First, multiple-choice questions (3 points for each small question, 36 points for * * *)
1. In the formula, the number of fractions is ()
A.2 B.3 C.4 D.5
2. The following operation is correct ()
A.B. C. D。
3. If a (,b) and b (- 1, c) are two points on the function image, and < 0, then the size relationship between b and c is ().
A.b < c.b > c.b = c.d can't judge.
4. As shown in the figure, it is known that point A is the intersection of images of functions of y=x and y= in the first quadrant, point B is on the negative semi-axis of X axis, and OA=OB, then the area of △AOB is ().
A.2 B. C.2 D.4
Question 4, question 5, question 8, question 10
5. As shown in the figure, in triangular paper ABC, AC=6, A = 30? ，∠C=90？ , fold ∠A along DE to make point A coincide with point B, then the length of the crease DE is ().
BC 1 year
6. The lengths of the three sides of 6.△ ABC are, b and c respectively, which meet the following conditions: ① ∠ A = ∠ B-∠ C; ②∠A:∠B:∠C = 3:4:5； ③ ; ④ Among them, the number that can judge that △ABC is a right triangle is ().
1。
7. A quadrilateral, for the following conditions: ① A group of opposite sides are parallel and a group of opposite corners are equal; ② A group of opposite sides are parallel, and one diagonal line is equally divided by another diagonal line; ③ A group of opposite sides are equal, and one diagonal line is equally divided by another diagonal line; (4) The bisectors of the two diagonal lines are parallel respectively, and it cannot be judged as a parallelogram ().
A.① B.② C.③ D.④
8. As shown in the figure, it is known that E is a point on the BC of the diamond ABCD, and ∠DAE=∠B=80? , then the degree of ∠CDE is ()
.20 caliber? B.25？ C.30？ D.35？
9. Six students from a class were selected for the physical education test, and the results were as follows: 80, 90, 75, 80, 75, 80. The following description of this set of data is incorrect ().
A. mode 80 b, average 80 c, median 75 d, interval 15.
10. The daily water consumption of a residential quarter from/kloc-0 to 6 this month is as shown in the figure, so the average water consumption of these 6 days is ().
A.33 tons B.32 tons C.3 1 ton D.30 tons
1 1. As shown in the figure, straight line y= KX (k > 0) and hyperbola y= intersect at point A and point B, BC⊥x axis is at point C, and connecting line AC and Y axis intersect at point D, and the following conclusions are drawn: ①A and B are symmetrical about the origin; ② The area of △ ABC is constant; ③D is the midpoint of AC; ④S△AOD=。 The number of correct conclusions is ()
1。
1 1 title 12 title 16 title 18 title.
12. As shown in the figure, in the trapezoidal ABCD, ∠ABC=90? , AE∨CD passes through BC to E, O is the midpoint of AC, AB=, AD=2, BC=3, the following conclusions: ①∠CAE=30? ; ②AC = 2AB； ③S△ADC = 2S△ABE； (4) Bo ⊥ CD, of which the correct one is ()
A.①②③ B.②③④ C.①③④ D.①②③④
Fill in the blanks (3 points for each small question, *** 18 points)
13. It is known that the mode of a set of data 10, 10, x, 8 is equal to its average value, then the median of this set of numbers is.
14. Observe the formula:,-,-,... According to the law you found, the eighth formula is.
15. It is known that the midline length of the trapezoid 10cm is divided into two sections by a diagonal line. The difference between these two paragraphs is 4 cm, so the lengths of the two bottom sides of the trapezoid are respectively.
16 The straight line Y =-x+b intersects with the hyperbola Y =-(x < 0) at point A and intersects with the X axis at point B, so OA2-OB2 =.
17. Please select a set of values and write a fractional equation about, so that its solution can be _ _ _ _ _ _ _ _.
18. In the known rectangular coordinate system, the quadrilateral OABC is a rectangle with point A (10,0), point C (0,4), point D is the midpoint of OA, and point P is the moving point on the side of BC. △ When △POD is an isosceles triangle, the coordinate of point P is _ _ _ _ _ _ _.
III. Answer questions (***6 questions, ***46 points)
19.(6 points) Solve the equation:
20.(7 points) Simplify first, then evaluate:, in which.
2 1.(7 points) As shown in the figure, it is known that the image of the linear function y=k 1x+b and the image of the inverse proportional function y= intersect at A( 1, -3) and B(3, m) to connect OA and OB.
(1) Find the analytical expressions of two functions; (2) Find the area of △AOB.
22.(8 points) See the table below for the math scores of Xiaojun's eighth grade last semester:
test
Category average time period
At the end of the exam
check
Test 1 Test 2 Test 3 Test 4
Score1101059511012.
(1) Calculate Xiaojun's average score last semester;
(2) If the total evaluation score of the semester is calculated according to the weight shown in the sector chart, what is Xiaojun's total evaluation score last semester?
23.(8 points) As shown in the figure, take three sides of △ABC as sides, and make three equilateral △ABD, △BEC and △ ACF on the same side of BC.
