Name, class score
First, multiple-choice questions (3 points for each small question, 30 points for * * *)
1, in the algebraic expression, the fraction is ()
a，4 B，3 C，2 D， 1
2, sensitive to inverse ratio letter, the following statement is incorrect ()
A, the point (-2,-1) is on its image. B, its image is in the first and third quadrants.
C. when x>0, y increases with the increase of x. D, when x
3. If the score is 0, the value of x is ().
a 、-3 B、3 C、3 D、0
4. The following is the result after the denominator of the fractional equation, in which the correct one is ().
A, B, C, D,
5. As shown in the figure, point A is any point on the function image.
AB⊥x axis is at point B, AC⊥y axis is at point C,
The area of quadrilateral OBAC is ()
A, 2 B, 4 C, 8 D, uncertain
6. It is known that the inverse proportional function passes through point A (x 1, y 1) and point B (x2, y2). If y 1
a、x2 & gtx 1 & gt； 0 B、x 1 & gt； x2 & gt0°C、x2 & ltx 1 & lt； 0 D、x 1 & lt； x2 & lt0
7. The following four groups of line segments are known:
①5, 12, 13 ; ② 15,8, 17 ; ③ 1.5,2,2.5 ; ④ 。
Among them, can form a right triangle ().
A, four groups B, three groups C, two groups D and one group
8. If the equation about x has an increasing root, the value of m is ().
a、2 B、0 C 、- 1 D、 1
9, the following operations, the error is ()
A, B,
C, D,
10, as shown in the figure, are chess pieces with length 1, width 6cm, height 4cm and height 3cm respectively.
Cuboid block, an ant should start from vertex A and climb along the surface of the cuboid.
To eat food at vertex B opposite A, it needs the shortest route to crawl.
The length of is ()
A, B, C, D,
Fill in the blanks (3 points for each small question, 30 points for * * *)
1 1. Write the expression of the inverse proportional function of the image in the first and third quadrants.
12, and the image of the inverse proportional function passes through point A (-3, 1), then the value of k is.
13, if the score is negative, then the value range of x is.
14, simplified:
15. If the hyperbola is in the second and fourth quadrants, the straight line does not pass through the fourth quadrant.
16, as shown in the figure, it is known that △ABC, △ ∠ABC=900,
Take each side of △ABC as the intersection, and make three lines outside △ABC.
Square, S 1, S2 and S3 represent these three respectively.
Square area, S 1=8 1, S3=225,
Then S2=.
17, it is known that the two intersections of the images of inverse proportional function and linear function are A(-3, -2) and B( 1, m) respectively.
18. Given that the length of each side of △ABC is an integer and the circumference is 8, the area of △ABC is.
19. Place a pair of diagonal plates as shown in the figure, and then the upper and lower triangular plates.
Area of S 1: S2 =.
20. As we all know,
The value of the score is.
Third, solve the problem (***40 points, write the necessary calculus reasoning process)
2 1, (6 points) simplify before evaluating:
22.(6 points) In △ABC, AB= 10, BC= 12, and the center line of BC side = 8, so find the length of AC.
23.(6 points) Someone rides a bike 8 kilometers faster than the first hour of walking, and rides a car faster than cycling 16 kilometers. This person starts from a place, walks 4 kilometers first, then takes the bus 10 kilometers, and then goes to b place. He rode his bike from B to A again. The round trip time is exactly the same. Ask for the speed of this man's walking.
24.(7 points) As shown in the figure, in △ABC, ∠ACB=900, AC=7, BC=24, and CD⊥AB is in D.
(1) Find the length of AB;
(2) Find the length of the CD.
25.(7 points) As shown in the figure: In a square ABCD, e is the midpoint of AB, and f is the upper point of AD. Find the degree of ∠FEC.
26.(8 points) As shown in the figure, in the rectangular coordinate system, O is the origin, point A is in the first quadrant, its ordinate is three times the abscissa, and the image of the inverse proportional function passes through point A..
(1) Find the coordinates of point A. ..
(2) If the image of the linear function passing through point A intersects with the positive semi-axis of the axis of point B, OB=AB, find the analytical expression of the linear function.
or
1. Fill in the blanks (2 points for each blank, ***30 points)
1.0.000043 is expressed by scientific notation.
