Mathematics final examination questions in the second volume of the eighth grade.
One, multiple-choice questions * * * 3 points for each small question, ***2 1 point * * *
1. The calculation result is * * * *.
A.B. C. D。
2. If the score is meaningful, the value range of is * * * * *.
A.B. C. D。
3. Among parallelograms, rectangles, diamonds and squares, there are * * * * * which are both axisymmetric and centrally symmetric.
1。
4. The variance of a set of data 8, 9, 10,1,12 is * * *.
A.4 B.2 C. D. 1
5. The distance from the point to the axis is * * * *.
A.B.3 C.5 D. 4
6. In the same rectangular coordinate system, if the straight line is parallel to the straight line, then * * * * * *.
A.、b、c、d、
7. As shown in the figure, a point is a moving point on the hyperbola, which is the intersection point.
When the axis is on the point and the point moves from left to right, * * * * * *.
A. gradually increase
B. Gradually decreasing
C. Increase first and then decrease
D. remain unchanged
2. Fill in the blanks * * * 4 points for each small question, ***40 points * * *
8. Calculation:;
9. The diameter of bacterial virus is meters, and meters are expressed as meters by scientific notation.
10. Calculation: =.
1 1. In the proportional function, the value of increases with the increase of.
The range is _ _ _ _ _ _ _.
12. As we all know, the image of linear function is expressed in rectangular coordinate system.
Then * * * fill in ","or "=" "* *.
13. As shown in the figure, fold the rectangular piece of paper along a straight line passing through the point so that the point
Fall on the edge of the point, if, then.
14. If the two branches of the inverse proportional function image are distributed in the second and fourth quadrants, the integer can be
* * * Just write a * *.
15. As shown in the figure, in □,, and then
16. As shown in the figure, the circumference of the diamond is 20, and the diagonal line intersects with the point, then
.
17. It is known that the right-angle side length of an isosceles right angle is equal to the right-angle side length of a square, the points are on the same straight line, the moving distance of the points is, and the area of the overlapping part is.
*** 1*** When the point moves to the right, the area of the overlapping part;
***2*** When, the functional relationship with is _ _ _ _ _ _ _ _.
Three. Answer the question * * * * 89 points * * *
18.***9 points * * * calculation:.
19.***9 points * * * Simplify first, then evaluate:, in which.
20.***9 points * * As shown in the figure, at □, the point and the point are respectively, and a point on the side.
Prove that a quadrilateral is a parallelogram.
2 1.***9 points * * As shown in the figure, straight lines intersect with the axis at points and points respectively.
(1) Find the coordinates of points and points;
(2) If the point is a point on the axis, the areas set separately.
For and, and, find the coordinates of the point.
22.***9 o'clock * * * A school held a "scholarly campus" reading activity. After statistical analysis of the reading of each of the 42 students in Class * *1* *, a bar chart is obtained, as shown in the figure:
(1) Fill in the blanks: the number of books read by each student in this class.
Most of them are books, and the median is books;
If the bar chart is converted into a fan.
The statistical chart shows the "reading number" of the students in this class.
Fan corresponds to the number of four books.
The degree of the central angle.
23.***9 o'clock * * In the campus manual activities, both Party A and Party B received the task of handmade paper flowers. It is known that Party A makes 20 fewer paper flowers per hour than Party B, and the time for Party A to make 120 paper flowers is the same as that for Party B to make 160 paper flowers. How many paper flowers does Party B make per hour?
24. * * * Nine points * * are known: the middle point, the edge point, and the edge point are respectively.
(1) If ∨, ∨, and, the quadrilateral is _ _ _ _ _ shape;
As shown in the figure, if it is at the point, at the point, at the point,
Verification:
25.*** 13 point * * * is known, as shown in the figure, the image of the proportional function and the image of the inverse proportional function intersect at this point, and the coordinates of this point are.
*** 1***① and value;
② Try to write the solution set of inequality directly with function images;
***2*** is a moving point on the axis, which is connected to make a point a symmetrical point about a straight line. Is there a point in the movement of a point that makes the quadrilateral become a diamond? If it exists, find the coordinates of the point; If it does not exist, please explain why.
26.*** 13 point * * * As shown in the figure, on the coordinate axis, the point coordinate of the square is, rotate the square counterclockwise around the point to get a square, the intersection line is at the point, the extension line is at the point, and it is connected.
*** 1*** Verification: equal share;
***2*** Find the quantitative relationship between line segments, and when the square rotates counterclockwise around a point;
***3*** Connecting lines,,, In the process of rotation, can a quadrilateral become a rectangle?
If yes, try to find the analytical formula of the straight line; If not, please explain why.