(1) judge the shape of the quadrilateral ADEF and prove your conclusion;
(2) When △ABC meets what conditions, the quadrilateral ADEF is a diamond? Is it rectangular?
24.( 10) In order to prevent influenza A (H 1N 1), a school disinfected the classroom by spraying drugs. It is known that the drug content per cubic meter of air is directly proportional to the time x (minutes) when spraying drugs, and Y is inversely proportional to X after spraying drugs (as shown in the figure). Now it is 10.
(1) Find the functional relationship between Y and X during and after spraying;
(2) If the drug content per cubic meter in the air is less than 2mg, students can enter the classroom. How many minutes does it take for students to return to the classroom after disinfection begins?
(3) If the drug content in the air is not less than 4 mg per cubic meter and the duration is not less than 10 minute, is this disinfection effective? Why?
Fourth, ask questions (this question 10)
25. As shown in the figure, in isosceles Rt△ABC and isosceles Rt△DBE, ∠ BDE = ∠ ACB = 90, and BE is on the side of AB. Take the midpoint f of AE and the midpoint g of CD to connect GF.
(1) The positional relationship between FG and DC is that the quantitative relationship between FG and DC is;
(2) If △BDE rotates counterclockwise around point B 180, other conditions remain unchanged, please complete the following figure to judge whether the conclusion in (1) still holds. Please prove your conclusion.
Verb (abbreviation of verb) comprehensive question (subject 10)
26. As shown in the figure, the straight line y=x+b(b≠0) intersects with the coordinate axis at points A and B, and the hyperbola y= intersects with point D. The intersection D is the DC and Germany perpendicular to the two coordinate axes, connecting OD.
(1) Verification: AD divides equally ∠ CDE;
(2) For any real number b(b≠0), verify AD? BD is a fixed value;
(3) Is there a straight line AB that makes the quadrilateral OBCD a parallelogram? If it exists, find the analytical formula of the straight line; If it does not exist, please explain why.
Reference answer
First, multiple-choice questions (3 points for each small question, 36 points for * * *)
The title is123455678911112.
Answer B D B C D C C C C C C C B C D D D d d d d
Fill in the blanks (3 points for each small question, *** 18 points)
13. 10 14.- 15.6cm， 14cm，
16.2, 17. Omitted, 18. (2,4), (2.5,4), (3,4), (8,4)
III. Answer questions (***6 questions, ***46 points)
19.X=-
20. The original formula =-and the value is -3.
2 1.( 1)y=x-4，y=-。 (2)S△OAB=4
22.( 1) The average score at ordinary times is:
(2) The total grade of the semester is:105×10%+108× 40%+12× 50% =109.7 (points).
23.( 1) (omitted) (AB = AC is a diamond, and ∠BAC= 150? Time is rectangular.
24.( 1) y = (0 < x ≤ 10)，y =。 (2)40 minutes.
(3) Substituting y=4 into y= to get X = 5；; Substituting y= gives x=20.
∵ 20-5 = 15 > 10.∴ Disinfection is effective.
Fourth, ask questions (this question 10)
25.( 1)FG⊥CD，FG= CD。
(2) Extend the extension line from ED to AC to m to connect FC, FD and FM.
The quadrilateral BCMD is a rectangle.
∴CM=BD.
And △ABC and △BDE are isosceles right triangles.
∴ED=BD=CM.
∠∠E =∠A = 45？
∴△AEM is an isosceles right triangle.
F is the midpoint of AE.
∴MF⊥AE,EF=MF,∠E=∠FMC=45？ .
∴△EFD≌△MFC.
∴FD=FC,∠EFD=∠MFC.
∠ EFD+∠ DFM = 90？
∴∠MFC+∠DFM=90？
That is, △CDF is an isosceles right triangle.
G is the midpoint of CD.
∴FG= CD,FG⊥CD.
Verb (abbreviation of verb) comprehensive question (subject 10)
26.( 1) certificate: get A(b, 0) and B(0, -b) from y = x+b.
∴∠DAC=∠OAB=45？
And DC⊥x axis, DE⊥y axis ∴∠ACD=∠CDE=90?
∴∠ADC=45？ That is to say, ∠CDE is divided equally in AD.
(2) (1) shows that △ACD and △BDE are isosceles right triangles.
∴AD= CD，BD= DE。
∴AD？ BD=2CD？ DE=2×2=4 is a constant value.
(3) There is a straight line AB, which makes OBCD a parallelogram.
If OBCD is a parallelogram, AO=AC and OB=CD.
According to (1), AO=BO and AC=CD.
Let ob = a (a > 0), ∴B(0,-a), D(2a, a).
∫d is on y=, ∴2a? A = 2 ∴ A = 1 (negative numbers are rounded off)
∴B(0,- 1),D(2, 1).
And b is on y = x+b, ∴ b =- 1.
That is, there is a straight line AB: y = x- 1, which makes the quadrilateral OBCD a parallelogram.