翰林刷题
首页
题库市场
个人中心
登录
题目详情
单选题
（中学）数学学科知识与教学能力
A
充分不必要条件
B
必要不充分条件
正确答案
C
充要条件
D
既不充分也不必要条件
正确答案：
B
详细解析
所属课程：
（中学）数学学科知识与教学能力
考试类型：
教师考试
相关题目
简述《标准》中总体目标四个方面的关系？
问答题
学生的数感主要表现在哪些方面？?
问答题
在学生的学习活动中，教师的“组织”作用主要体现在哪些方面？
问答题
怎样理解学生主体地位和教师主导作用的关系，如何使学生成为学习的主体？
问答题
数学是研究_________和_________的科学。
问答题
基本
文件
流程
错误
SQL
调试
请求信息 : 2026-08-18 14:32:47 HTTP/2.0 GET : web.20230611.cn/index/question/detail/id/2422794.html
运行时间 : 0.068919s [ 吞吐率：14.51req/s ] 内存消耗：391.30kb 文件加载：143
查询信息 : 3 queries 0 writes
缓存信息 : 0 reads,1 writes
配置加载 : 78
/www/wwwroot/learn/thinker/admin/public/index.php ( 0.88 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/start.php ( 0.72 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/base.php ( 2.60 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Loader.php ( 21.07 KB )
/www/wwwroot/learn/thinker/admin/vendor/composer/autoload_static.php ( 17.49 KB )
/www/wwwroot/learn/thinker/admin/vendor/symfony/polyfill-php80/bootstrap.php ( 1.50 KB )
/www/wwwroot/learn/thinker/admin/vendor/symfony/polyfill-mbstring/bootstrap.php ( 8.26 KB )
/www/wwwroot/learn/thinker/admin/vendor/symfony/polyfill-intl-normalizer/bootstrap.php ( 0.71 KB )
/www/wwwroot/learn/thinker/admin/vendor/symfony/polyfill-intl-idn/bootstrap.php ( 4.52 KB )
/www/wwwroot/learn/thinker/admin/vendor/symfony/deprecation-contracts/function.php ( 0.98 KB )
/www/wwwroot/learn/thinker/admin/vendor/ralouphie/getallheaders/src/getallheaders.php ( 1.60 KB )
/www/wwwroot/learn/thinker/admin/vendor/guzzlehttp/promises/src/functions_include.php ( 0.16 KB )
/www/wwwroot/learn/thinker/admin/vendor/guzzlehttp/promises/src/functions.php ( 9.89 KB )
/www/wwwroot/learn/thinker/admin/vendor/guzzlehttp/psr7/src/functions_include.php ( 0.15 KB )
/www/wwwroot/learn/thinker/admin/vendor/guzzlehttp/psr7/src/functions.php ( 13.09 KB )
/www/wwwroot/learn/thinker/admin/vendor/guzzlehttp/guzzle/src/functions_include.php ( 0.16 KB )
/www/wwwroot/learn/thinker/admin/vendor/guzzlehttp/guzzle/src/functions.php ( 9.70 KB )
/www/wwwroot/learn/thinker/admin/vendor/symfony/polyfill-php73/bootstrap.php ( 0.99 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/abs.php ( 0.81 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/acos.php ( 1.04 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/acosh.php ( 0.90 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/acot.php ( 0.74 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/acoth.php ( 0.76 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/acsc.php ( 0.83 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/acsch.php ( 0.86 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/argument.php ( 0.81 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/asec.php ( 0.83 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/asech.php ( 0.85 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/asin.php ( 1.01 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/asinh.php ( 0.91 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/atan.php ( 1.34 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/atanh.php ( 1.08 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/conjugate.php ( 0.74 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/cos.php ( 0.92 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/cosh.php ( 0.90 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/cot.php ( 0.83 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/coth.php ( 0.74 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/csc.php ( 0.82 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/csch.php ( 0.84 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/exp.php ( 0.92 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/inverse.php ( 0.87 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/ln.php ( 0.94 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/log2.php ( 1.06 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/log10.php ( 1.08 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/negative.php ( 0.76 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/pow.php ( 1.27 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/rho.php ( 0.84 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/sec.php ( 0.71 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/sech.php ( 0.74 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/sin.php ( 0.87 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/sinh.php ( 0.90 