1. The scoring rules of a football match are: 3 points for winning a game, 0 points for losing a game, 1 point for drawing a game, 14 points for kicking a team and 19 points for losing five games. Then the team won ().
3 games; 4 games; 5 games; Six games.
2, the original price of a commodity after two price cuts, the current price is yuan, if the percentage of each price reduction is, then the following statement is correct ().
; ;
; .
The output value of a factory rose from 500,000 in March last year to 720,000 in May. What is the average monthly growth rate in these two months? If the percentage of the average monthly growth rate is, the equation listed is (00).
00(A)00000(B)
0000(D)
4. Use a rectangular thin steel plate with a length of 80㎝ and a width of 60㎝, cut four small squares with the same side length at four corners, and then make an uncovered rectangular box with a bottom area of 1500㎝2. In order to make it clear, the equations are listed according to the meaning of the question and sorted out to get (00).
(A)00 (B)00
00 (D)
Second, fill in the blanks
1, the product of two consecutive natural numbers is 56, so the sum of these two natural numbers is _ _ _ _ _ _ _ _.
2. The length of two right-angled sides of a right-angled triangle is, and the length of the hypotenuse is, so = _ _ _ _ _ _.
3. On June 5, 2003, 5438+ 10/5, the Shanghai Composite Index was 1608, and it rose to 1622 on June 5, 2003. If the daily average exponential growth rate is 0, the equation can be listed as _ _ _ _ _.
A factory plans to increase its output by 44% in two years. If the annual growth rate is the same as the previous year, the growth rate is _ _ _ _ _ _ _ _ _ _.
The lower bottom of the trapezoid is 3 longer than the upper bottom, the height is shorter than the upper bottom 1, and the area is 26. If the ground is set to, then the equation _ _ _ _ _ _ _ _ can be listed.
6. Everyone in a group sent a photo to others, and 90 photos were sent in the whole group, so there are _ _ _ _ _ _ _ _ individuals in this group.
7. Forging a cube steel with a length of 30mm into a cylindrical part blank with a radius of mm and a height of 100mm, then the equation that can be listed is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
8, a two-digit number, its value is equal to three times the square of the number in its unit, and the number in the tenth place is 2 larger than the number in its unit. If the number on the unit is set to, list the equation _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Third, short answer questions
1 has a two-digit number, and the sum of the number on the tenth and the number on the fourth is 8. If the number on the tenth digit is exchanged with the number on the fourth digit, the two digits obtained are multiplied by the original two digits, and 1855 is obtained. Find the original two digits.
2. Yiqun Boutique buys a batch of goods at the price of 2 1 yuan per piece, and can set its own price. If the price of each product is one yuan, you can sell (350- 10a) pieces, but the price bureau limits the profit of each product to no more than 20%. How many pieces do you need to purchase if the store plans to make a profit in 400 yuan? How much should each commodity be priced?
3. For the first time, 1 0,000 yuan lucky money was hidden in children's bank in Wang Hongmei. After the expiration, he took out the principal and interest, donated 500 yuan to Project Hope, and saved all the rest for one year. At this time, the annual interest rate of the deposit has been reduced to 90% of the annual interest rate at the time of the first deposit. After the maturity, he can get the principal and interest * * 530 yuan. When looking for the first deposit,
4. The sales of a commercial building in September was 2 million, which decreased by 20% in 10. Since 1 1 month, the management and operation of commercial buildings have been strengthened, which has led to a steady increase in sales.1February sales reached 654.38+0.936 million yuan. Let's find the average growth rate in these two months.
5. Make a rectangular wasteland with a length of 18m and a width of 15m into a garden (shaded part), accounting for two thirds of the original wasteland area (accurate to 0. 1m).
(1) design scheme 1 (as shown in figure 1) There are two paths in the garden that are perpendicular to each other and have the same width.
(2) Design Scheme 2 (as shown in Figure 2) Every corner of the garden has the same fan shape.
Can the above two schemes meet the requirements? If yes, please calculate the width of the path in Figure 2 and the radius of the sector in Figure 3. If you can't meet the requirements, please explain the reasons.
Ability improvement
As shown in Figure 3, at △ABC, ∠ C = 90, AC = 6 cm, BC = 8 cm, point P moves from point A to point C along AC at a speed of 1cm/s, and point Q moves from point C to point B along CB at a speed of 2 cm/s. 。
(1) If p and q start at the same time, after a few seconds, can the area of △PCQ be 8 square centimeters?
(2) Whether there is a certain moment in the movement of points P and Q, so that the area of △PCQ is equal to half the area of △ABC. If yes, find out the exercise time; If it does not exist, explain why.
Answer:
First, multiple choice questions
1.C 2。 B 3。 D 4。 A
Second, fill in the blanks
1.7 and 8 or -7 and -8 2.5 3. 4.20%
5.6. 10 7.8.
Third, short answer questions
2. Solution: According to the meaning of the question, (a-21) (350-10a) = 400,
Finishing, A2-56a+775 = 0,
Solve this equation to get A 1 = 25, A2 = 3 1.
Because 2 1× (1+20%) = 25.2,
So a2=3 1 is irrelevant, so it is discarded.
So 350-10a = 350-10× 25 =100 (piece).
Answer 0 needs to purchase 100 pieces, and each piece should be priced in 25 yuan.
Let's assume that the annual interest rate of the first deposit is X.
According to the meaning of the question, [1000 (1+x)-500] (1+0.9x) = 530.
90x2+ 145x-3 = 0。
Solving this equation, we get X 1 ≈ 0.0204 = 2.04%, X2 ≈- 1.63.
Since the deposit interest rate cannot be negative, X 2 ≈- 1.63 is omitted.
The annual interest rate of the first deposit is about 2.04%.
0 let the average growth rate of these two months be x,
Then according to the meaning of the question, 200 (1-20%) (1+x) 2 =193.6,
That is (1+x) 2 = 1.5438+0,
Solving this equation, we get x 1 = 0. 1, x2 =-2. 1 (excluding).
Answer 0 The average growth rate in these two months is 10%.
5. All solutions can be solved.
(1) Let the width of the path be x, then18x+16x-x2 =×18×15,
That is x2-34x+ 180 = 0,
Solve this equation to get x =, that is, x≈6.6.
(2) Let the sector radius be r, then 3.14R2 =×18×15,
That is r2≈57.32, so r≈7.6.
Ability improvement
Solution 0 because ∠ c = 90, AB = = = 10 (cm).
(1) After setting xs, the area of △PCQ can be 8cm2, so AP = xcm, PC = (6-x) cm and CQ = 2xcm.
Then according to the meaning of the question, we get (6-x) 2x = 8. After sorting, we get x2-6x+8 = 0. If we solve this equation, we get x 1 = 2 and x2 = 4.
Therefore, starting from p and q at the same time, the area of △PCQ after 2s or 4s can be 8cm2.
(2) X seconds from point P, the area of △PCQ is equal to half the area of △ABC.
According to the meaning of the question, (6-x) 2x =×× 6× 8. After sorting, x2-6x+ 12 = 0.
Since this equation has no real root, there is no time to make the area of △PCQ equal to half the area of ABC.