The first volume (multiple choice questions ***30 points)
First, multiple-choice questions (*** 10 small questions, 3 points for each small question, 30 points)
1. If 5℃ above zero is recorded as +5℃, then 7℃ below zero can be recorded as ().
A.-7 degrees Celsius B.+7 degrees Celsius C.+ 12 degrees Celsius D.- 12 degrees Celsius
2. As shown in the figure, it is a geometry composed of three identical small cubes, and the left view of the geometry is ().
3. The result of calculation is ()
A.B. C. D。
4. A middle school held a singing contest, taking the class as the unit. The judges of the jury rated the singing skills of Class 3, Grade 9 in the table below (full score 100). If you remove a highest score and a lowest score, the average score of the remaining scores is ().
Scores (points)
Eighty-nine
92
95
96
97
Judge (post)
1[ Source: Xue, Ke, Wang Z, X, X, K]
2
2
1
1
Recommendations 92, 93, 94 and 95
5. As shown in the figure, if there are two midlines, then ()
A. 1∶2 B.2∶3
C. 1∶3
6. In the following four groups of points, a group of points that can be on the same image of a proportional function is ().
A.(2.-3)，(-4，6) B.(-2，3)，(4，6)
C.(-2，-3)，(4，-6) D.(2，3)，(-4，6)
7. As shown in the figure, in the diamond, the diagonal line intersects with the point, and the vertical foot is, if, the size is ().
A.75 B.65
C.55 D.50
8. In the same plane rectangular coordinate system, if a function image intersects a point, the coordinate of the point is ().
A.(- 1，4) B.(- 1，2) C.(2，- 1) D.(2， 1)
9. As shown in the figure, in a circle O with a radius of 5, AB and CD are two mutually perpendicular chords, the vertical foot is P, AB=CD=8, and the length of OP is ().
A.3 B.4
C.D.
10. In the plane rectangular coordinate system, the parabola is translated up (down) or left (right) by one unit, so that the translated parabola just passes through the origin, and the minimum value is ().
A. 1
Volume 2 (non-multiple choice questions ***90 points)
Fill in the blanks (***6 small questions, 3 points for each small question, 18 points)
1 1. Calculation:. [Source: Xue, Ke, Wang]
12. Decomposition factor:.
13. Please choose one of the following two small questions to answer. If you choose more than one question, you will be graded according to the first question you choose.
A. In a plane, rotate a line segment with a length of 4 30 counterclockwise around its midpoint, and the swept area of the line segment is.
B. Calculate with a scientific calculator: (accurate to 0.0 1).
14. Xiaohong is going to use 50 yuan money *** 10 bottle to buy two kinds of drinks, A and B. Since each bottle of A drink is 7 yuan and each bottle of B drink is 4 yuan, Xiaohong can only buy one bottle of A drink at most.
15. In the same plane rectangular coordinate system, if the image of an inverse proportional function and the image of a linear function have nothing in common, then the expression of this inverse proportional function is (only write one that meets the conditions).
16. As shown in the figure, a beam of light emitted from a point passes through the point after being reflected by the axis, so the path length of this beam of light from one point to another is.
Third, solve the problem (*** 9 small questions, 72 points. Answer the writing process)
17. (The full score of this question is 5)
Simplify:
18. (The full mark of this question is 6)
As shown in the figure, in, the bisector of intersects with, points and.
(1) Verification:;
(2) The value of when.
19. (The full mark of this question is 7)
A school plans to buy a batch of new books in order to meet students' borrowing needs. For this reason, the librarian of this school has made statistics on the number of books borrowed from the library by students in this school in a week, and the results are as follows.
Please answer the following questions according to the information in the statistical chart:
(1) to complete the bar chart and fan chart;
(2) What kind of books do students like to borrow best?
(3) The school plans to buy 600 new books. How many books should we buy if we determine the purchase amount of comic books, popular science books and literature books according to the percentage in the fan-shaped statistical chart?
20. (The full mark of this question is 8)
As shown in the picture, Xiao Ming wants to use his knowledge to measure the distance between the welcome Sophora japonica and the pavilion on the shore on the island in the middle of the lake. He first measured the welcome Sophora japonica in the northeast at the pavilion on the island in the middle of the lake. Then, he walked 100 meters along the shore from the pavilion to this place, and measured that the welcoming Sophora japonica on the island in the middle of the lake was in the northeast direction (the point was on the same horizontal plane). Please use Xiaoming's measurement.
(Reference data:,
)
2 1. (The full mark of this question is 8)
Scientific research has found that the relationship between oxygen content (g/m3) in the air and altitude (m) approximately satisfies a linear function. According to the measurement, the oxygen content in the air at 0 m above sea level is about 299 g/m3. At an altitude of 2000 meters, the oxygen content in the air is about 235 g/m3.