2. calculation: calculation; __________;
= ; = 。
3. When x, the score is meaningful; When x, the value of the score is zero.
4. If the image of the inverse proportional function is in the first and third quadrants, the range of values is; In each quadrant, y increases with X.
5. If the inverse proportional function passes through A(2, -3), then m=.
6. Let the inverse proportional function y= have two points A(x 1, y 1) and B(x2, y2), and when x 1
7. As shown in the figure, due to the influence of typhoon, a tree breaks from the ground and the top of the tree falls off from the bottom of the trunk, so the length of the tree before breaking (excluding the roots) is m. 。
8. The two sides of a triangle are 3 and 5 respectively, so this triangle is a right triangle A D.
Form, the length of the third side is.
9. As shown in the figure, if the side length of the square ABCD is 4, BE= 1, find a point P E on AC.
Minimize the value of PE+PB, and the minimum value is. B C 10。 As shown in the figure, highway PQ and highway MN intersect at point P and ∠ NPQ = 30.
There is a school A on PQ Highway, AP = 160m, if there is a tractor.
Driving in the direction of MN at the speed of 18 m/s and affecting the school,
Then the impact time is seconds.
2. Multiple choice questions (3 points for each question, *** 18 points)
12. Among the following correct propositions, the inverse proposition is ().
A the internal angles on the same side are complementary and the two straight lines are parallel. The corresponding sides of congruent triangles are equal.
C the distance from the point on the bisector of the angle is equal to both sides of the angle. Equal vertex angle
13. In the following groups, triangles with side lengths A, B and C are not right triangles ().
Answer. B.
c。 D.
14. In the same rectangular coordinate system, the image of function y=kx+k is roughly ().
15. As shown in the figure, if the number represented by point A on the number axis is a, the value of a is ().
A.+ 1 B.- + 1 C. - 1 D。
16. As shown in the figure, it is known that rectangular ABCD is folded along a straight line BD, so that point C falls at C/, BC/ intersects with AD at e, AD=8, AB=4, and the length of DE is ().
a3 b . 4 c . 5d . 6
Third, answer questions:
18.(6 points) Simplify the algebraic expression first, and then select a value that makes the original expression meaningful and substitute it for evaluation.
20.(6 points) Known: As shown in the figure, quadrilateral ABCD, AB=8, BC=6, CD=26, AD=24, AB⊥BC.
Find the area of quadrilateral ABCD.
2 1.(6 points) Have you ever eaten Lamian Noodles? In fact, the making process of Lamian Noodles is permeated with mathematical knowledge: a certain volume of dough is made into Lamian Noodles, and the total length of noodles is an inverse proportional function of the thickness (cross-sectional area) of noodles, and its image is as shown in the figure.
(1) Write the functional relationship of and;
(2) When the total length of noodles is 50m, what is the thickness of noodles?
(3) If the thickness of noodles should not be less than, what is the maximum total length of noodles?
22.(8 points) Practical problems for solving a series of equations: (8 points for this small question)
A project bidding, received the bidding documents of two teams, A and B. 1 day for construction, the project of Team A needs to pay 1.5 million yuan, and the project of Team B needs to pay 1. 1.00 million yuan. According to the bidding documents of Team A and Team B, the project leading group can calculate three construction schemes:
Scheme (1): Team A completed the project alone and completed it as scheduled;
Scheme (2): Project Team B completed the project alone, 5 days longer than the specified date;
Scheme (3): If Team A and Team B cooperate for 4 days, the remaining work will be completed by Team B alone and on schedule.
Which scheme do you think is the most economical without delaying the construction period? Please provide a justification for the answer.
23.( 10) It is known that the inverse proportional function image passes through the point A(-2, m)AB⊥x axis in the second quadrant, and the area of Rt△AOB is 3. If the straight line y=ax+b passes through point A and another point C (n,-) on the inverse proportional function image,
The analytical formula of (1) inverse proportional function is, m=, n =；;
(2) Find the analytical formula of straight line y=ax+b;
(3) Whether there is a point p on the Y axis, so that △PAO is an isosceles triangle. If yes, please write down the coordinates of point P directly. If not, explain why.