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/sqrt.php ( 0.81 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/tan.php ( 1.21 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/tanh.php ( 1.11 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/functions/theta.php ( 1.25 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/operations/add.php ( 1.26 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/operations/subtract.php ( 1.28 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/operations/multiply.php ( 1.41 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/operations/divideby.php ( 1.75 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/complex/classes/src/operations/divideinto.php ( 1.75 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/adjoint.php ( 0.69 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/antidiagonal.php ( 0.74 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/cofactors.php ( 0.70 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/determinant.php ( 0.71 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/diagonal.php ( 0.70 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/identity.php ( 0.70 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/inverse.php ( 0.69 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/minors.php ( 0.69 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/trace.php ( 0.69 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Functions/transpose.php ( 0.71 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Operations/add.php ( 0.93 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Operations/directsum.php ( 0.95 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Operations/subtract.php ( 0.96 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Operations/multiply.php ( 0.98 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Operations/divideby.php ( 0.96 KB )
/www/wwwroot/learn/thinker/admin/vendor/markbaker/matrix/classes/src/Operations/divideinto.php ( 1.00 KB )
/www/wwwroot/learn/thinker/admin/vendor/topthink/think-helper/src/helper.php ( 2.88 KB )
/www/wwwroot/learn/thinker/admin/vendor/karsonzhang/fastadmin-addons/src/common.php ( 15.07 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Route.php ( 60.23 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Config.php ( 6.38 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Hook.php ( 4.71 KB )
/www/wwwroot/learn/thinker/admin/vendor/overtrue/wechat/src/Kernel/Support/Helpers.php ( 2.63 KB )
/www/wwwroot/learn/thinker/admin/vendor/overtrue/wechat/src/Kernel/Helpers.php ( 1.89 KB )
/www/wwwroot/learn/thinker/admin/vendor/topthink/think-captcha/src/helper.php ( 1.59 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Validate.php ( 42.78 KB )
/www/wwwroot/learn/thinker/admin/vendor/topthink/think-queue/src/common.php ( 1.19 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Console.php ( 23.13 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Error.php ( 3.75 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/convention.php ( 10.37 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/App.php ( 21.58 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Request.php ( 50.00 KB )
/www/wwwroot/learn/thinker/admin/application/config.php ( 12.14 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Env.php ( 1.21 KB )
/www/wwwroot/learn/thinker/admin/application/database.php ( 2.09 KB )
/www/wwwroot/learn/thinker/admin/application/extra/addons.php ( 0.56 KB )
/www/wwwroot/learn/thinker/admin/application/extra/jwt.php ( 0.34 KB )
/www/wwwroot/learn/thinker/admin/application/extra/mcp.php ( 0.27 KB )
/www/wwwroot/learn/thinker/admin/application/extra/queue.php ( 0.55 KB )
/www/wwwroot/learn/thinker/admin/application/extra/site.php ( 0.96 KB )
/www/wwwroot/learn/thinker/admin/application/extra/upload.php ( 0.84 KB )
/www/wwwroot/learn/thinker/admin/application/tags.php ( 1.23 KB )
/www/wwwroot/learn/thinker/admin/application/common.php ( 23.67 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/helper.php ( 17.30 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Debug.php ( 7.13 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Log.php ( 6.05 KB )
/www/wwwroot/learn/thinker/admin/addons/alioss/Alioss.php ( 3.68 KB )
/www/wwwroot/learn/thinker/admin/vendor/karsonzhang/fastadmin-addons/src/Addons.php ( 7.05 KB )
