3. If m < 0, n > 0, | m |
4. Let (3x-1) 7 = A7X7+A6X6+…+A1X+A0, and try to find the value of A0+A2+A4+A6.
5. Known equation
If there is a solution, find the value of k.
6. Solve equation 2 | x+ 1 |+x-3 | = 6.
7. Solving equations
8. Solve the inequality || x+3 |-x- 1 || > 2.
9. Compare the following two figures:
10.x, y and z are nonnegative real numbers and satisfy:
x+3y+2z=3，3x+3y+z=4，
Find the maximum and minimum values of u = 3x-2y+4z.
1 1. Find the quotient and remainder of x4-2x3+x2+2x- 1 divided by x2+x+ 1.
12. As shown in figure 1-88, Zhu Xiao lives in village A and grandma lives in village B. On Sunday, Zhu Xiao went to visit her grandmother. She first cut a bundle of grass on the north slope, and then cut a bundle of firewood on the south slope to send it to her grandmother. Excuse me, which route should Zhu Xiao take for the shortest journey?
13. As shown in figure 1-89, AOB is a straight line, OC and OE are bisectors of ∠AOD and ∠DOB, respectively, and ∠ COD = 55. Find the complementary angle of ∠DOE.
14. As shown in figure 1-90, the bisected line ∠ABC, ∠ CBF = ∠ CFB = 55, ∠ EDF = 70. Verification: BC ∠ AE.
15. As shown in figure 1-9 1. In △ABC, EF⊥AB, CD⊥AB, ∠ CDG = ∠ BEF. Verification: ∠ AGD = ∠ ACB.
16. As shown in figure 1-92. In △ABC, ∠B=∠C, BD⊥AC is in D.
17. As shown in figure 1-93. In △ABC, e is the midpoint of AC, d is on BC, BD∶DC= 1∶2, and AD and BE intersect at F. Find the ratio of the area of △BDF to the area of quadrilateral FDCE.
18. As shown in figure 1-94, two opposite sides of quadrilateral ABCD extend and intersect at K and L, and diagonal AC‖KL and BD extension lines intersect at F. Verification: KF = FL.
19. Can the sum of the number obtained by arbitrarily changing the order of a three-digit number and the original number be 999? Explain why.
20. There is a piece of paper with 8 rows and 8 columns, in which 32 squares are randomly painted black and the remaining 32 squares are painted white. Next, the color grid paper is operated, and each operation changes the color of each square in any horizontal or vertical column at the same time. Can you finally get a grid paper with only one black square?
2 1. If both positive integers p and p+2 are prime numbers greater than 3, then verify: 6 | (p+ 1).
22. Let n be the smallest positive integer satisfying the following conditions, which is a multiple of 75 and has exactly
23. There are several stools and chairs in the room. Each stool has three legs and each chair has four legs. When they are all seated, * * * has 43 legs (including everyone's two legs). How many people are there in the room?
24. Find the integer solution of the indefinite equation 49x-56y+ 14z=35.
25. Eight men and eight women dance in groups.
(1) If there are two substations, male and female;
(2) If men and women stand in two rows, in no particular order, only consider how men and women form a partner.
How many different situations are there?
26. 1, 2, 3, 4, 5, how many numbers are greater than 34 152?
27.A train is 92 meters long and B train is 84 meters long. If they travel in the opposite direction, they will miss each other after 1.5 seconds. If they travel in the same direction, they will miss each other in six seconds. Find the speed of two trains.
28. The two production teams of Party A and Party B grow the same vegetables. Four days later, Team A will finish the rest alone. It will take two more days. If Party A finishes all the tasks by itself three days faster than Party B, how many days does it take to ask Party A to finish it by itself?
29. A ship starts from a port 240 nautical miles apart, and its speed decreases by 65,438+00 nautical miles per hour before reaching its destination 48 nautical miles. The total time it takes after its arrival is equal to the time it takes for the whole voyage when its original speed is reduced by 4 nautical miles per hour, so that we can find out the original speed.
30. Last year, two workshops A and B of a factory planned to complete tax profits of 7.5 million yuan. As a result, workshop A exceeded the plan 15%, workshop B exceeded the plan 10%, and two workshops * * * completed tax profits of 8.45 million yuan. How many million yuan of tax profits did these two workshops complete last year?
3 1. It is known that the sum of the original prices of two commodities is 150 yuan. Due to market changes, the price of the first commodity decreased by 10%, and the price of the second commodity increased by 20%. After the price adjustment, the sum of the unit prices of the first and second commodities decreases by 1%. What are the original unit prices of the first and second commodities respectively?
Xiaohong bought two children's toothbrushes and three toothpastes in the shop last summer vacation, and just ran out of money with her. It is known that each toothpaste is more than each toothbrush 1 yuan. This summer, she took the same money to the store and bought the same toothbrush and toothpaste. Because each toothbrush rose to 1.68 yuan this year and the price of each toothpaste rose by 30%, Xiaohong had to buy two toothbrushes and two toothpastes, and she got back 40 cents. How much is each toothpaste?
