Analysis of the final mathematics test papers for the second semester of the eighth grade in the 2021-2022 school year at the High School Affiliated to Guangxi University in Guangxi Zhuang Autonomous Region. This famous school test paper is very unique and is a relatively good review material, worthy of reference by eighth grade students. Analysis of the final mathematics test papers for the second semester of the eighth grade in the 2021-2022 school year at the High School Affiliated to Guangxi University in Guangxi Zhuang Autonomous Region. This famous school test paper is very unique and is a relatively good review material, worthy of reference by eighth grade students.
A． ① B. ②C． ③D. ④
Answer: B
[Analysis]
Rotate a figure 180° around a certain point. If the rotated figure can coincide with the original figure, then this figure is called a centrally symmetric figure, and you can make a judgment based on this.
[Detailed explanation]
Solution: Graphics ①③④ cannot find such a point, so that the graphic will completely coincide with the original graphic after rotating 180 degrees around a certain point, so it is not centrally symmetrical Graphics,
Graphics ② can find such a point that the graphic will completely coincide with the original graphic after being rotated 180 degrees around a certain point, so it is a centrally symmetrical graphic,
, so choose: B.
[Finding Point] This question mainly examines the concept of centrally symmetrical figures. For a centrally symmetrical figure, you need to find the center of symmetry and rotate it 180 degrees to coincide with the original figure.
3． It is known that the radius of ⊙O is 6, and the distance between point A and point O is 5, then the positional relationship between point A and ⊙O is ( )
A. Point A is outside the circle B. Point A is inside the circle C. Point A is on the circle D. Not sure
Answer: B
[Analysis]
Answer according to when d＜r, the point is in the circle.
[Detailed explanation]
Solution: ∵OA=5, r=6,
∴OA＜r,
∴ Point A is in the circle,
Therefore, choose: B.
[Finding Point] This question examines the positional relationship between the point and the circle. The key is to remember that if the radius is r and the distance from the point to the center of the circle is d, then: when d>r, the point is outside the circle; when d=r When , the point is on the circle. When d
4． In the plane rectangular coordinate system xOy, the coordinates of the point A (-2, 3) that is symmetrical about the center of the point O are ( )
A. (2,3) B. (-2, -3) C. (2, -3) D. (-2, 3)
Answer: C
[Analysis]
directly uses the characteristics of the symmetric point about the center of the origin to get the answer.
[Detailed explanation]
Solution: ∵ Point A (-2, 3) and point B are symmetrical about the center of the origin O,
∴ The coordinates of point B are: (2, -3).
so choose: C.
[Finding Point] This question examines the properties of central symmetry. Mastering the knowledge points is the key to solving the problem.
6. After moving the image of the quadratic function y = x2 to the right by 1 unit and then upward by 2 units, the function expression of the resulting image is ( )
A. y=(x-1)2+2 B. y=(x+1)2+2 C. y=(x-1)2-2 D. y=(x+1)2-2
Answer: A
[Analysis]
According to the function image, the answer can be obtained by moving right to subtract, left to add, up to add, and down to subtract.
[Detailed explanation]
Solution: After the image of the quadratic function y=x2 is translated to the right by 1 unit, and then translated upward by 2 units, the function expression of the resulting image is y=（x﹣1）2+2,
, so choose: A.
[Finding Point] Test points: Quadratic function images and geometric transformations.
7. Among the following statements, the correct one is ( )
A. The chord is the diameter B. A semicircle is an arc
C. The line segment passing through the center of the circle is the diameter D. Two circles with the same center and the same radius are concentric circles
Answer: B
[Analysis]
[Detailed Explanation]
test question analysis: The chord passing through the center of the circle is the diameter, not all chords are diameters, so option A is wrong; the part between any two points on the circle is an arc, so the semicircle is an arc, so B is correct; the chord passing through the center of the circle is the diameter , so option C is wrong; two circles with the same center and unequal radius Circles are concentric circles, so D is wrong, so choose B for this question. On February 4, 2020, the Winter Olympics were held in Beijing. A company seized the business opportunity to develop two commemorative medals with mascots for the opening ceremony of the Winter Olympics. They were deeply loved by people. After they were put into the market, they found that their daily sales volume was y (sets). The function graph between it and the sales unit price x (yuan) is as shown in the figure (it is required that the sales price of each set cannot be lower than the cost of each set, and the cost of each set is 100 yuan).
Beijing 2022 Winter Olympics Opening Ceremony Commemorative Medal
(1) Try to find the functional relationship between y and x;
(2) If the price management department stipulates that the sales profit of each set cannot be higher than 45% of the cost of each set, then at this time each What is the maximum daily profit when the price is set? What is the maximum profit?
Interested students can print it out on A4 paper for use.
