{"code":0,"msg":"success","data":[[{"head_title":"单选题","questions":[{"question_id":"8176065","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"1","master_level":"2","exam_type":"2","evaluated":"0","region_ids":"11","grade_id":"9","question_source":"浙江省台州市书生中学2017-2018学年九年级上学期数学开学试卷","mode":"2","title":"下列电视台的台标,是中心对称图形的是( )","kid_num":"1","paperid":"1122521","save_num":"14","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"下列电视台的台标,是中心对称图形的是( )","options":{"A":"","B":"","C":"","D":""},"sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0},"sort":1,"sort2":1,"is_use":0},{"question_id":"6491689","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"3","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"一枚质地均匀的正方体骰子,其六个面分别刻有 1, 2, 3, 4, 5, 6 六个数字,投掷这个骰子一次,则向上一面的数字大于3的概率是( )","kid_num":"2","paperid":"663491","save_num":"22","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"一枚质地均匀的正方体骰子,其六个面分别刻有 六个数字,投掷这个骰子一次,则向上一面的数字大于3的概率是( )
","options":{"A":"","B":"","C":"","D":" "},"sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0},"sort":2,"sort2":2,"is_use":0},{"question_id":"6491691","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"3","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"关于 x 的方程 (m−2)x2+x−3=0 为一元二次方程的条件是( )","kid_num":"1","paperid":"663491","save_num":"26","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"关于 的方程 为一元二次方程的条件是( )
","options":{"A":"","B":"","C":"","D":""},"sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0},"sort":3,"sort2":3,"is_use":0},{"question_id":"6491693","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"1","master_level":"2","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"抛物线 y=(x−3)2−2 的顶点坐标为( ) ","kid_num":"1","paperid":"663491","save_num":"32","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"抛物线 的顶点坐标为( )
","options":{"A":"","B":"","C":"","D":""},"sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0},"sort":4,"sort2":4,"is_use":0},{"question_id":"6491695","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"3","master_level":"2","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"童装专卖店销售一种童装,已知这种童装每天所获得的利润y(元)与童装的销售单价x(元)之间满足关系式y=-x<sup>2</sup>+50x+500,则要想...","kid_num":"2","paperid":"663491","save_num":"32","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"童装专卖店销售一种童装,已知这种童装每天所获得的利润y(元)与童装的销售单价x(元)之间满足关系式y=-x2+50x+500,则要想每天获得最大利润,单价需为( ).
","options":{"A":"25元","B":"20元","C":"30元","D":"40元"},"sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0},"sort":5,"sort2":5,"is_use":0},{"question_id":"6491697","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"3","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"如图,反比例函数y= kx (k≠0)与一次函数y=kx+k(k≠0)在同一平面直角坐标系内的图象可能是( )","kid_num":"4","paperid":"663491","save_num":"39","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"如图,反比例函数y= (k≠0)与一次函数y=kx+k(k≠0)在同一平面直角坐标系内的图象可能是( )
","options":{"A":"","B":"","C":"","D":""},"sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0},"sort":6,"sort2":6,"is_use":0},{"question_id":"6491699","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"3","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"如图, AB 是⊙ O 的直径, ∠AOC=110∘ ,则 ∠D 等于( )","kid_num":"1","paperid":"663491","save_num":"25","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"如图, 是⊙ 的直径, ,则 等于( )
∴顶点坐标为:(-1,-2)
","answer_json":["解:y=x2+2x-1=(x+1)2-2,∴顶点坐标为:(-1,-2)
