First, multiple-choice questions (3 points for each small question, 30 points for * * *)
1, (Guangzhou, 2008) The calculation result is ().
A B C D 8
2. (Guangzhou, 2008) The number 1 is rotated 90 clockwise, and the result is ().
3. (Guangzhou, 2008) Among the following four figures, the one that is the plane expansion diagram of triangular prism is ().
4. (Guangzhou, 2008) If the real number and the reciprocal are opposite, the following equation is ().
A B C D
5. The root of the (2008 Guangzhou) equation is ().
A B C D
6. (Guangzhou, 2008) The image of linear function does not pass ()
A first quadrant b second quadrant c third quadrant d fourth quadrant
7.(2008 Guangzhou) The following statement is true ()
A "80% probability of rain tomorrow" means that it will rain 80% of the time tomorrow.
B "The probability of flipping a coin is 0.5" means that every time a coin is flipped twice, 1 coin faces up.
C "Lottery winning probability is 1%" means that buying 100 lottery tickets will definitely win.
D "The probability of throwing cube dice with odd faces is 0.5" means that if the dice are thrown many times, the average number of points is odd, that is, every two times 1 time.
8. (Guangzhou, 2008) If each of the following letters is regarded as a graph, then the center of this graph is ().
O L Y M P I C
A 1 B 2 C 3 D 4
9. (Guangzhou, 2008) As shown in Figure 2, the side length of each small square is 1. Cut out the shadow and make a square with the cut shadow, so the side length of the new square is ().
A B 2 C D
10, (Guangzhou, 2008) Four children are playing on the seesaw. Their weights are p, q, r and s respectively. As shown in Figure 3, their weight relation is ().
A B C D
Fill in the blanks (3 points for each small question, *** 18 points)
The reciprocal of 1 1 and (2008 Guangzhou) is
12, (Guangzhou, 2008) as shown in Figure 4, ∠ 1 = 70, if m ∠ n, ∠2=
13, (Guangzhou, 2008) function independent variable value range is
14, (Guangzhou, 2008) translate the line segment AB 1cm to get the line segment A'B', and the distance from point a to a' is
15, (Guangzhou, 2008) The proposition that the circumference angle of the diameter of a circle is a right angle is a proposition (fill in "true" or "false").
16, (Guangzhou, 2008) for arbitrary convex quadrilateral ① ab = CD; On the plane, the following four relations are given: ① AB = CD;
②AD = BC； ③AB‖CD； (4) With any two of ∠ A = ∠ C as conditions, the probability that this quadrilateral ABCD is a parallelogram can be obtained.
Iii. Answer questions (* *102)
17, (Guangzhou, 2008) (9 points) Decomposition coefficient
18, (Guangzhou, 2008) (9 points) Xiaoqing's math scores in the ninth grade last semester are as follows.
Normal terminology of test category
At the end of the exam
check
Test 1 Test 2 Test 3 Project Learning
Achievement 88 70 98 86 90 87
(1) Calculate the average grade this semester;
(2) If the overall grade of the semester is calculated according to the weights shown in Figure 5,
Please calculate Xiaoqing's overall evaluation score this semester.
19, (2008 Guangzhou) (10 minute) as shown in Figure 6, real number, position on the number axis,
simplify
20. (Guangzhou, 2008) (10 minute) As shown in Figure 7, in the rhombic abCD, ∠ dab = 60, the intersection point C is CE⊥AC, and it intersects with the extension line of AB at point E, which proves that the quadrilateral AECD is an isosceles trapezoid.
2 1, (2008 Guangzhou) (12 minutes) As shown in Figure 8, the image of the linear function and the image of the inverse proportional function intersect at point A and point B.
(1) Write the coordinates of A and B respectively according to the image;
(2) finding two resolution functions;
(3) Answer according to the diagram: When the value is what,
The function value of linear function is greater than that of inverse proportional function.
22. (Guangzhou, 2008) (12) At the beginning of 2008, there was a snowstorm in southern China, and the power lines in a certain place were crushed by snow, so the maintenance team of the power supply bureau had to go to the suburbs 30 kilometers away for emergency repair. The repairman rides the motorcycle first, 15 minutes later, the repair vehicle is loaded with the required materials and set off. As a result, the two cars arrived at the maintenance point at the same time. It is known that the speed of emergency repair vehicle is 1.5 times that of motorcycle. Find the speed of two cars.
23. (Guangzhou, 2008) (12 minutes) As shown in Figure 9, the ray AM intersects with the circle at points B and C, and the ray AN intersects with the circle at points D and E.
(1) verification: AC=AE
(2) Draw with a ruler, and make the median vertical line of the line segment CE and the bisector of ∠MCE. The two lines intersect at point F (the drawing trace is reserved, and the writing method is not used) to prove that the bisector of EF is ∠CEN.
24. (Guangzhou, 2008) (14) As shown in figure 10, the radius OA of fan-shaped OAB is 3, the central angle ∠ AOB is 90, point C is a moving point different from A and B, and the intersection point C is CD⊥OA and CE ⊥ of point D.
(1) Prove that the quadrilateral OGCH is a parallelogram.
(2) When point C moves on the plane, are there any line segments with constant length in CD, CG and DG? If yes, request the length of the line segment.
(3) verification: it is a fixed value
25. (Guangzhou, 2008) (14 points) as shown in figure 1 1, in trapezoidal ABCD, AD‖BC, AB=AD=DC=2cm, BC=4cm, in isosceles △PQR, ∠. If the isosceles △PQR moves at a uniform speed 1cm/ s along the direction indicated by the arrow of the straight line L, the area of the overlapping part between the trapezoidal ABCD and the isosceles △PQR in t seconds is recorded as s square centimeters.
(1) When t=4, find the value of s.
(2) If the functional relationship between S and T is found, the maximum value of S is found.
/page/08-06- 13/2523 1 . html