The inverse proportional function of the math problem in the second volume of the eighth grade should be y=- root sign 2/x.
In the problem, it is said to be an inverse proportional function, and the coefficient is negative, so it monotonically increases in the definition domain.
If a 1
If a 1
If it is 0
10^(2x)=25
10 x = 5 or -5 (omitted)
10^(-x)= 1/5
The seventh question on page 68 of mathematics in the second volume of the eighth grade proves: ∫be∨df, ∴ BEF = ∠ DFE.
∴∠AEB=∠DFC (complementary angles of equal angles are equal),
ABCD is a parallelogram,
∴AB=CD,AB∥CD，
∴∠BAE=∠DCF，
∴δabe≌δcdf(aas)，
∴BE=CF，
∴ Quadrilateral BEDF is a parallelogram (BE and DF are parallel and equal),
∴DE∥CF，
∴∠ 1=∠2。
The eighth grade, the second volume of mathematics, page 32 1 the process of problem 4, thank you. Type the problem urgently.
Question 13, page 29, Book 2, Grade 8 Mathematics Book: △ACD is a right triangle.
∴AC？ +CD？ =AD？
∴S shadow =π. 100 (? AC)？ +? π。 (? CD)？ =SRt△ACD-？ π(? AD)？ = 1/8π(AC？ +CD？ -Advertising? )+SRt△ACD=SRt△ACD
The eighth grade second volume mathematics examination questions Jiangbei District second semester second semester final mathematics examination paper.
Description of this volume:
1, full mark 100, and the examination time is 90 minutes;
2. Answer the question with a blue (black) steel (ball) pen and write the answer in the corresponding position; Pencils for drawing;
3. It is allowed to use a calculator for learning, and there must be a corresponding calculation process for solving problems. Only the results will not be graded.
First, multiple-choice questions. (2 points for each small question, ***20 points)
1, in order to make the quadratic radical meaningful, the condition that the letter X must meet is ().
a、X≥2 B、X≤2 C、X≥-2 D、X≤-2
2. Given that the external angle of a regular polygon is 36, the number of sides of this regular polygon is ().
a、7 B、8 C、9 D、 10
3. As shown in the figure, D, E and F are the midpoint of the three sides of △ABC, and
S △ def = 1, then the area of S△ABC is ().
a、2 B、3 C、4 D、6
4. In the figure below, the number of centrally symmetric figures is ().
a，2 B，3 C，4 D， 1
5, a clothing seller in the market share survey, he should be most concerned about is ().
A, the average number of fashion models b, the number of fashion models.
C, the median of clothing model D, the smallest clothing model.
6. The correct proposition in the following propositions is ()
A, two quadrangles with vertical diagonals are diamonds.
Congruence of Two Graphs with Central Symmetry at a Point
C, a group of parallelograms with parallel opposite sides and another group of parallelograms with equal opposite sides.
D, connecting the midpoints of the sides of the quadrilateral in turn to obtain a rectangle.
7. As shown in the figure, in ABCD, diagonal lines AC and BD intersect at point O,
E and f are two points on the diagonal AC. When e and f satisfy which of the following?
Conditionally, the quadrilateral DEBF is not necessarily a parallelogram ()
a、AE=CF B、DE=BF
C, ∠ Ade =∠CBF D, ∠AED=∠CFB
8. If one root of the quadratic equation of x (a-1) x2+a2-1= 0 is X = 0, then a is equal to ().
a、 1 B 、- 1 C、 1 D
9. As shown on the right, it is known that AD‖BC and BE are equally divided in trapezoidal ABCD.
∠ABC,BE⊥CD,∠A= 1 10，AD=3，AB=5，
The length of BC is ()
a、6 B、7 C、8 D、9
10, as shown in the figure, a square ABCD with a side length of 1, where m and n are respectively AD,
At the midpoint of BC, fold point C onto MN and fall at the position of point P,
If the crease is BQ and PQ is connected with BP, the length of NP is ().