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"45181325","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"","create_uid":"0","create_date":"2016-02-28 09:05:09","update_by":"","update_uid":"0","update_date":"2021-04-21 19:37:51","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"6491721","sort":19,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"当x取何值时,y随x的增大而增大;∴当x>-1时,y随x的增大而增大
","answer_json":["解:∵y=x2+2x-1=(x+1)2-2的对称轴为:x=-1,开口向上,∴当x>-1时,y随x的增大而增大
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2},{"question_id":"45181327","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"","create_uid":"0","create_date":"2016-02-28 09:05:09","update_by":"","update_uid":"0","update_date":"2021-04-21 19:37:51","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"6491721","sort":20,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求出图象与x轴的交点坐标.","options":"","answer":"解:令y=x2+2x-1=0,解得:x=-1- 或x=-1+ ,∴图象与x轴的交点坐标为(-1- ,0),(-1+ ,0)
","answer_json":["解:令y=x2+2x-1=0,解得:x=-1- 或x=-1+ ,∴图象与x轴的交点坐标为(-1- ,0),(-1+ ,0)
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":3}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0,"subScore":[0,0,0]},"sort":18,"sort2":18,"is_use":0},{"question_id":"6491729","question_type":"5","question_channel_type":"6","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"如图,已知反比例函数y = 的图象经过点A(1,-3),一次函数y =kx +b的图象经过点A与点C(0,-4),且与反比例函数的图象相交于另一点B...","kid_num":"3","paperid":"663491","save_num":"95","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"如图,已知反比例函数y = 的图象经过点A(1,-3),一次函数y =kx +b的图象经过点A与点C(0,-4),且与反比例函数的图象相交于另一点B.试确定点B的坐标.①将△ABC向x轴正方向平移5个单位长度得△A1B1C1.. 。
\n\n②再以O为旋转中心,将△A1B1C1.旋转180°得△A2B2C2 。画出平移和旋转后的图形,并标明对应字母。
","options":"","sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0},"sort":22,"sort2":20,"is_use":0},{"question_id":"6491733","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"如图,在△ABC中,∠C=90°,AD是∠BAC的平分线,O是AB上一点,以OA为半径的⊙O经过点D。","kid_num":"5","paperid":"663491","save_num":"32","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"如图,在△ABC中,∠C=90°,AD是∠BAC的平分线,O是AB上一点,以OA为半径的⊙O经过点D。","options":"","sub_explanation":null,"list":[{"question_id":"45181329","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1348058075_O54gFl","create_uid":"7693066","create_date":"2016-02-28 09:05:09","update_by":"","update_uid":"0","update_date":"2024-01-24 12:13:39","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"6491733","sort":23,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求证:BC是⊙O切线;","options":"","answer":"证明:连接OD;∵AD是∠BAC的平分线,∴∠1=∠3.∵OA=OD,∴∠1=∠2.
∴∠2=∠3.∴OD∥AC.
∴∠ODB=∠ACB=90°.∴OD⊥BC.
∴BC是⊙O切线.
","answer_json":["证明:连接OD;∵AD是∠BAC的平分线,∴∠1=∠3.∵OA=OD,∴∠1=∠2.
∴∠2=∠3.∴OD∥AC.
∴∠ODB=∠ACB=90°.∴OD⊥BC.
∴BC是⊙O切线.
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"45181331","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1348058075_O54gFl","create_uid":"7693066","create_date":"2016-02-28 09:05:09","update_by":"","update_uid":"0","update_date":"2024-01-24 12:13:40","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"6491733","sort":24,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"若BD=5,DC=3,求AC的长。","options":"","answer":"蛸:过点D作DE⊥AB,∵AD是∠BAC的平分线,
∴CD=DE=3.
在Rt△BDE中,∠BED=90°,由勾股定理得:BE= =4,
∵∠BED=∠ACB=90°,∠B=∠B,
∴△BDE∽△BAC.
∴ .∴ .∴AC=6.
","answer_json":["蛸:过点D作DE⊥AB,∵AD是∠BAC的平分线,
∴CD=DE=3.
在Rt△BDE中,∠BED=90°,由勾股定理得:BE= =4,
∵∠BED=∠ACB=90°,∠B=∠B,
∴△BDE∽△BAC.
∴ .∴ .∴AC=6.
