1.C 2。 B 3。 D 4。 C 5。 B 6。 A seven. D 8。 A

Step 2 fill in the blanks

9.√5 10.4 1 1.-( 1/2) 12.0 & lt； a & lt 1 13.(0,4/3) 14.4 15.48/5

Three. solve problems

16. Solution:

( 1)f(x)= 4 cosx . sin(x+π/6)+a = 4 cosx。 (√3/2 sinx+ 1/2 cos x)+a = 2√3 sinxcosx+2 cos？ x- 1+ 1+a =√3s in2x+cosx+ 1+a = 2s in(2x+π/6+ 1+a)

When sin(2x+π /6),

F(x) gives the maximum value of 2+1+a = 3+a.

And the maximum value of f(x) is 2,

∴3+a=2, which means a=- 1.

The minimum positive period of f(x) is T=2π/2=π.

(2) f(x)=2sin(2x+π /6) is obtained from (1).

∴-(π/2)+2kπ≤2x+π /6≤π/2+2kπ

∴-(π/3)+kπ≤x≤π/6+kπ

The monotonic increasing range of ∴f(x) is [0, π/6] and [2π/3, π].

17. Solution:

( 1)

Always love sports and don't like sports

Male 10 6 16

Female 6 8 14

Total 16 14 30

(2) Hypothesis: Whether you like sports has nothing to do with gender, which can be obtained from the known data:

k？ =[30×( 10×8-6×6)]/( 10+6)(6+8)( 10+6)(6+8)≈ 1. 1575 & lt； 20706

Therefore, under the premise that the probability of making mistakes does not exceed 0. 10, it cannot be judged that the love of sports is related to gender.

(3) The number of people who like sports is 0, 1 2, and its probability is:

P(￡=0)=28/9 1

p(655438+0)= 48/9 1

p(655438+0)= 15/9 1

The percentage of people who like sports to the total number is:

￡ 0 1 2

p 28/9 1 48/9 1 15/9 1

So the number of people who like sports is%, and the value is:

e \ = 0×(28/9 1)+ 1×(48/9 1)+2×( 15/9 1)= 78/9 1

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Sorry, landlord, because it is too difficult to type the answer, and many symbols and tables are difficult to edit, so I will type the question 17. )