7 +357212,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$12120$", "solution": "", "duration": -1, "usages": [], @@ -357234,7 +357234,7 @@ "第八单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -357256,7 +357256,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -357278,7 +357278,7 @@ "第九单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -357300,7 +357300,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -357322,7 +357322,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $1$; (2) $\\arcsin\\dfrac{\\sqrt{3}}4$", "solution": "", "duration": -1, "usages": [], @@ -357344,7 +357344,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\sqrt{7}$; (2) $-1-\\dfrac{\\sqrt{3}}2$", "solution": "", "duration": -1, "usages": [], @@ -357366,7 +357366,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(x-2)^2+y^2=\\dfrac{12}7$; (2) $\\dfrac{3\\sqrt{2}}2$或$\\dfrac{\\sqrt{2}}2$", "solution": "", "duration": -1, "usages": [], @@ -357388,7 +357388,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 25$; (2) $X\\sim \\begin{pmatrix} 0 & 1 & 2 \\\\ \\dfrac{6}{25} & \\dfrac{13}{25} & \\dfrac{6}{25}\\end{pmatrix}$; (3) 不认为人数有变化, 理由略", "solution": "", "duration": -1, "usages": [], @@ -357410,7 +357410,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=x-1$; (2) $(-\\infty,\\dfrac{3}{2}]$; (3) $(-\\infty,\\dfrac{\\sqrt{2}}2)$", "solution": "", "duration": -1, "usages": [], @@ -357432,7 +357432,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -357454,7 +357454,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -357476,7 +357476,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 12$", "solution": "", "duration": -1, "usages": [], @@ -357498,7 +357498,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(0,2)$", "solution": "", "duration": -1, "usages": [], @@ -357520,7 +357520,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -357542,7 +357542,7 @@ "第九单元" ], "genre": "填空题", - "ans": "", + "ans": "$0.57$", "solution": "", "duration": -1, "usages": [], @@ -357564,7 +357564,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 72+\\sqrt{6}$", "solution": "", "duration": -1, "usages": [], @@ -357586,7 +357586,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi 3$或$\\dfrac{2\\pi}3$", "solution": "", "duration": -1, "usages": [], @@ -357608,7 +357608,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{5}$", "solution": "", "duration": -1, "usages": [], @@ -357630,7 +357630,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{7\\sqrt{3}}3$", "solution": "", "duration": -1, "usages": [], @@ -357652,7 +357652,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 83$", "solution": "", "duration": -1, "usages": [], @@ -357674,7 +357674,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 32$", "solution": "", "duration": -1, "usages": [], @@ -357696,7 +357696,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -357718,7 +357718,7 @@ "第九单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -357740,7 +357740,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -357762,7 +357762,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -357784,7 +357784,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $\\dfrac\\pi 6$", "solution": "", "duration": -1, "usages": [], @@ -357806,7 +357806,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $(\\dfrac 94,\\dfrac{15}4)$", "solution": "", "duration": -1, "usages": [], @@ -357828,7 +357828,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $l=\\dfrac{1}{\\sin \\theta}+\\dfrac{1}{\\cos\\theta}+\\dfrac{1}{\\sin\\theta\\cdot \\cos\\theta}$, $\\theta\\in (\\dfrac\\pi 6,\\dfrac\\pi 3)$; (2) $2+2\\sqrt{2}$, 此时$\\theta=\\dfrac\\pi 4$", "solution": "", "duration": -1, "usages": [], @@ -357850,7 +357850,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{\\sqrt{2}}2$; (2) $t=\\dfrac{\\sqrt{6}}3b$", "solution": "", "duration": -1, "usages": [], @@ -357872,7 +357872,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a=1$, $b=0$; (2) $3$; (3) 证明略", "solution": "", "duration": -1, "usages": [],