1. There are 30 boys and 20 girls in one class. 60% of the boys and 30% of the girls participated in the astronomy group, accounting for () of the class.
A.60% B.48% C.45% D.30%
2.=( )
Answer. -b-c-d-
3. Points A, B and C on the number axis correspond to numbers: 0,-1.x, and the distance from C to A is greater than that from C to B, then ().
Answer. x & gt0b . x & gt； - 1 c . x & lt； -D . x & lt； - 1
4. For any three integers, then ().
It is unlikely that their total numbers will be equal. It is very unlikely that their sum is odd.
C. there must be an odd number d and an even number d.
A car with a full tank is driving at a constant speed. When the fuel tank is half full, it will be full of fuel. Then, if you drive at the original speed, when you arrive at your destination, there will be a certain volume of gasoline left in the tank. Let the remaining amount of gasoline in the fuel tank be V (liter) and the time be T (minute). So the v and t are like ().
6. Cut the line segment with the length of 12 into three segments with integer length and make them three sides of the triangle, then the triangle is formed ().
A cannot be an isosceles triangle. B can't be a right triangle.
C. it can't be an equilateral triangle. D. it can't be an obtuse triangle.
7. There is a kind of spring scale that can weigh 16 kg. When weighing, it is found that the length (cm) of the spring has a certain relationship with the weight (kg) of the object. According to the table below, the longest spring is () cm within the weighing range of springs.
Weight (kg)
0 .5
1 .O
1 .5
2 .O
2 .5
3 .O
Length (cm)
5 .5
6 .0
6 .5
7 .0
7 .5
8 .0
a . 18 16. 19 c . 20d . 2 1
8.If (a) = For all integers (a), and B =
36 13.72
9. There is a series of numbers: -2003,-1999,-1995,-199 1 ... arranged according to a certain rule, then the sum of the first () numbers in this series is the smallest.
A.500 B.50 1 C.502 D.503
1o。 "Hope Cup" four schools football invitational tournament regulations:
(1) The competition adopts the form of single round robin;
(2) If there is a winner, the winning team will get 3 points and the losing team will get 0 points;
(3) The average score of each team 1 point.
After the game, the total scores of the four teams can't be ().
A.8, B.7, C.6 and d.5.
Fill in the blanks (5 points for each small question. * * * 50 points)
1 1. If the root of equation 2003x+4a = 2004a-3x is x=l, then a =.
12. As shown in the figure, the side lengths of large and small squares are integers (centimeters), and the sum of their areas is equal to 74 square centimeters. Then the area of the shadow triangle is square centimeters.
13. If x2+x2+x- 1=0 = 0, then x3+2x2+3 =.
14. If a, b, c and d are rational numbers, | A-B |≤ 9, | C-D |≤ 16 and | A-B-C+D | = 25, then | B-A |-D-.
15.a and both are positive integers, then a =.
16. As shown in the figure, ABCD is a parallelogram, e is on AB, f is on AD, S△BCE=2S△CDF= S□ABCD= 1, then S △ CEF =.
17. Roll a cone with a central angle of 120 and a radius of 6 cm. The surface area of this cone is cm2.
18. Draw a straight line to divide the plane into two parts, draw two straight lines to divide the plane into four parts at most, then draw six straight lines to divide the plane into four parts at most.
19.a and b are reciprocal, and | A-B | =. So =
20. Positive integers m and n have the greatest common divisor greater than 1 and satisfy m3+n=37 1, then mn=.
Three. Problem solving (2 1, 23 questions each 15, 22 questions 20 points ***50 points)
2 1. A classmate wants to make a big square with five squares with different sides as shown in the figure. Can this classmate's idea come true? If it can be realized, try to find the side lengths of these five squares; If not, please explain why.
22. the "h operation" of positive integer n is defined as
(1) When n is odd, h = 3n+13;
② When n is even, h = n×× font-size:11.0pt; ×… (where h is an odd number).
For example, the number 3 is 22 after 1 H operation and 1 1 after 2 H operation. After three "H operations", the result is 46.
Please answer:
(1) The number 257 is the result of 257 "h operations".
(2) If the result of "H operation" ② is always constant, find the value of a. 。
23. The disaster relief headquarters packed the relief items into 34 containers: 4 tons, 3 containers, 3 tons, 4 containers and 2.5 tons, 5 containers. There are 10 containers 1.5 tons and l2 containers 1 ton. How many cars with a load of 5 tons are needed to transport these relief items at a time? Put forward your transportation plan.