Reference answer
I. Multiple choice questions: * * 3 points for each small question, ***2 1 point * * *
1.c； 2.b； 3.c； 4.b； 5.d； 6.a； 7.d；
Fill in the blanks: * * 4 points for each small question, ***40 points * * *
8. 1; 9.； 10. 1; 1 1.； 12.； 13.25; 14.0*** The answer is not unique * * *;
15. 1 10; 16.6; 17.*** 1*** 8; ***2*** .
Three. Problem solving: * * * * * 89 points * * *
18.***9 points * * * solution: original formula
Six points.
Eight points.
Nine points
19.***9 minutes * * solution: original formula 1 minute.
Three points
Five points.
Six points.
Seven points
When, the original formula 8 points.
Nine points
20.***9 points * * *
Prove:
∵ quadrilateral is a parallelogram,
Four points.
∵
∴
That is, 8 points.
Also, that's ∨.
∴ Quadrilateral is parallelogram. ........................................................................................................................ scored 9 points.
2 1.***9 points * * *
Solution:
*** 1*** in the middle, make, and then, solution:,
∴ The coordinate of the point is ...................................................................................... 2 points.
So, the coordinate order of the ∴ point is ...........................................................................................................................................................
* * * 2 * * *∫ point is a point on the axis, and the coordinates of ∴ point are
The coordinates of this point are,
Five points.
∵ ,
Say it again,
∴, solution: or.
The coordinate of the point is 9 o'clock.
22.***9 points * * *
* * *1* * * 4 ... 6 points.
***2***
∴: The number of students reading four books in this class corresponds to the degree of the fan-shaped central angle of 9 points.
23.***9 points * * *
Solution: Suppose B makes a paper flower every hour, and according to the meaning of the question, we get: …………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… "
Five points.
Solution: 7 points.
After checking, it is the solution of the original equation, which accords with the meaning of the question: .................................................................. scored 8 points.
Answer: Party B makes 80 paper flowers every hour. ....................................................................................................................................................................
24.***9 points * * *
Solution: * * *1* * * ling ... 3 points.
***2*** Scheme 1: as shown in figure 1, connection,
∵ , ,
Say it again,
............................................., 7 points.
Say it again,
∴ ………………………………………………………………………………………………………………………………………………………………………………………………… 9 points.
Scheme 2: As shown in Figure 2, if the cross extension line is on the point,
∵ ,
A quadrilateral is a rectangle,
Seven points.
∵ , ,
By understanding:
∴ ,
Say it again,
∴ ,
∵ , ,
∴ ≌ ,
∴ ,
∴ ………………………………………………………………………………………………………………………………………………………………………………………………… 9 points.
25.*** 13 * * *
Solution:
*** 1***① Replace the coordinates of this point with:
∴ The coordinate of this point is ................................................................. 2 points.
Substitute the point into:, and the solution is: ................................................................................................ 4 points.
② According to the bifunctional image,
The solution set of is 8 points or ............................
* * * 2 * * * * 2 * * * When the point is on the positive semi-axis of the shaft, the quadrilateral is a diamond.
Points and points are symmetrical about a straight line.
∴ , ,
∴ .
A quadrilateral is a diamond.
From the coordinates of the midpoint of * * *1* *, we can get:
Points and points are symmetrical about the origin,
∴ The coordinates of the point are,
∴ , ,
∴ .
If the axis is on the point, then.
In, we get: from Pythagorean theorem, once again.
∴ ,
∴ The coordinate of the point is ..................... 1 1.
When the point is on the negative semi-axis of the shaft, the quadrilateral is a diamond. When important official was at this point,
Similarly, we can also get:
∴ ,
∴ The coordinates of the point are,
To sum up, when the coordinates of a point are or, a quadrilateral is a diamond. ..........................................................................................................................................................
26.*** 13 * * *
* * *1* * Proof:
∵ Square rotates around a point to get a square ..................................... 1 minute.
∴ ,
In and,
∴≌ ......................................................................................................................................................................
∴
That is, the average score is 3 points.
***2***
Reference *** 1***: ≌∴
In and,
∴ ≌ .
Six points.
................................................................., 7 points.
***3*** The quadrilateral can be a rectangular .............................................................................................. with 8 points.
When the point is the midpoint, the quadrilateral is a rectangle. As shown in the figure, it is proved by ***2***:, and then, again.
∴ The quadrilateral is a rectangle. ............................................................................................. scored 9 points.
∴ .
∵ ,
∴ The coordinates of the point are ....................................................................................................................................................................
So, the coordinates of the set point are.
∴ , ,
∵ , ,
In,,, and, Pythagorean theorem is made up of:
∴ The coordinate of the point is ............................................................................................ 12 minute.
Let the analytical formula of a straight line be:
After a little bit, ∴' s solution is:
The analytical formula of a straight line is:
..................................... 13.