A, B, C, D,
Second, fill in the blanks. (2 points for each small question, ***20 points)
1 1, simplified =;
In 12 and △AB=AC, if AB=AC and ∠ A = 40, then ∠ACB's external angle is;
13. It is known that the two right-angled sides of a right-angled triangle are 3cm and 4cm respectively, then the length of the high line on the hypotenuse is;
14, there are 400 students in grade 8 in a school. In order to understand the eyesight of these students, the eyesight of 20 students was randomly selected and the obtained data were sorted out. In the frequency distribution table, if the frequency of the data is 0.95 ~ 1. 15, it can be estimated that the vision of the eighth-grade students in this school is 0.95.
15, when x =, the value of x (X(X-8)) equals the value of-16;
16, the upper bottom of the isosceles trapezoid is 2cm long, the lower bottom is 10cm long and the height is 3cm, so its waist length is cm;
17, the following propositions: ① the vertex angles are equal; ② The two bottom angles on the same bottom of the isosceles trapezoid are equal; ③ The diagonals of the rhombus are equal; (4) Two straight lines are parallel and have the same angle. Among them, the inverse proposition is false.
(Fill in serial number)
18, with each vertex of the quadrilateral ABCD as the center and 1cm as the radius.
Arc, the sum of shadow areas in the figure is cm2.
19. Cut a small square with a side length of 4cm from each corner of the square iron sheet to make a box without a cover. It is known that the volume of the box is 400cm3, so the side length of the original iron sheet is cm;
20. As shown in the figure, it is densely paved with isosceles trapezoid with exactly the same shape and size.
The top and bottom surfaces of the isosceles trapezoid in this pattern.
The ratio is.
Third, answer the question.
2 1, calculation: (1)-3 (2) known A = 3+2 B = 3-2.
Find the value of a2b-ab2.
22, solve the equation:
(1) x2 = x (2) Solve the equation by collocation method: 2x2-4x+ 1 = 0.
23. In order to let students know about environmental protection knowledge and enhance the significance of environmental protection, a middle school held an "environmental protection knowledge competition". * * * 850 students took part in the competition. In order to know the results of this competition, some students are selected for statistics (the score is rounded off, and the full score is 100). Please answer the following questions according to the unfinished local pollution frequency distribution table and frequency distribution histogram:
Packet frequency
50.5~60.5 4 0.08
60.5~70.5 0. 16
70.5~80.5 10
80.5~90.5 16 0.32
90.5~ 100.5
Total 50 1.00
(1) Fill in the blank space of the frequency distribution table;
(2) Complete the frequency histogram and draw the frequency distribution line graph directly on this graph;
(3) In this question, what are the population, individual, sample and sample size?
(4) Among all the students, which group scored the most in the competition?
(5) If the score is above 90 (excluding 90), how many people in this school have excellent grades?
24. As shown in the figure, in the rectangle ABCD, AB = 8, BC = 6, draw three diamonds with different areas, so that the vertices of the diamonds are all on the sides of the rectangle, and calculate the areas of the drawn diamonds respectively. (The following figures are for drawing. )
25. In order to improve the quality of atmospheric environment in a certain area, it is decided to treat it in two phases, so as to reduce the annual emission of waste gas to 2.88 million cubic meters. If the percentage of waste gas reduction in each treatment is the same. (1) What is the percentage reduction in each period? (2) It is estimated that 30,000 yuan will be invested for each reduction of 6,543.8+0,000 cubic meters in the first phase of treatment, and 45,000 yuan will be invested for each reduction of 6,543.8+0,000 cubic meters in the second phase of treatment. How many ten thousand yuan do you need to invest after the two-stage treatment is completed?
26. As shown in the figure, in the trapezoidal ABCD, AD‖BC, ∠B = RT∞, AD = 2 1 cm, BC = 24 cm, the moving point P starts from point A and moves along the edge of AD at the speed of 1cm/s, and the other moving point Q is from point C. Set point p and exercise time t
What is the value of (1)t, and the quadrilateral PQCD is a parallelogram?
(2) At what value of t, the quadrilateral PQCD is an isosceles trapezoid?
