高考数学解答题规范专题练 （含答案）

这是一份高考数学解答题规范专题练 （含答案），共11页。试卷主要包含了已知函数f＝xex＋ax2，已知点M为圆O等内容，欢迎下载使用。
(1)求B和b的值；
(2)求AC边上高的最大值．
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2．(2023·潍坊模拟)如图，在三棱台ABC－A1B1C1中，△ABC为等边三角形，AA1⊥平面ABC，将梯形AA1C1C绕AA1旋转至梯形AA1D1D的位置，二面角D1－AA1－C1的大小为30°.
(1)证明：A1，B1，C1，D1四点共面，且A1D1⊥平面ABB1A1；
(2)若AA1＝A1C1＝2AB＝4，设G为DD1的中点，求直线BB1与平面AB1G所成的角的正弦值．
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3．(2023·深圳模拟)已知函数f(x)＝xex＋ax2(a∈R)．
(1)当a＝－eq \f(1,2)时，求曲线y＝f(x)在点(1，f(1))处的切线方程；
(2)若函数g(x)＝xln x＋xex－f(x)有两个极值点，求实数a的取值范围．
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4．(2023·杭州第二中学模拟)数列{an}满足a1＝1，a2＝2,3an＝an－1＋2an－2，n≥3，n∈N*.
(1)求{an}的通项公式；
(2)若λ≠0，eq \b\lc\(\rc\)(\a\vs4\al\c1(\f(4,3)))n>eq \f(an－\f(8,5),λ)恒成立，求λ的取值范围．
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5．(2023·广东深圳中学模拟)某制药公司研制了一款针对某种病毒的新疫苗．该病毒一般通过病鼠与白鼠之间的接触传染，现有n只白鼠，每只白鼠在接触病鼠后被感染的概率为eq \f(1,2)，被感染的白鼠数用随机变量X表示，假设每只白鼠是否被感染之间相互独立．
(1)若P(X＝5)＝P(X＝95)，求均值E(X)；
(2)接种疫苗后的白鼠被病鼠感染的概率为p(0