Math test questions
(Full score:150; Examination time: 120)
1. Multiple choice questions (4 points for each small question, ***24 points) each question has four answers, of which one and only one answer is correct. Please answer in the answer area of the corresponding topic on the answer sheet. If you answer correctly, you will get 4 points, and if you answer incorrectly, you can't answer or have more than one answer, you will get 0 points.
1. Calculate 2-3 = ()
A.- 1 B. 1 C.-5 D.5
2. The average scores of the two students A and B in the last five 100 meter running tests are the same. The score variance of A is 4, and that of B is 3. 1, so it is correct to judge the stability of their test scores ().
A.a's grades are relatively stable, while B. B's grades are relatively stable.
The stability of C.A and B is the same. The stability of class d and class b cannot be compared.
3. Observe the following figure, in which the expanded diagram is () instead of a cube.
4. As shown in the figure, A, B and C are all on ⊙ O. If ∠ BOC = 80, the degree of ∠A is equal to ().
A.20 B.40 C.60 D.80
5. The solution set of inequality group is ()
A.x & lt- 1 b . x & lt； 0 degrees celsius-1< X<0 D. No solution.
6. Rotate the point A (4 4,0) 30 degrees clockwise around the origin O to the corresponding point, and the coordinate of this point is ().
A.B.(4，-2) C. D
2. Fill in the blanks (3 points for each small question, ***36 points) and answer in the answer area of the corresponding topic on the answer sheet.
7. Calculation:
8. Factorization:
9. According to the data published by Quanzhou Statistical Information Network, the total tourism revenue of Quanzhou in 2006 was about14.6 billion, and the scientific number was about RMB.
10. Original price of a commodity 120 yuan. If it is sold at a 20% discount (that is, 20% off the original price), the current price should be RMB.
1 1. The sales volume (unit: kg) of a fruit shop from 1 to June is 450,440,420,480,580,550, so the extreme range of this set of data is kg.
12. Calculation:
13. The sum of the internal angles of a Pentagon is equal to degrees.
14. There is a diamond ABCD (A(A, B, C, D are all grid points in the grid paper on the right).
If the side length of each smallest square in the grid paper is 1, then the area of the diamond is
15. The image of the inverse proportional function is in the first quadrant and the fourth quadrant.
16. Given that the radius of the cone bottom is 10 and the side area is 300π, the length of the generatrix of the cone is
17. There are 1 yellow, white and red balls in the pocket. There is no difference among the three balls except the color. Randomly take 1 ball from your pocket and write a possible event in this experiment:
18. The graph (1) is a black regular triangle, and the midpoints of its three sides are connected in turn to obtain the second graph (with a white regular triangle in the middle) as shown in Figure (2); Repeat the above method for each black regular triangle in Figure (2) to obtain the third figure as shown in Figure (3). If this continues, the number of white regular triangles in the sixth figure is
……
3. Answer the questions in the answer area of the corresponding questions on the answer sheet (***90 points).
19.(8 points) Calculation:
20.(8 points) Simplify the following algebraic expression before evaluating it:
, in which
2 1.(8 points) as shown in the figure, e is the midpoint of BC, ∠ 1=∠2, AE=DE.
Verification: AB=DC
22.(8 points) In the voluntary donation activity in the "heart-stricken area", the donations of 30 students in one class are as follows:
Donation (RMB) 5 10 15 20 25 30
Number1196211.
(1) What is the total donation for this class?
(2) Find the average donation of these 30 students.
23.(8 points) As shown in the figure, pull the cable to the ground at the 6-meter-high C in the telephone pole, and the cable
Make an angle of 63 with the ground, and find the cable length AC (accurate to 0.0 1m).
24.(8 points) A graduation party will be held in Class Kloc-0, Grade 3, and each student is required to rotate the two turntables ① and ② in the picture below at the same time (each turntable is divided into two parts and three parts respectively). If the sum of the numbers pointed by the hands after the two turntables stop is odd, students will perform singing programs; If the sum of the numbers is even, other programs will be executed. Try to find out the probability of this classmate performing a singing program (using tree diagram or list method)
25.(8 points) As shown in the figure, in trapezoidal ABCD, AD‖BC, ∠B=∠ACD.
(1) Please write another isometric angle in the diagram;
⑵ If AC=6 and BC=9, try to find the midline length of trapezoidal ABCD.
26.(8 points) It is known that the circumference of a regular N-shape is 60 and the side length is a..
(1) When n=3, please write the value of a directly;
⑵ When the perimeter and the number of sides of a regular N polygon increase by 7 at the same time, it is assumed that it is still a regular polygon, with the number of sides being n+7, the perimeter being 67, and the side length being b ... Some people take n as 3, 20, 120 respectively, then find out the corresponding A and B, and then assert: "No matter whether N takes any positive integer greater than 2, A and B must not be equal." Do you think this statement is correct? If not, find a value of n that does not conform to this statement.
27.( 13 minutes) Li Ming takes a bus from Quanzhou to a place along the expressway. It is known that the average speed of the bus is 100 km/h, and the distance from Quanzhou after driving for t hours is s 1 km.
(1) Please express s1with an algebraic expression containing t;
(2) Suppose another Wang Hong takes a bus from A to Quanzhou along the same expressway at the same time. It is known that the functional relationship between the distance s2 (km) from Quanzhou and the driving time t (h) is S2 = kt+b (k and t are constants, k≠0). If it takes 9 hours for Li Hong to return to Quanzhou from A, when t=2, s2=560.
① Find the values of k and b;
② Before the two cars meet, when the driving time t is in what range, the distance between the two cars is less than 288km?
28.( 13 point) It is known that the parabola (m is a constant) passes through point (0,4).
(1) Find the value of m;
⑵ First translate the parabola to the right, and then translate it down to get another parabola. It is known that this translation parabola satisfies the following two conditions: its axis of symmetry (set as a straight line l2) is symmetrical with the axis of symmetry of the parabola before translation (set as l 1) about y axis; The minimum value of the corresponding function is -8.
(1) Try to find the functional relationship corresponding to the parabola after translation;
② Is there a point P on the parabola after translation, which makes the ⊙P with radius of 3 tangent to the X axis and intersect with the straight line l2? If it exists, find the coordinates of the point P and the length of the chord AB of the straight line l2 cut by ⊙P; If it does not exist, please explain why.
Fourth, additional questions: (*** 10) answer in the answer area of the corresponding question on the answer sheet.
Friendly reminder: Please check the above questions carefully and estimate your score. If your score is below 90 (passing line), the score of this question will be counted as the score of the whole paper, but the total score of the whole paper will not exceed 90 at most. If the total score of your whole paper has reached or exceeded 90 points, the score of this question will not be included in the total score.
1.(5 points) Fill in the blank: (-2)×(-3)= 1
2.(5 points) Fill in the blanks as shown in the figure: in △ABC, ∠ A = 70, ∠ B = 60,