Reference answers and grading standards

Mathematics (a)

Description:

1. If the candidate's solution is different from this solution, you can make corresponding scoring rules with reference to this scoring standard.

2. When a candidate gives an incorrect answer in a certain step, which affects the subsequent part, if the answer after this step does not change the content and difficulty of this question, the score for the latter part can be determined according to the degree of influence, but it shall not exceed half of the score for the latter part. If the answer after this step has serious mistakes, it will not be graded.

3. In order to facilitate marking, the calculation steps in this solution are written in detail, but candidates are allowed to reasonably omit non-critical calculation steps in the process of solving problems.

4. Answer the score on the right, which means that the candidate should get the accumulated score if he does this step correctly.

First, multiple-choice questions (this big question * * is a total of 12 small questions, with 4 points for each small question and 48 points for * * *).

The title is123455678911112.

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

Fill in the blanks (this big question has 8 small questions, each with 4 points and * * * 32 points).

13. and; 14.； 15.④; 16.； 17.5

18.90.6; 19.； 20.2

Third, solve the problem (this big problem ***8 questions, * * * 70 points, write the necessary text description, proof process or calculus steps when solving the problem)

2 1. (The full mark of this question is 6)

(1) As shown in figure 1, it is the shadow of the wooden pole in the sun; 2 points

(2) As shown in Figure 2, the point is the light source of the shadow; 4 points

Is the shadow of the person under the light source. 6 points

22. (The full mark of this question is 7 points)

Solution: (1). 1.

The equation has two unequal real roots, 0.2 points.

That's 0.3 points.

(2) Judging from the meaning of the question: 0.4 points.

,

.6 points

.7 points

23. (The full mark of this question is 7 points)

Solution: (1) Xiao Cong's score is: (score) 1.

Xiao Liang's score is 2.

Xiao Cong and Xiao Liang have reached the level of "excellent graduates".

Graduates from Liang Xiao University get better grades. Three points

(2) Xiao Cong should strengthen physical exercise and pay attention to cultivating comprehensive quality. Four points.

Xiao Liang still needs to work hard in the study of cultural knowledge, and his grades need to be further improved. Five points.

(3) The excellent and good rate is .6.

(4) The central angle of "failing" in the sector statistical chart is:

.7 points

24. (The full mark of this question is 9 points)

Solution: (1) Score 1 from the meaning of the question.

Solve.

So the expression of the proportional function is, and the expression of the inverse proportional function is .2 points.

Solution, get. Here, get 0.4 points.

So the coordinates of the intersection of the two function images are (2,2), 0.5 point.

(2) Because the images of the inverse proportional function are in the first quadrant and the third quadrant respectively,

The value of decreases with the increase of the value, 6 points.

So when it's .7.

When, .8 points

When, because,, so .9 points.

25. (The full mark of this question is 9 points)

(1) proves that when,

Say it again,

A quadrilateral is a parallelogram. 3 points

(2) Prove that quadrilateral is parallelogram,

.

.

5 points

(3) The quadrilateral can be a diamond. 6 points

Reason: As shown in the figure, connection,

As can be seen from (2),

Equal to each other.

When, the quadrilateral is a diamond. Seven points

In,,

, again, 8 points.

,

When rotating clockwise around a point, the quadrilateral is a diamond. Nine points

26. (The full mark of this question is 10)

Solution: (1) According to the subject conditions, the coordinates are. 1 point respectively.

Let the analytical formula of parabola be 2 points.

Substituted coordinates, get 3 points.

Get 0.4 points.

So the expression of parabola is 0.5 minutes.

② It can be set, so

6 points

So the length of the column is 0.7 meters.

(3) Assuming that the width of the isolation belt is the sum of the widths of three cars,

Then the point coordinates are .8 points.

If the intersection is a parabola that crosses vertically, score 0.9.

According to the characteristics of parabola, one lane can drive such three cars side by side. 10.

27. (The full mark of this question is 10)

(1) Proof: union, division,.

. .

.3 points

, .

.

It is the tangent of 0.5 point.

② is the diameter.

,

.6 points

Divide equally.

.8 points

Yes,.

Yes,.

Its length is 1cm, and its length is 4 cm. 10 minute.

28. (The full mark of this question is 12)

Solution: (1) According to the meaning of the question, the crease is the symmetry axis of the quadrilateral.

In ..

. .

Point coordinates are (2,4) .2 minutes.

In the middle again.

Solution:.

Point coordinates are three points.

(2) As shown in Figure ①.

I know again,

, again.

Obviously, a quadrilateral is a rectangle.

5 points

, again

At most, there are 0.6 points.

(3)(i) If it is the bottom of an isosceles triangle, then (Figure ①)

In,,, yes, the midpoint,

.

So is this.

Over-acting, the vertical foot is, it is the center line,

, ,

When, is an isosceles triangle.

At this point, the point coordinate is 0.8 points.

(ii) If the waist is an isosceles triangle, (Figure ②)

Yes,.

If you work too hard, you will lose your foot.

, .

.

, .

, ,

When, (), the point coordinate is. 1 1.

According to (1) and (2), a triangle with vertices is an isosceles triangle, and the coordinates of the corresponding points are or. 12 points.