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0,"subScore":[0,0]},"sort":23,"sort2":21,"is_use":0},{"question_id":"6491739","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"某商场销售一批名牌衬衫,平均每天可售出20件,每件盈利40元。为了扩大销售,增加盈利,尽快减少库存,商场决定采取适当的降价措施,经调查...","kid_num":"4","paperid":"663491","save_num":"34","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"某商场销售一批名牌衬衫,平均每天可售出20件,每件盈利40元。为了扩大销售,增加盈利,尽快减少库存,商场决定采取适当的降价措施,经调查发现,如果每件衬衫每降价1元,商场平均每天可多售出2件。答:每天销售这种衬衫的盈利要达到1200元,则每件衬衫应降价20元
","answer_json":["解:设每件衬衫应降价x元,根据题意,得:(40-x)(20+2x)=1200,解得:x=10或x=20,∵商场要尽快减少库存,∴x=20,答:每天销售这种衬衫的盈利要达到1200元,则每件衬衫应降价20元
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"33404053","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"","create_uid":"0","create_date":"2016-02-28 09:05:09","update_by":"","update_uid":"0","update_date":"2021-04-21 19:37:51","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"6491739","sort":26,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"每件衬衫降价多少元,商场平均每天盈利最多?答:当每件降价15元时,商场平均每天盈利最多
","answer_json":["解:设每套降价x元,商场平均每天赢利y元,则y=(40-x)(20+2x)=-2x2+60x+800=-2(x-15)2+1250,当x=15时,y有最大值为1250元,答:当每件降价15元时,商场平均每天盈利最多
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0,"subScore":[0,0]},"sort":25,"sort2":22,"is_use":0},{"question_id":"6491745","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"一个不透明的袋中装有5个黄球,13个黑球和22个红球,这些球除颜色外其他都相同.","kid_num":"4","paperid":"663491","save_num":"37","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"一个不透明的袋中装有5个黄球,13个黑球和22个红球,这些球除颜色外其他都相同.∴摸出一个球摸是黄球的概率为:
","answer_json":["解:∵一个不透明的袋中装有5个黄球,13个黑球和22个红球,∴摸出一个球摸是黄球的概率为:
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"45181349","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1348058075_O54gFl","create_uid":"7693066","create_date":"2016-02-28 09:05:09","update_by":"","update_uid":"0","update_date":"2023-11-03 23:52:54","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"6491745","sort":28,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"现在从袋中取出若干个黑球,并放入相同数量的黄球,搅拌均匀后,使从袋中摸出一个球是黄球的概率不小于 ,问:至少取出多少个黑球?由题意,得 ,
解得:x≥ ,
∵x为整数,
∴x的最小正整数解是x=9.
答:至少取走了9个黑球
","answer_json":["解:设取走x个黑球,则放入x个黄球,由题意,得 ,
解得:x≥ ,
∵x为整数,
∴x的最小正整数解是x=9.
答:至少取走了9个黑球
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0,"subScore":[0,0]},"sort":27,"sort2":23,"is_use":0},{"question_id":"6491751","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"5","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"在⊙O中,AB为⊙O的直径,AC是弦, OC=4 , ∠OAC=60∘ .","kid_num":"5","paperid":"663491","save_num":"58","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"在⊙O中,AB为⊙O的直径,AC是弦, , .∴∠P=90°-∠AOC=30°,
∴在Rt△POC中,CO= PO=4,则PO=2CO=8
","answer_json":["解:∵CP与⊙O相切,OC是半径.∴CP⊥OC,又∵∠OAC=∠AOC=60°,∴∠P=90°-∠AOC=30°,
∴在Rt△POC中,CO= PO=4,则PO=2CO=8
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"45181345","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1348058075_O54gFl","create_uid":"7693066","create_date":"2016-02-28 09:05:09","update_by":"","update_uid":"0","update_date":"2024-01-24 12:13:45","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"6491751","sort":30,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"如图2,一动点M从A点出发,在⊙O上按逆时针方向运动一周,当 时,求半径OM所扫过的扇形的面积.易得S△M1AO=S△CAO , ∠AOM1=60°∴当点M运动到M1时,S△MAO=S△CAO ,
此时点M经过的弧长为 ,∴半径OM所扫过的扇形的面积= ;
②过点M1作M1M2∥AB交⊙O于点M2 , 连接AM2 , OM2 , 易得S△M2AO=S△CAO .
