Reference answers to liberal arts mathematics

1. Multiple-choice questions: (This topic is entitled * * 10, with 5 points for each question and 50 points for * * *).

The title is 1 23455 6789 10.

Answer d c d b b b b b b b b d d

Fill in the blanks (this big topic is a small topic, and each small topic is divided into * * * points)

1 1. 12. 13. 14.60

15.Ab； C.

Third, solve the problem (this big question is ***6 small questions, and the score is ***75. The answer should be written in proof process or calculus steps. )

16. solution: (I) all possible results are ... 6 points.

(2) If the absolute value of the difference between two ball numbers is, the value of can only be 1, including (1, 2), (2,3), (3,4) and (4,5), so the probability of finding it is.

Answer: The probability that the absolute value of the difference between two ball numbers is less than 2 is ..........................................................................................................................................................

17. Solution: (i), 4 points.

Six points.

(2) In,,,

Nine points

According to sine theorem: .................................................................. 10.

= ...............................12.

18. Answer: (i) If yes, it does not meet the meaning of the question, Ⅷ

When, by.

∴ ................................................. 6 points.

(ii) * .................................................................. 7 points.

9 points.

= = ...12 point

19. Solution: (1) As shown in the figure, the connecting line is a parallelogram.

Yes intersection, yes midpoint.

It's the midpoint again,

Say it again, ... six points.

(Ⅱ) ............................................................................................................................................................................

20. Solution: (i) If a parabola is set, then,

Accordingly, it is verified that point (3,) and point (4, 4) are on a parabola, and it is easy to get ....................................................................................................................................

Suppose: Substituting points (2,0) and (,) gives:

The solution of equation∴is ..................................... 5 points.

(ii) When it is easy to verify that the slope of the straight line does not exist, the meaning of the problem is not satisfied. ................................................................................................................................................

When the slope of a straight line exists, suppose there is a straight line passing through the parabolic focus, and its equation is, and the coordinates of the intersection of the sum are.

By excluding and arranging,

So ... ① ..................................................... scored 8 points.

.

That is, ....................................................................................................... scored 9 points.

Press, that is, press (*).

Substitute ① and ② into formula (*) to obtain, obtain,

So there is a condition that a straight line satisfies, and the equation is: or ... 12 points.

2 1. Solution (1)

When, when,

It decreases monotonously in history and increases monotonously in history.

There is a minimum value.

(ii) Timeliness and guidance

When the world is monotonously decreasing;

When the world is monotonous.

Seven points

.......................................... scored 9 points when the inequality was established.

(iii) Assuming the existence of positive real numbers, the minimum value is 3,

10 integral.

When, monotonously decreasing in the world, monotonously increasing in the world.

Meet the conditions.

(2) When ≥, it is monotonically decreasing, so there is no minimum value at this time. ....................................................................................................................................................

To sum up, there are real numbers, so there is a minimum value of 3 ......................14.