33. If a shopping mall sells goods with a unit price of 8 yuan per piece 12 yuan, it can sell 400 pieces every day. According to experience, if each piece is sold less 1 yuan, you can sell more than 200 pieces every day. How much should each piece be reduced to get the best benefit?
34. The distance from Town A to Town B is 28 kilometers. Today, A rode his bike at a speed of 0.4km/min, and set out from Town A to Town B. After 25 minutes, B rode his bike to catch up with A at a speed of 0.6km/min. How many minutes does it take to catch up with A?
35. There are three kinds of alloys: the first contains 60% copper and 40% manganese; The second type contains manganese 10% and nickel 90%; The third alloy contains 20% copper, 50% manganese and 30% nickel. Now a new alloy containing 45% nickel is composed of these three alloys, and its weight is 1 kg.
(1) Try to express the weight of the second alloy by the weight of the first alloy in the new alloy;
(2) Find out the weight range of the second alloy in the new alloy;
(3) Find out the weight range of manganese in the new alloy.
05 ~ 06 school year (1) Mid-term exam for Grade 7.
Mathematics Test
I. Fill in the blanks (2 points for each small question, 26 points for * * *)
1、│-7│=7
2. The reciprocal of-7 is -( 1/7).
3. The approximate value of 0.5 19 accurate to the percentile is 0.52.
4. Calculation: (-1) 2006 =-2006
5、(-7.5)+6.9 =-0.6
The reciprocal of 6 and -5 is 5.
7. expressed by scientific counting method: 457100 = 4.571x10 to the fifth power.
8. The number represented by a point with a distance of 3 from the point representing 1 on the number axis is 4 or -2.
9, given that m < 0, then
10, if x 2 = 4, then x =2.
1 1, comparison size: -3 is less than -2.
12, if x = 4 is the solution of the equation ax-2x = 4, then a =3.
13, known as:, then.
Second, multiple-choice questions (3 points for each small question, *** 15 points)
14. Among the following approximate figures, the figure with four significant figures is ......................... ().
(A)0.0320(B)0.0032(C)0.3200(D)0.0302
15. Among the following statements, the correct one is ................................ ().
(1) Positive numbers and negative numbers are collectively called rational numbers.
(b) The sum of two opposite numbers is zero.
(c) If the absolute values of two numbers are equal, then the two numbers must be equal.
(D) 0 is the smallest rational number.
17, the scoring rule of football match is to win a game and get 3 points; 1 is a draw; Negative competition gets 0 points,
A team played 14 games, lost 5 games and got 19 points, so this team won ..................................................... ().
(A)3 games (B)4 games (C)5 games (D)6 games.
18, the sum of two numbers is negative and the product is positive. Then these two numbers are .................... ().
(a) Two negative numbers; (b) two positive numbers; (c) One positive and one negative; (d) One is 0.
Iii. Calculate the following questions (5 points for each small question, 20 points for * * *)
19、9+(-2)- 10-(-8) 20、∣-48∣÷8-(-4)×
2 1、-2 4+(-75)÷(-5)2-(-4)×(-3)
26. Observe the following:
1 3 = 1 2
1 3+2 3 =3 2
1 3+2 3+3 3 = 6 2
1 3+2 3+3 3+4 3 = 10 2
…………………………
According to the above law, write the seventh formula:
27. Shareholder Xiao Li bought 1 000 shares of a company last Friday, and each share was 27 yuan. The following table shows the daily share of this week.
The fluctuation range of the stock (unit: yuan).
Sidereal period 12345
Up and down +4+4.5- 1-2.5-6 per share.
(1) At the close of trading on Wednesday, RMB per share;
(2) The highest price per share this week is RMB, and the lowest price is RMB;
(3) It is known that Xiao Li paid a handling fee of 1.5‰ when he bought the stock, and also paid a handling fee of 1.5‰ when he sold it.
And 1‰ transaction tax. If Xiao Li sells all his stocks at the close of Friday, what is his profit and loss?
Six, column equation to solve application problems (8 points)
28.a fish farm warehouse stores 30 tons of fish, and B warehouse stores 40 tons of fish. Now we need to transport them to these two warehouses.
Send 80 tons of fish, so the stock of fish in warehouse A is 1.5 times that of warehouse B. It should be divided into warehouse A and warehouse B.
Don't transport many tons of fish.
A functional test paper
1. Fill in the blanks: (30 points)
1. Given that the circumference of a rectangle is 24 and one side of it is X, Then the functional relationship between its area Y and X is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
2. Plan to spend 500 yuan to buy basketball. The functional relationship between the total number of purchasable pieces n (pieces) and the unit price a (yuan) is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _, where _ _ _ _ _ _ _ is the independent variable and _ _ _ _ _ _ _.