∴∠AOM1=∠M1OM2=∠BOM2=60°
∴ 或 ,∴当点M运动到M2时,S△MAO=S△CAO , 此时点M经过的弧长为 ,
∴半径OM所扫过的扇形的面积= × ×4= π;
③过点C作CM3∥AB交⊙O于点M3 , 连接AM3 , OM3 , 易得S△M3AO=S△CAO∴∠BOM3=60°,∴ = ×240或 = ×2= ∴当点M运动到M3时,S△MAO=S△CAO , 此时点M经过的弧长为 ,∴半径OM所扫过的扇形的面积= × ×4= ;④当点M运动到C时,M与C重合,S△MAO=S△CAO ,此时点M经过的弧长为 ×300°或 π+ =
∴半径OM所扫过的扇形的面积= × ×4=
","answer_json":["解:如图, ①作点C关于直径AB的对称点M1,连接AM1,OM1.易得S△M1AO=S△CAO,∠AOM1=60°∴当点M运动到M1时,S△MAO=S△CAO,
此时点M经过的弧长为 ,∴半径OM所扫过的扇形的面积= ;
②过点M1作M1M2∥AB交⊙O于点M2,连接AM2,OM2,易得S△M2AO=S△CAO.
∴∠AOM1=∠M1OM2=∠BOM2=60°
∴ 或 ,∴当点M运动到M2时,S△MAO=S△CAO,此时点M经过的弧长为 ,
∴半径OM所扫过的扇形的面积= × ×4= π;
③过点C作CM3∥AB交⊙O于点M3,连接AM3,OM3,易得S△M3AO=S△CAO∴∠BOM3=60°,∴ = ×240或 = ×2= ∴当点M运动到M3时,S△MAO=S△CAO,此时点M经过的弧长为 ,∴半径OM所扫过的扇形的面积= × ×4= ;④当点M运动到C时,M与C重合,S△MAO=S△CAO,此时点M经过的弧长为 ×300°或 π+ =
∴半径OM所扫过的扇形的面积= × ×4=
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0,"subScore":[0,0]},"sort":29,"sort2":24,"is_use":0},{"question_id":"6491757","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"5","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"13","grade_id":"9","question_source":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷","mode":"2","title":"如图,抛物线 y=−(x−1)2+c 与 x 轴交于点 A、B (点 A、B 分别在 y 轴的左右两侧)两点,与 y 轴的正半轴交于点 C ,顶点为 D ,已知点 A(−1,0) .","kid_num":"5","paperid":"663491","save_num":"55","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663491","title":"福建省仙游县第六片区2016届九年级上学期数学期末考试试卷"},"extra_file":"","question_text":"如图,抛物线 与 轴交于点 (点 分别在 轴的左右两侧)两点,与 轴的正半轴交于点 ,顶点为 ,已知点 .∵点A(-1,0)在抛物线y=-(x-1)2+c上,
∴0=-(-1-1)2+c,得c=4,
∴抛物线解析式为:y=-(x-1)2+4,
令x=0,得y=3,∴C(0,3);
令y=0,得x=-1或x=3,∴B(3,0).
","answer_json":["解:如答题1所示:∵点A(-1,0)在抛物线y=-(x-1)2+c上,
∴0=-(-1-1)2+c,得c=4,
∴抛物线解析式为:y=-(x-1)2+4,
令x=0,得y=3,∴C(0,3);
令y=0,得x=-1或x=3,∴B(3,0).
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"45181335","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1348058075_O54gFl","create_uid":"7693066","create_date":"2016-02-28 09:05:09","update_by":"","update_uid":"0","update_date":"2024-01-24 12:13:42","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"6491757","sort":32,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"判断△ 的形状,并说明理由;","options":"","answer":"解:△CDB为直角三角形.理由如下:由抛物线解析式,得顶点D的坐标为(1,4).
如答图1所示,过点D作DM⊥x轴于点M,则OM=1,DM=4,BM=OB-OM=2.
过点C作CN⊥DM于点N,则CN=1,DN=DM-MN=DM-OC=1.
在Rt△OBC中,由勾股定理得:BC= ;
在Rt△CND中,由勾股定理得:CD= ;
在Rt△BMD中,由勾股定理得:BD= .
