Mathematics Examination (1) Reference Answers and Scoring Instructions
First, multiple-choice questions (3 points out of 36 points for each question)
The title is123455678911112.
Answer D C B B C B A A C A D B
Fill in the blanks (3 points for each small question, full mark 15)
13. 14. 15.3 16. 17.47
Three, solve the problem (out of 69 points)
18. (The full mark of this question is 6)
Solution:
3 points
6 points
19. (The full mark of this question is 7)
Solution: Suppose a classmate donates 10 yuan and a classmate donates to 20 yuan. According to the meaning of the question, they get.
3 points
Simplify, get 4 points
Solve this system of equations and get 6 points.
Answer: Donation1There are 4 students in 0 yuan and 38 students in 20 yuan. Seven points
20. (The full mark of this question is 8)
Solution:
.2 points
Namely.
Get 0.4 points.
Similarly, you can learn from.
So Xiao Ming's figure became shorter by 3.5 meters and 8 minutes.
2 1. (The full mark of this question is 8)
Solution: (1); 3 points
(2) Make up the histogram as shown in the figure: 5 points.
(3) The sales frequency of No.4 1 running shoes is 30%, so when shopping malls plan to buy 1000 pairs of running shoes, No.41shoes should be around 300 pairs. Eight points.
22. (The full mark of this question is 8)
(1) proves that a quadrilateral is a rectangle,
(The diagonal of the rectangle is divided equally),
The opposite sides of a rectangle are parallel.
, .
(USA) 4 points
(2) When the quadrilateral is a diamond. Five points.
Prove that quadrilateral is rectangular,
The diagonal of the rectangle is divided equally.
Also obtained by (1),
A quadrilateral is a parallelogram (diagonal lines bisect each other).
The quadrilateral is a parallelogram) 6 points
Say it again,
A quadrilateral is a diamond (four parallel sides with diagonal lines perpendicular to each other).
The edge is diamond). 8 points
(Note: If the reasons in brackets are not written, no points will be deducted).
23. (The full mark of this question is 10)
Solution: (1) Let the relation of linear function be, and the relation of inverse proportional function be,
The image passing point of the inverse proportional function,
.
The relationship of the inverse proportional function is .2 points.
Substituting the coordinates of this point into the above formula,
The coordinates of this point are.
Because the image of the linear function is over.
Besides,
solve
The relationship of linear function is 0.4 point.
(2) The approximate images of the two functions are shown in Figure 6.
(3) It can be seen from the images of the two functions.
When summing, the value of the linear function is greater than that of the inverse proportional function. Eight points.
When summing, the value of the linear function is less than that of the inverse proportional function. 10.
24. (The full mark of this question is 10)
Solution: (1) easy to know,
Connection, let the arc radius be.
In, obtained by Pythagorean theorem.
.
Get 0.2 points.
By, by
.3 points
Arc length (cm) .4 minutes
(2) Sector area (cm2) .5 points
Sector area (cm2) .6 points
Trapezoidal area (cm2) .7 points
Area of one side of rain cover
Sector area+trapezoid area-sector area
(cm2) 8 points
(Note: If calculated by other methods, as long as the error does not exceed 2cm2, full marks can be given. )
(3) The top area of rain cover (cm2) .9 points
Total area of rain cover (cm2) (cm2).
It takes about 2.2 square meters of FRP material to make this rain cover. 10.
25. (The full mark of this question is 12)
Solution: (1) Let the side length of a square be cm, then
. 1 point
Namely.
Solve (irrelevant, give up),
The side length of the cut square is 1 cm.3 minutes.
(Note: Write the correct result directly through observation and verification, give 3 points)
(2) The lateral area is the largest.
Let the side length of a square be cm, and the side area of the box be cm.
The functional relationship between and is:
.
That's 0.5 points.
Rewrite to.
When.
That is, when the side length of the cut square is 2.25cm, the maximum lateral area of the rectangular frame is 40.5 cm2.7 minutes.
(3) The lateral area is the largest.
Let the side length of a square be cm, and the side area of the box be cm. ..
If it is cut as shown in figure 1, the functional relationship with is:
.
Namely.
When, .9 points
If it is cut as shown in Figure 2, the functional relationship with is:
.
Namely.
When,. 1 1 point.
Comparing the above two cutting methods, it can be seen that the lateral area of the box cut by the method shown in Figure 2 is the largest, that is, when the side length of the cut square is cm, the lateral area of the folded rectangular box with cover is the largest, and the largest area is cm2. ..
Note: Only one answer and scoring explanation are given for each small question. Other solutions, as long as the steps are reasonable and the answers are correct, should be given corresponding scores.