3. In the function, the value range of the independent variable x is _ _ _ _ _ _ _ _ _ _ _. In the function y= 15-x, the value range of the independent variable x is
4. The following function: ① y = 2x2+x+1② y = 2π r3y = ④ y = (-1) x.
⑤ y =-(a+x) (A is a constant) has _ _ _ _ _ _ _ _.
5. The coordinates of the intersection of the straight line y=3-9x and the X axis are _ _ _ _ _ _ _ _ _ _ _ _ _.
6. If the straight line y = kx+b is parallel to the straight line y = 3x+4 and passes through (1, -2), then k=.
7. If it is known that the image of the linear function y =(m+4)x+m+2(m is an integer) does not pass through the second quadrant, then m =；;
8. The image of linear function y = kx+b passes through points A (0 0,2) and B (- 1, 0). If the image is translated by 2 units along the Y axis, the resolution function corresponding to the new image is:
9. The spring will stretch when it is hung on an object. According to the measurement, the length y(cm) of the spring has the following relationship with the mass x(kg) of the suspended object:
x 0 1 2 3 4 5 6 7 8
y 12 12.5 13 13.5 14 14.5 15 15.5 16
Then the functional relationship between the total length y(cm) of the spring and the mass x(kg) of the suspended object is:
Second, the choice (30 points)
1. In the same rectangular coordinate system, for the function: ① y =–x–1; ②y = x+ 1； ③y =–x+ 1； (4) y =-2 (x+ 1) image, the following statement is correct ().
A, ① and ③ B pass through the point (–1,0), ② and ④ intersect on the Y axis.
C, ① and ③ D are parallel to each other, and ② and ③ are symmetrical about X axis.
2, known function y=, when x=a, the function value is 1, then the value of a is ().
A.3 B.- 1 C.-3 D. 1
3. If the image of function y=kx passes through point P(3,-1), then the value of k is ().
a3 B- 3 c d-
4. In the following function, the image passing through the origin is ()
a . y = 5x+ 1 b . y =-5x- 1 c . y =-d . y =
5. Both point A (–5, y 1) and point B (–2, y2) are on the straight line y =–12x, so the relationship between y 1 and y2 is ().
a、y 1≤y2 B、y 1=y2 C、y 1y2
6. Function y = k (x–k) (k < 0 = no image ().
A, the first quadrant b, the second quadrant c, the third quadrant d and the fourth quadrant
7. To get the straight line y= from the image of y= x, we should put the straight line y= x ().
(a) upward translation by unit; (b) Downward translation by unit.
(c) translate 2 units up; (d) translate 2 units down.
8, a pool of water storage of 20 m3, open the valve after the outflow of 5 m3 per hour, the cubic number of remaining water in the pool after the water Q (m3) and the functional relationship between the water time t (when) is graphically represented as ().
9. it is known that the linear function y=kx+b, y decreases with the increase of x, and kb
(A) (B) (C) (D)
10. After dinner on Sunday, Xiaohong set out from home for a walk. The chart describes the functional relationship between walking time and walking time. According to the picture, the following description conforms to Xiaohong's walking scene ().
(1) Starting from home, I went to a newspaper column, read the newspaper for a while, and then went home.
(b) Start from home, go straight (non-stop) and then go home.
(c) From home, I went to a newspaper column and read the newspaper for a while.
Go for a while, then go home.
(d) Starting from home, I walked a long way to find my classmates. 18 minutes later.
Before starting to return.
Third, answer questions:
The image of linear function y = kx+b passes through points (-2,3) and (1, 3).
① Find the values of k and b; ② Judge whether (-1, 1) is on this straight line?
2. Knowing that the image of a linear function is parallel and passes through the point (2,-1), find the analytical expression of this linear function. And draw the image of linear function.
The starting price of taxis in a city within 3.5㎞ is 8 yuan. For each increase of 1㎞ and 1 yuan in the future, please write down the functional relationship between the taxi distance x㎞ and the charge y yuan, and draw a picture. How much did Xiao Ming pay for taking 10㎞, if Liang Xiao paid it?
A factory in Beijing and a factory in Shanghai made several computers at the same time. The factory in Beijing can support 10 foreign computers, and the factory in Shanghai can support 4 foreign computers. It is now decided to give Chongqing 8 sets and Hankou 6 sets. If the freight rates from Beijing to Hankou and Chongqing are 400 yuan/Taiwan and 800 yuan/Taiwan respectively, then the freight rates from Shanghai to Hankou and Chongqing are 300 yuan/Taiwan and 500 yuan/Taiwan respectively. Q:
(1) Write the functional relationship between the total transportation cost from Beijing to Chongqing X Station and transportation;
(2) If the total freight is 8400 yuan, how many units will be shipped from Shanghai to Hankou?