∵BC2+CD2=BD2 ,
∴△CDB为直角三角形(勾股定理的逆定理)
","answer_json":["解:△CDB为直角三角形.理由如下:由抛物线解析式,得顶点D的坐标为(1,4).
如答图1所示,过点D作DM⊥x轴于点M,则OM=1,DM=4,BM=OB-OM=2.
过点C作CN⊥DM于点N,则CN=1,DN=DM-MN=DM-OC=1.
在Rt△OBC中,由勾股定理得:BC= ;
在Rt△CND中,由勾股定理得:CD= ;
在Rt△BMD中,由勾股定理得:BD= .
∵BC2+CD2=BD2,
∴△CDB为直角三角形(勾股定理的逆定理)
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2},{"question_id":"45181337","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1348058075_O54gFl","create_uid":"7693066","create_date":"2016-02-28 09:05:09","update_by":"","update_uid":"0","update_date":"2024-01-24 12:13:42","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"6491757","sort":33,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"将△ 沿 轴向右平移 个单位( )得到△ .△ 与△ 重叠部分(如图中阴影)面积为 ,求 与 的函数关系式,并写出自变量 的取值范围.在△COB向右平移的过程中:
(I)当0<t≤ 时,如答图2所示:
设PQ与BC交于点K,可得QK=CQ=t,PB=PK=3-t.设QE与BD的交点为F,则: ,解得 ,∴F(3-t,2t).S=S△QPE-S△PBK-S△FBE= PE•PQ- PB•PK- BE•yF= ×3×3- (3-t)2- t•2t=- t2+3t;
(II)当 <t<3时,如答图3所示:
设PQ分别与BC、BD交于点K、点J.∵CQ=t,
∴KQ=t,PK=PB=3-t.直线BD解析式为y=-2x+6,令x=t,得y=6-2t,∴J(t,6-2t).S=S△PBJ-S△PBK= PB•PJ- PB•PK= (3-t)(6-2t)- (3-t)2= t2-3t+ .
综上所述,S与t的函数关系式为:S= .
","answer_json":["解:设直线BC的解析式为y=kx+b,∵B(3,0),C(0,3),∴ ,解得k=-1,b=3,∴y=-x+3,直线QE是直线BC向右平移t个单位得到,∴直线QE的解析式为:y=-(x-t)+3=-x+3+t;设直线BD的解析式为y=mx+n,∵B(3,0),D(1,4),∴ ,解得:m=-2,n=6,∴y=-2x+6.连接CQ并延长,射线CQ交BD于点G,则G( ,3).在△COB向右平移的过程中:
(I)当0<t≤ 时,如答图2所示:
设PQ与BC交于点K,可得QK=CQ=t,PB=PK=3-t.设QE与BD的交点为F,则: ,解得 ,∴F(3-t,2t).S=S△QPE-S△PBK-S△FBE= PE•PQ- PB•PK- BE•yF= ×3×3- (3-t)2- t•2t=- t2+3t;
(II)当 <t<3时,如答图3所示:
设PQ分别与BC、BD交于点K、点J.∵CQ=t,
∴KQ=t,PK=PB=3-t.直线BD解析式为y=-2x+6,令x=t,得y=6-2t,∴J(t,6-2t).S=S△PBJ-S△PBK= PB•PJ- PB•PK= (3-t)(6-2t)- (3-t)2= t2-3t+ .
综上所述,S与t的函数关系式为:S= .