Mathematics at the end of the second semester of the 2006 school year in Jiangbei District.
Reference answers and grading standards
First, multiple-choice questions (2 points for each small question, 20 points for * * *)
The title is 1 23455 6789 10.
Answer a, d, c, b, b, b, b, b, b, b, b.
Fill in the blanks (2 points for each small question, 20 points for * * *)
The title is11213141516171819 20.
Answer 2
1 10 120 4 5 ① ③ π 18 1:2
III. Answer questions (2 1 22, 5 points for each minor question, ***20 points, 23 ~ 26, 10, 40 points for each minor question).
2 1, solution: (1) Original formula =-… (4 points)
= … (5 points)
⑵ b-a
= ab (a-b) .............................. (2 points)
= (3+) (3-) (3+2-3+2) ...(3 points)
=-44 ............................. (5 points)
22. Solution: (1) x (x- 1) = 0...(3 points)
∴ x 1 = 0, x2 = 1...(5 points)
(2) Divide both sides by 2.
x2-2x+ =0
∴ (x- 1)..............(2 points)
(x- 1) =+/-(4 points)
∴ x1=1+x2 =1-... (5 points)
23.( 1) Fill in 8 in the frequency column,12; Fill in 0.2 and 0.24 in the frequency column. ............. (2 points) (0.5 points for each grid)
(2) Omit (4 points)
(3) Generally speaking, it is the sum of the competition results of 850 students;
Individual is the result of competition of each student;
The sample is the competition results of 50 students;
The sample size is 50. ............. (6 points) (0.5 points per grid)
(4) 80.5 ~ 90.5 ...(8 points)
5] 204 ............( 10)
24、⑴
Take df = AE = 6, ………………… (2 points)
S diamond aefd = 6× 6 = 36 ....................... (3 points)
⑵
Take cf = AE =...........(5 points).
S diamond aecf =× 6 = ……………………………………………………………………………………………………………… (6 points).
⑶
Take the midpoint of four sides of a rectangle as A', B', C', D '...(8 points)
S diamond A 'b 'c'd' = = 24 .............. (10 points).
(2 points for each picture, 2 points for the last area, and the rest 1 point)
25. Solution: (1) Let the percentage of reduction in each period be X.
Then 450 (1-x) 2 = 288...(3 points)
X 1 = 1.8 (excluding) X2 = 0.2...(5 points)
A: Omit.
2 450× 0.2× 3+450× 0.8× 0.2× 4.5 = 594 (ten thousand yuan) ... (10)
A: Omit.
26. solution: (1) when PD = CQ, the quadrilateral PQCD is a parallelogram.
2 1-t=2t
T = 7...(5 points)
⑵ When CQ-PD = 6, the quadrilateral PQCD is an isosceles trapezoid.
2t-(2 1-t)=6
T = 9...( 10)
Basket vine, plain wax, old gull pot, bouncing, 8 surname, copying green, avoiding seeds, depicting female soldiers, carrying mule tail.
Ton-sheng qualitative debate
In the second volume of the eighth grade mathematics question bank, A did it for 6 days and B did it for 5 days, which can be regarded as 5 days of cooperation between A and B, and A did it 1 day.
Party A and Party B cooperate for 5 days.
1/8×5=5/8
1 day completed
27/40-5/8= 1/20
If this project is done by Party A alone, it will be completed.
1- 1/20 = 20 days.
Is the second question on page 36 of mathematics in the second volume of the eighth grade the People's Education Edition? The answer to the question 1 is (s+2t) 2s(s-2t) 2: (x -y) 1. Question 3: 2 (4)(u square -4v square) (u-2v square -2.
5. the sixth power of y and the ninth power of z. 6.(x+2y)3 times (x-y)3 times.
The math problems in the second volume of the eighth grade need a process of m 2+m ≠ 0 to be advanced by experts.
m(m+ 1)≠0
M≠0 and m ≠-1;
m^2-3m-5=- 1
m^2-3m-4=0
(m-4)(m+ 1)=0
M=4 or m=- 1
So m=4
y=4/x