(1) Function expression for finding sum;
(2) The known elevation of a mountain is 1200m. Would you please check the oxygen content in the air at the top of the mountain?
[Source: Xue. Ke. Net Z.X.X.K]
22. (The full mark of this question is 8)
Xiaofeng and Xiao Xuan play games with two dice with uniform texture. The rules are as follows: each person randomly throws two dice once (if the two dice are stacked together, they will be thrown again), and the one with the sum of points wins; The score is the same as the draw.
According to the above rules, answer the following questions:
(1) Throw two dice at random once, and find the probability that the sum of points is 2 by list method;
(2) Xiaofeng randomly throws two dice once, and the sum of points is 7. Throw two dice at random, and find out the probability of Xiao Xuan winning Xiaofeng.
Dice: A cube with 1, 2, 3, 4, 5 and 6 points engraved on six faces. Sum of points: the sum of points with two dice facing up.
23. (The full mark of this question is 8)
As shown in the figure, the vertical foot of the point tangent to the upper and the lower respectively is.
(1) Verification:;
(2) If the radius of, find the length.
24. (Full score of this question 10) [Source: Subject Network]
If a parabola has two intersections with the axis, then the triangle composed of the vertex of this parabola and these two intersections is called a parabola triangle.
(1) "Parabolic triangle" must be a triangle;
(2) If the parabolic triangle of the throwing line is an isosceles right triangle, the value of;
(3) As shown in the figure, △ is a parabola "parabola triangle". Is there a rectangle with the origin as the center of symmetry? If it exists, find the expression of parabola passing through three points; If it does not exist, explain why.
[Source: Xue Ke # net Z#X#X#K]
25. (The full mark of this question is 12)
As shown in the figure, the side length of a regular triangle is.
(1) As shown in Figure ①, the vertex of a square is on the side, and the vertex is on the side. In the regular triangle and its interior, the square is like a square centered on similarity, and the square area is maximized (without any writing);
(2) Find the side length of the square made in (1);
(3) As shown in Figure (2), put a square and a square in the regular triangle so that the point is on the side, find the maximum and minimum values of the sum of the areas of the two squares, and explain the reasons.
Reference answer
1, answer a.
Through the analysis of the meaning of the question, we can think that the number axis, zero degrees Celsius is the origin, greater than zero degrees Celsius is the positive direction, and the value is positive.
Below zero degrees Celsius is negative. So choose a.
2. answer c
Three-view analysis mainly examines students' spatial imagination ability, which is a necessary test point for the senior high school entrance examination in recent years. From the picture, we can know that it is positive.
The face is three squares (two below and one above), and the left view is viewed from the left, with one square above and one square below.
Look at a square when two cubes overlap, and choose C.
3. answer d
The analysis of this problem mainly examines the powers and powers of numbers. On the whole, the outside is square, so this number must be positive.
Number, exclude A and C, and then see that the square of 5 is 25, the square of is, the product is, and choose D.
4. answer c
Analysis and statistics is also a compulsory question every year, which pays attention to students' practical application ability and removes the highest ones according to the law of question types.
Sum the lowest points, that is, exclude 89 points and 97 points, and then average the rest to get 94 points. In fact, this
There is a trick to this calculation. We see that they are all above 90 points, and we just need to calculate the average of their single digits, and then
Add 90 and you will get the result quickly. The average number of single digits is 0, so the rest of these numbers
The average score is 94, so C.
5. answer d
The analysis of this topic mainly investigates the nature of the triangle midline. From the meaning of the question, we can know that if the median line is 0, the area ratio is 0.
, so choose D.
Step 6 answer a
This paper studies the image properties and applications of linear functions. Several points are on the same image of the proportional function,
It can be seen that the ratio of sum is equal, and it can be seen that A is the correct solution. Choose one.
7.answer b
Analyzing this problem examines the nature of diamonds. We know that the diagonal of the diamond is divided into two and perpendicular to each other, and we can get it by adding them.
Get out. Choose B.
8. answer d
Analyzing the intersection of a linear function can be transformed into solving a binary linear equation system, and the solution is x=2, y = 1. Choose D.
9. answer c
Analyze this problem to investigate the angular relationship between the chord and radius of a circle, connecting OB, OD, cross O and intersection.
In, we can know that OH=3 from Pythagorean theorem, and the same can be said, OE=3, which is also easy to prove.
So OP= choose C.
10, answer b
This paper discusses the translation of parabola and the properties of its images.
The axis has two intersections, namely, drawing and combining numbers and shapes, and we get that the parabola is shifted to the right by 2.