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":3}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":0,"subScore":[0,0,0]},"sort":31,"sort2":25,"is_use":0}],"scores":[],"sum_score":0,"question_num":10}],33,[{"is_old_zujuan663491":""},{"is_old_zujuan663491":{"1":""}},{"is_old_zujuan663491":{"list":["","",""]}}],[{"question_id":"8176065","parent_id":"0","question_type":"1","myanswer":"","X1":0,"x2":0},{"question_id":"6491689","parent_id":"0","question_type":"1","myanswer":"","X1":1,"x2":0},{"question_id":"6491691","parent_id":"0","question_type":"1","myanswer":"","X1":2,"x2":0},{"question_id":"6491693","parent_id":"0","question_type":"1","myanswer":"","X1":3,"x2":0},{"question_id":"6491695","parent_id":"0","question_type":"1","myanswer":"","X1":4,"x2":0},{"question_id":"6491697","parent_id":"0","question_type":"1","myanswer":"","X1":5,"x2":0},{"question_id":"6491699","parent_id":"0","question_type":"1","myanswer":"","X1":6,"x2":0},{"question_id":"6491701","parent_id":"0","question_type":"1","myanswer":"","X1":7,"x2":0},{"question_id":"6491703","parent_id":"0","question_type":"1","myanswer":"","X1":8,"x2":0},{"question_id":"6491705","parent_id":"0","question_type":"4","myanswer":{"1":""},"X1":9,"x2":0},{"question_id":"6491707","parent_id":"0","question_type":"4","myanswer":{"1":""},"X1":10,"x2":0},{"question_id":"6491709","parent_id":"0","question_type":"4","myanswer":{"1":""},"X1":11,"x2":0},{"question_id":"6491711","parent_id":"0","question_type":"4","myanswer":{"1":""},"X1":12,"x2":0},{"question_id":"6491713","parent_id":"0","question_type":"4","myanswer":{"1":""},"X1":13,"x2":0},{"question_id":"6491715","parent_id":"0","question_type":"4","myanswer":{"1":""},"X1":14,"x2":0},{"question_id":"6491717","parent_id":"0","question_type":"5","myanswer":"","X1":15,"x2":0},{"question_id":"6491719","parent_id":"0","question_type":"5","myanswer":"","X1":16,"x2":0},{"question_id":"6491721","parent_id":"0","question_type":"7","myanswer":"","X1":17,"x2":0},{"question_id":"45181323","parent_id":"6491721","question_type":"5","myanswer":"","X1":18,"x2":0},{"question_id":"45181325","parent_id":"6491721","question_type":"5","myanswer":"","X1":18,"x2":1},{"question_id":"45181327","parent_id":"6491721","question_type":"5","myanswer":"","X1":18,"x2":2},{"question_id":"6491729","parent_id":"0","question_type":"5","myanswer":"","X1":18,"x2":0},{"question_id":"6491731","parent_id":"0","question_type":"5","myanswer":"","X1":19,"x2":0},{"question_id":"6491733","parent_id":"0","question_type":"7","myanswer":"","X1":20,"x2":0},{"question_id":"45181329","parent_id":"6491733","question_type":"5","myanswer":"","X1":21,"x2":0},{"question_id":"45181331","parent_id":"6491733","question_type":"5","myanswer":"","X1":21,"x2":1},{"question_id":"6491739","parent_id":"0","question_type":"7","myanswer":"","X1":21,"x2":0},{"question_id":"33403661","parent_id":"6491739","question_type":"5","myanswer":"","X1":22,"x2":0},{"question_id":"33404053","parent_id":"6491739","question_type":"5","myanswer":"","X1":22,"x2":1},{"question_id":"6491745","parent_id":"0","question_type":"7","myanswer":"","X1":22,"x2":0},{"question_id":"45181347","parent_id":"6491745","question_type":"5","myanswer":"","X1":23,"x2":0},{"question_id":"45181349","parent_id":"6491745","question_type":"5","myanswer":"","X1":23,"x2":1},{"question_id":"6491751","parent_id":"0","question_type":"7","myanswer":"","X1":23,"x2":0},{"question_id":"45181343","parent_id":"6491751","question_type":"5","myanswer":"","X1":24,"x2":0},{"question_id":"45181345","parent_id":"6491751","question_type":"5","myanswer":"","X1":24,"x2":1},{"question_id":"6491757","parent_id":"0","question_type":"7","myanswer":"","X1":24,"x2":0},{"question_id":"45181333","parent_id":"6491757","question_type":"5","myanswer":"","X1":25,"x2":0},{"question_id":"45181335","parent_id":"6491757","question_type":"5","myanswer":"","X1":25,"x2":1},{"question_id":"45181337","parent_id":"6491757","question_type":"5","myanswer":"","X1":25,"x2":2}]],"_timestamp":null,"action":"test"}