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, PQ Highway and MN Highway 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)
1 1. In the formula,,,,, the number of fractions is ().
a，2 B，3 C，4 D，5。
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:
17.(8 points) Calculation:
( 1) (2)
18.(6 points) Simplify the algebraic expression first, and then select a value that makes the original expression meaningful and substitute it for evaluation.
19.(8 points) Solve the equation:
( 1) (2)
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.
Reference answer
I . 1 . 4 . 3× 10-5 2.4； ; 1; 3.≠5 ; = 1 4 . m & gt； 1; Minus 5. -6 6.m
Second, 1 1. B 12。 D 13。 A 14。 C 15。 C 16.C。
Three. 17.( 1) solution: original formula =... 1 (2) solution: original formula =... 1.
=...2 points =..................2 points.
= ................................................. 3 points.
=-x-y ……
18.(6 points) solution: original formula =.................... 1 minute.
= …2 points = …3 points = …4 points
Select a number and substitute it into the calculation of ............................................................ 6 points.
19.(8 points) Solve the equation:
(1) Solution: … 1 (2) Solution: … 1.
Multiply both sides by (x-3) and both sides by (x+2)(x-2).
1 = 2 (x-3)-x ......................................................................................................................................................
X = 7 ………………………………………。
After testing, x=7 is the solution of the original equation ... 4 points, after testing, x=-2 is not the solution of the original equation, so the original equation has no solution ... 4 points.
20. Solution: Connected communication, ∵AB⊥BC, ∴∠ B = 90. ............................................................................................................................
∴ AC = =10 ..................................... 2 points.
∵.. 3 points
∴⊿ACD is a four-point right triangle.
The square ∴ area ABCD = =144 ............................... 6 points.
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) ...2 points
② When y=50, x=2.56∴ The thickness of noodles is 2.56. ........................................................................................................................................
(3) When x= 1.6 and ∴ the thickness of noodles is not less than, the maximum total length of noodles is 80m…6 minutes.
22. Solution: I think scheme (3) is the most economical without delaying the construction period. ............... 1 point
Reason: If the specified date is X days, it will take X days for Group A to complete the project alone and (x+5) days for Group B to complete the project alone. According to the meaning of the problem, the equation is obtained:
........................., 4 points.
The solution is x = 20, .................... 5 points.
It is verified that x=20 is the solution of the original equation. ................................................................................................................................................................
The project cost required for the scheme (1) is:1.5× 20 = 300,000 yuan.
The project cost required for Scheme (2) is:1.1× 25 = 275,000 yuan.
The project cost required for scheme (3) is:1.5× 4+1./kloc-0 /× 20 = 280,000 yuan.
I think scheme (3) is the most cost-effective without delaying the construction period. ............................................................................................................................................
23.( 1) ; m = 3； N = 4 ... three points (2) ... six points.
(3) A: One point P makes △PAO an isosceles triangle;
The coordinates of point p are:
P 1(0，)； P2(0，6)； P3(0，)； P4 (0 P4(0,) ...10 point.