Unit, let the parabola pass through the origin, and the moving distance is the smallest. Choose B.
1 1, answer
Analysis primitive
12, answer
analyse
13, an answer
When a line segment with length 4 rotates 30 counterclockwise around its midpoint, the line segment will sweep the shape of the part.
The shape is two sectors with a radius of 2 and a central angle of 30, so its area is.
B answer 2.47
14, answer 3
Xiaohong can buy a bottle of A drink, so she can buy a bottle of B drink.
solve
So Xiaohong can buy up to 3 bottles of a drink.
15, answer (as long as satisfied)
The analytical expression of this inverse proportional function is.
I see.
Because this inverse proportional function does not intersect with the image of linear function, the equation has no solution.
Therefore, a solution is obtained.
16, the answer
Solution 1: Let this beam of light intersect the axis, and the intersection point is the vertical line of the axis.
Passing the point is the axis of the point.
According to the nature of reflection, we know.
So ... So ...
Known.,,, So.
So ...
From Pythagorean theorem, we get,, so.
Method 2: Set the intersection of this beam and the axis, make a symmetrical point about the axis, and intersect with the axis.
At this moment.
From the nature of reflection, we know that these three points are on the same straight line.
Then from the nature of symmetry, we know.
Then.
It is easy to know from the meaning of the question, which is obtained from Pythagorean theorem. So ...
17, answer: original formula =
=
=
=
= .
18, answer: (1) As shown in the figure, in the middle,
∴ .
The bisector of ∵ Yes,
∴ .
∴ .
∴ .
(2)
∴△ ∽△ ,
∴ ,
∴ .
19, the answer is: (1) as shown in the figure.
Statistics on the number of books borrowed from the library by our students within one week.
Students in this school like to borrow comic books best.
(3) Comics: 600×40%=240 (Ben), Popular Science: 600×35%=2 10 (Ben),
Literature: 600× 10%=60 (book), other categories: 600× 15%=90 (book).
20. solution: as shown in the figure, the extension line of the intersection line is at the point.
Then.
In rt delta and rt delta,
Settings, and then,
.
∴ .
∴ (meter)
∴: The distance between Yingbin Sophora japonica and the pavilion on the island in the middle of the lake is about 207 meters.
2 1, the answer solution: (1) set, then there is.
Solve it and get it.
∴ .
(2) When, (g/m3).
The oxygen content in the mountaintop air is about 260.6 g/m3.
22. Solution: (1) Throw two dice at random once, and all possible results are shown in the right table:
Dice 2
Dice 1
1
2
three
four
five
six
1
2
three
four
five
six
seven
2 [Source: Subject Network]
three
four
five
six
seven
eight
three
four
five
six
seven
eight
nine
four
five
six
seven
eight
nine
10
five
six
seven
eight
nine
10
1 1
six
seven
eight
nine
10
1 1
12
On the right table * * *, there are 36 equal possible results, in which the sum of points is.
There is only one result of 2.
∴ (The sum of points is 2) =.
(2) As can be seen from the right table, the sum of points is greater than 7.
There are 15 species.
(Xiao Xuan wins Xiaofeng) = =
23. solution to the answer: (1) proof: as shown in the figure, connect and then.
∵ ,
∴ .
∵ ,
A quadrilateral is a rectangle.
∴ .
(2) Connect, and then.
[Source: Xue. Ke. Net]
∴ , .
∴ .
∴ .
Okay, then.
Yes, there is.
That is.
24. Solution: (1) Isosceles
(2)∵ The "parabola triangle" of parabola is an isosceles right triangle, [source: Z.xx.k.]
∴ The vertex of parabola is satisfied.
∴ .
(3) existence.
As shown in the figure, let △ and △ be symmetrical about the center of the origin,
Then this quadrilateral is a parallelogram.
When a parallelogram is a rectangle.
Say it again,
△ is an equilateral triangle.
Work, hang your feet.
∴ .
∴ .
∴ .
∴ , .
∴ , .
Set the parabola to pass three points, and then
Solve it and get it.
The expression of parabola is.
25, the answer solution: (1) as shown in figure 1, the square is what you want.
(2) Let the side length of a square be.
∵△ is a regular triangle,
∴ .
∴ .
Right is right without denominator, right.
(3) Connect as shown in Figure ②, and then.
Let the side length of a square and a square be,
So, the sum of their areas is.
∴ .
∴ .
Then extend the intersection.
Yes,.
That is.
∴ I) When, that is, when, the minimum.
∴ .
Ⅱ) Maximum, maximum.
That is, the biggest and smallest time is the biggest.
∫ From (2),
∴ .
∴ .
[Source: Subject Network]