(hour120min, total120min)
Shift: _ _ _ _ _ _ Name: _ _ _ _ _ Student ID: _ _ _ _ _ _
The total score of the topic is one two three four five six.
score
I. Fill in the blanks (3 points for each question, 30 points for * * *)
1, the root of the equation x2=2 x is: _ _ _ _ _ _ _ _
2. Write an unary quadratic equation: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
3、cos60+tan 30 = _ _ _ _ _ _ _ _ _ _ _ _ _ _
4. In △ABC, ∠ C = 90, cosA=0.8746, then SINB = _ _ _ _ _ _ _ _ _ _
5. Divide a turntable into six equal parts, namely red, yellow, blue, green, white and black. The probability that the turntable turns red twice is: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
6. As shown in the figure (1), the stair surface should be carpeted with a height of 3m and a slope angle of 30. The length of the carpet should be at least _ _ _ _ _ _ _ meters (accurate to 0. 1 meter).
Figure (3)
7. The inverse proposition of the proposition "A trapezoid with two equal diagonals is an isosceles trapezoid" is: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
8. In △ABC, AB=9, AC= 12, BC= 18, D is a point above AC, and DC= AC. Take a little e from AB and get △ADE. If the two triangles in the diagram are similar, the length of DE is _ _ _ _ _ _ _ _. As shown in figure (2)
9. There are three different events: (1) throwing an ordinary coin into the air, face up; (2) Buy a lottery ticket with a grand prize of 6.5438+0 million yuan; (3) Touch a ball randomly from the bag with 10 white balls. It is a red ball, and the order of occurrence probability is _ _ _ _ _ _ _. (Fill in serial number)
10. Rewrite the proposition "Equal vertex angles" into "If"
Second, multiple-choice questions (3 points for each question, ***30 points)
1 1 and the solution of equation 2x (x-3) = 5 (x-3) is ().
a、x= B、x=3 C、x 1=3、x2= D、x=
12. If it is assumed that "there is just an even number among the integers A, B and C", there is ().
A, A, B and C are all odd numbers, and B, A, B and C are all even numbers.
There are at least two even numbers d, a, b and c in c, or both are odd numbers or at least two even numbers.
13. In △ABC, if sinA=sinB=, then △ABC is a triangle ().
A, acute angle b, obtuse angle c, right angle d, none of the above.
14. If the midpoints of the sides of the quadrilateral ABCD are connected in turn to form a square, then the quadrilateral ABCD must be ().
A, rectangle B, diamond C, square D, quadrilateral with equal vertical and diagonal lines
15.Rt△ABC, if the length of each side is enlarged by 2 times, the sine value and cosine value of acute angle a ().
One, nothing has changed. B, everything has expanded by 2 times. C, everything has shrunk by 2 times. D, not sure.
16, and the probability of an event is 0.0 1%, then the event ()
First, it won't happen. B, it will happen.
C, it may happen, but the possibility is very small. D, the possibility of happening is the same as the possibility of not happening.
17, if the whole newspaper is similar to half a newspaper, the aspect ratio of this newspaper is ().
a、2: 1 B、C、4: 1 D、
18, as shown in figure (3), d and e are the bisectors of AB, DF∨EG∨BC, S 1: S2: S3 = ().
a、 1:2:3 B、 1:4:9
c、 1:3:5 D、 1:3:6
The three sides of 19 and △ABC are 1 and △ ABC ∽△ a ′ b ′ c, respectively, so the length of the third side of △ a ′ b ′ c should be equal to ().
a、B、C、2 D、
20, throw two even dice in, the probability that the sum of positive points is 3 is ().
A, B, C, D,
Three. Problem solving (6 points for each question, *** 12 points)
2 1, as shown in figure AD? AB=AE？ AC, verification: △FDB∽△FEC.
22. calculation: sin 227+sin 253+cos 30 tan 30-sin 60? tan45？ tan60
Iv. Answer questions (7 points for each question, *** 14 points)
23. As shown in the figure, in the rectangular ABCD, AB= 12cm, BC=6cm, and point P moves from point A to point B at a speed of 2cm/s along the AB side, while point Q moves from point D to point A at a speed of 1cm/s along the DA side. If p and q start at the same time, the moving time is expressed in t seconds (0
(1) When t is what value, △QAP is an isosceles right triangle?
(2) When t is what value, is the triangle with points Q, A and P similar to △ABC?
24. It is known that the equation x2-(2m+ 1) x+m2 = 0 is about x.
(1) When m is taken, the equation has two real roots.
(2) Choose an appropriate integer for m, so that the equation has two unequal real roots, and find these two roots.
Verb (abbreviation of verb) solving problems (8 points for each question, *** 16 points)
25. As shown in the figure, the elevation angles of the roof A of building AB at two points C and D on the ground are 30 and 45 respectively, and the measured CD is =10m, and B, C and D are in the same straight line, so how many meters is the building height AB?
26. Party A and Party B each throw an ordinary cube dice. If the product of the points they cast is odd, Party A will get 1 point. If the product of the points thrown by two people is even, Party B will get 1 point. If you throw 20 times in a row, whoever scores higher will win.
(1) Who is likely to win? Briefly state your reasons.
(2) Do you think this game is fair? If it is unfair, please design a fair game for them.
6. Answer questions (9 points for each question, *** 18 points)
27. As shown in the figure, in △ABC, the bisector of ∠BAC intersects with the vertical line PQ of BC at point P, and the intersection point P is defined as PN⊥AB at point N and PM⊥AC at point M respectively. Verify BN=CM.
28. The two roads intersect at an angle of 30 degrees. On OM Road, there is a school 80 meters away from O'clock. When the tractor drives directionally along the road, it will be affected by the noise within 50 meters on both sides of the road. It is known that the speed of the tractor is 18km/ h, so when the tractor is driving in the ON direction, will it bring noise impact to the school? If affected, try to calculate the affected time.