First, multiple-choice questions (5 points for each small question. * * * 50 points)
1. There are 30 boys and 20 girls in one class. 60% of the boys and 30% of the girls participated in the astronomy group, which accounts for () of the class.
A.60% B.48% C.45% D.30%
2.=( )
Answer. -b-c-d-
3. Points A, B and C on the number axis correspond to numbers: 0,-1.x, and the distance from C to A is greater than that from C to B, then ().
Answer. x & gt0b . x & gt； - 1 c . x & lt； -D . x & lt； - 1
4. For any three integers, then ().
It is unlikely that their total numbers will be equal. It is very unlikely that their sum is odd.
C. there must be an odd number d and an even number d.
A car with a full tank is driving at a constant speed. When the fuel tank is half full, it will be full of fuel. Then, if you drive at the original speed, when you arrive at your destination, there will be a certain volume of gasoline left in the tank. Let the remaining amount of gasoline in the fuel tank be V (liter) and the time be T (minute). So the v and t are like ().
6. Cut the line segment with the length of 12 into three segments with integer length and make them three sides of the triangle, then the triangle is formed ().
A cannot be an isosceles triangle. B can't be a right triangle.
C. it can't be an equilateral triangle. D. it can't be an obtuse triangle.
7. There is a kind of spring scale that can weigh 16 kg. When weighing, it is found that the length (cm) of the spring has a certain relationship with the weight (kg) of the object. According to the table below, the longest spring is () cm within the weighing range of springs.
Weight (kg)
0 .5
1 .O
1 .5
2 .O
2 .5
3 .O
Length (cm)
5 .5
6 .0
6 .5
7 .0
7 .5
8 .0
a . 18 16. 19 c . 20d . 2 1
8.If (a) = For all integers (a), and B =
36 13.72
9. There is a series of numbers: -2003,-1999,-1995,-199 1 ... arranged according to a certain rule, then the sum of the first () numbers in this series is the smallest.
A.500 B.50 1 C.502 D.503
1o。 "Hope Cup" four schools football invitational tournament regulations:
(1) The competition adopts the form of single round robin;
(2) If there is a winner, the winning team will get 3 points and the losing team will get 0 points;
(3) The average score of each team 1 point.
After the game, the total scores of the four teams can't be ().
A.8, B.7, C.6 and d.5.
Fill in the blanks (5 points for each small question. * * * 50 points)
1 1. If the root of equation 2003x+4a = 2004a-3x is x=l, then a =.
12. As shown in the figure, the side lengths of large and small squares are integers (centimeters), and the sum of their areas is equal to 74 square centimeters. Then the area of the shadow triangle is square centimeters.
13. If x2+x2+x- 1=0 = 0, then x3+2x2+3 =.
14. If a, b, c and d are rational numbers, | A-B |≤ 9, | C-D |≤ 16 and | A-B-C+D | = 25, then | B-A |-D-.
15.a and both are positive integers, then a =.
16. As shown in the figure, ABCD is a parallelogram, e is on AB, f is on AD, S△BCE=2S△CDF= S□ABCD= 1, then S △ CEF =.
17. Roll a cone with a central angle of 120 and a radius of 6 cm. The surface area of this cone is cm2.
18. Draw a straight line to divide the plane into two parts, draw two straight lines to divide the plane into four parts at most, then draw six straight lines to divide the plane into four parts at most.
19.a and b are reciprocal, and | A-B | =. So =
20. Positive integers m and n have the greatest common divisor greater than 1 and satisfy m3+n=37 1, then mn=.
Three. Problem solving (2 1, 23 questions each 15, 22 questions 20 points ***50 points)
2 1. A classmate wants to make a big square with five squares with different sides as shown in the figure. Can this classmate's idea come true? If it can be realized, try to find the side lengths of these five squares; If not, please explain why.
22. the "h operation" of positive integer n is defined as
(1) When n is odd, h = 3n+13;
② When n is even, h = n×× font-size:11.0pt; ×… (where h is an odd number).
For example, the number 3 is 22 after 1 H operation and 1 1 after 2 H operation. After three "H operations", the result is 46.
Please answer:
(1) The number 257 is the result of 257 "h operations".
(2) If the result of "H operation" ② is always constant, find the value of a. 。
23. The disaster relief headquarters packed the relief items into 34 containers: 4 tons, 3 containers, 3 tons, 4 containers and 2.5 tons, 5 containers. There are 10 containers 1.5 tons and l2 containers 1 ton. How many cars with a load of 5 tons are needed to transport these relief items at a time? Put forward your transportation plan.