浙江省宁波市鄞州区2018学年第一学期九上期末数学卷（pdf含答案)

鄞州区2018学年度第一学期九年级期末考试 参考答案及评分标准 选择题：（每小题4分，共48分） 题号 1 2 3 4 5 6 7 8 9 10 11 12 答案 A D D C D B C B C A D A 填空题：（每小题4分，共24分） 题号 13 14 15 16 17 18 答案 120° tan46° 25 三、解答题（共78分） 19．解： ···································3分 ·····················································6分 20．解：(1)摸到白球的概率是 .······································· 3分 （2）图略.···················································· 6分 两次摸到红球的概率为 . ································ 8分 21．解：(1) 过点B作交AC于点D. 答：点B离开地面的距离为m.·································3分 过E作交AC、AB于点F、G. 答：AB的长为2.5m. ·····································8分 解：（1）连结BC、OC. AB为直径，∴∠ACB=90°. ∵AB=2BP, ∴AO=OB=BP. ∵AC=BP=OA,∴∠A=30°.······························2分 ∴∠COB=2∠A=60°.∵OB=OC，∴△OCB为正三角形. ∴OB=OC=BC=BP，∴∠BCP=∠P==30°. ∴∠OCP=∠OCB+∠PCB=90°,∴.·····················4分 ∵OC为半径，∴PC与⊙O相切.································5分 （2)∵， ·················7分 扇形OAC的面积为 ··················9分 ∴阴影部分弓形面积为.· ···························10分 23．解：（1）2，2 ···················································2分 （2）图略（扣分讨论） ······················ 6分 （3）B ···············································10分 24．解：（1）由题得：BC=x，AB=10-. 则································2分 x的取值范围为.····································3分 (2) ··················4分 又 ∴当时，s随着x的增大而增大. ∴当时，s的值最大，且最大s=32.····················6分 答：当为4时，矩形花园ABCD的面积最大，最大值为32. (3) 由题得：BC=x，DE=x-4, AB=. 则 ················8分 当时，s的值最大，且最大s=36. ···············10分 答：矩形花园ABCD的面积最大，面积为36. 解（1）画出点D的2个位置。 ·················2分 （2）∵四边形ABCD为被BD分割的友谊四边形 ∴△ABD与△DBC相似. 若△ABD∽△CBD则AB=BC=8. ···························4分 若△ABD∽△DBC则∴AB=6 ·····················6分 综上所述：AB=6或8. ①∵E是的中点，∴ ∴. ∵四边形ABCD内接于圆O，∴. ∵,.∴. ∴△ABF∽△FBC. ∴四边形ABCF为友谊四边形. ···········9分 ②过点A作AG⊥BC交BC与G. ∵△ABF∽△FBC，∴∴· ∴即··················11分 ∵，∴ ··········· ... ...