/www/wwwroot/learn/thinker/admin/addons/summernote/Summernote.php ( 1.01 KB )
/www/wwwroot/learn/thinker/admin/addons/user/User.php ( 2.53 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Cache.php ( 6.10 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/cache/driver/File.php ( 7.27 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/cache/Driver.php ( 5.98 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/View.php ( 6.77 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/view/driver/Think.php ( 5.64 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Template.php ( 44.92 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/template/driver/File.php ( 2.24 KB )
/www/wwwroot/learn/thinker/admin/application/common/behavior/Common.php ( 3.02 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Lang.php ( 7.42 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/lang/zh-cn.php ( 11.81 KB )
/www/wwwroot/learn/thinker/admin/application/index/lang/zh-cn.php ( 10.79 KB )
/www/wwwroot/learn/thinker/admin/extend/fast/Form.php ( 39.79 KB )
/www/wwwroot/learn/thinker/admin/addons/alioss/config.php ( 6.08 KB )
/www/wwwroot/learn/thinker/admin/application/index/controller/Question.php ( 3.29 KB )
/www/wwwroot/learn/thinker/admin/application/common/controller/Frontend.php ( 4.81 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Controller.php ( 6.07 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/traits/controller/Jump.php ( 4.92 KB )
/www/wwwroot/learn/thinker/admin/application/common/library/Auth.php ( 14.54 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Cookie.php ( 8.17 KB )
/www/wwwroot/learn/thinker/admin/application/common/model/Config.php ( 6.71 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Model.php ( 69.88 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Url.php ( 12.72 KB )
/www/wwwroot/learn/thinker/admin/addons/alioss/library/Auth.php ( 3.61 KB )
/www/wwwroot/learn/thinker/admin/addons/summernote/config.php ( 3.35 KB )
/www/wwwroot/learn/thinker/admin/application/common/model/CourseQuestion.php ( 3.24 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Db.php ( 6.67 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/db/connector/Mysql.php ( 3.89 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/db/Connection.php ( 29.98 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/db/Query.php ( 93.80 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/db/builder/Mysql.php ( 4.53 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/db/Builder.php ( 31.81 KB )
/www/wwwroot/learn/thinker/admin/runtime/temp/9da0f67e63f61dc8b3e98590381a4945.php ( 15.61 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/Response.php ( 8.28 KB )
/www/wwwroot/learn/thinker/admin/thinkphp/library/think/debug/Html.php ( 4.17 KB )
[ BEHAVIOR ] Run Closure @app_init [ RunTime:0.000025s ]
[ CACHE ] INIT File
[ BEHAVIOR ] Run \addons\alioss\Alioss @app_init [ RunTime:0.000627s ]
[ BEHAVIOR ] Run Closure @app_init [ RunTime:0.000653s ]
[ BEHAVIOR ] Run app\common\behavior\Common @app_init [ RunTime:0.000158s ]
[ LANG ] /www/wwwroot/learn/thinker/admin/thinkphp/lang/zh-cn.php
[ BEHAVIOR ] Run app\common\behavior\Common @app_dispatch [ RunTime:0.000023s ]
[ ROUTE ] array ( 'type' => 'module', 'module' => array ( 0 => 'index', 1 => 'question', 2 => 'detail', ), )
[ HEADER ] array ( 'accept-encoding' => 'gzip, br, zstd, deflate', 'user-agent' => 'Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)', 'accept' => '*/*', 'host' => 'web.20230611.cn', 'content-length' => '', 'content-type' => '', )
[ PARAM ] array ( 'id' => '2422794', )
[ LANG ] /www/wwwroot/learn/thinker/admin/public/../application/index/lang/zh-cn.php
[ BEHAVIOR ] Run app\common\behavior\Common @module_init [ RunTime:0.003305s ]
[ BEHAVIOR ] Run \addons\alioss\Alioss @module_init [ RunTime:0.000170s ]
[ BEHAVIOR ] Run \addons\user\User @upload_config_checklogin [ RunTime:0.000033s ]
[ BEHAVIOR ] Run \addons\alioss\Alioss @upload_config_init [ RunTime:0.000118s ]
[ BEHAVIOR ] Run \addons\summernote\Summernote @config_init [ RunTime:0.003154s ]
[ RUN ] app\index\controller\Question->detail[ /www/wwwroot/learn/thinker/admin/application/index/controller/Question.php ]
[ DB ] INIT mysql
[ VIEW ] /www/wwwroot/learn/thinker/admin/public/../application/index/view/question/detail.html [ array ( 0 => 'user', 1 => 'site', 2 => 'config', 3 => 'question', 4 => 'relatedQuestions', ) ]
0.082077s
