1. Calculation:
. (6)
Knowledge point: calculation
Difficulty: ★
Answer: 6.
2. There are ***20 12 green dragons and white tigers guarding the temple, of which the number of green dragons is more than three times that of white tigers, and there are 12 green dragons in the temple. ( 15 12)
Knowledge points: application questions
Difficulty: ★
Answer: 15 12.
3. Kalia prepared 300 grams of sugar water with the concentration of 15%, and used _ _ _ _ grams of water. (255)
Knowledge point: concentration problem
Difficulty: ★
Answer: 255.
4.
Is an eight-digit number, and Gao Xiao fills in a number in the blank, so that the eight-digit number can be divisible by 1 1, then the number filled with a smile is _ _ _ _ _. ( 1).
Knowledge points: divisible
Difficulty: ★
Answer: 1.
There are many papers to review after the Kose Cup exam. If there are 30 people to review, 75% of all papers can be reviewed in 8 hours, then _ _ _ _ individuals can complete 25% of all work in 4 hours. (Assume that everyone works at the same efficiency every hour) (20)
Knowledge point: calculation
Difficulty: ★★
Answer: 20.
Second, multiple-choice questions (this question ***5 small questions, each small question 4 points, 20 points * * *)
6. Calculation:
The result of is (). (4)
A. 340 BC to 350 BC
Knowledge point: calculation
Difficulty: ★★
Answer: D.
7. Put some apples side by side in four drawers. Make sure there are at least three apples in a drawer, and at least () apples are needed. b
A.5 B. 9 C. 10 D. 13
Knowledge point: pigeon cage principle
Difficulty: ★
Answer: B.
8. For a project, it takes 4 hours for Party A to complete it alone and 5 hours for Party B to complete it alone, so the efficiency of Party B is lower than that of Party A (). (1)
A.20% B.25% C.30% D. This question is wrong, and B is more efficient.
Knowledge points: engineering problems
Difficulty: ★
Answer: a.
9.a, B, C and D represent different prime numbers and satisfy:, then the sum of may be one of the following options (). (3)
A.24 B. 26 C. 27 D. 28
Knowledge points: prime numbers and composite numbers
Difficulty: ★★
Answer: C.
10. In the table shown in the figure, adding 1 or subtracting 1 to the numbers in two adjacent cells at the same time is called an operation. After several operations, the left table becomes the right table, and the number filled with G in the right table is _ _ _ _ _ _. (2).
nine
six
six
six
eight
eight
eight
eight
G
four
2
nine
2
1
2
A.0 B. 1 C. 3 D. 5
Knowledge point: combination problem
Difficulty: ★★★★
Answer: B.
Three. Fill in the blank 2 (there are 5 small questions in this question, each with 5 points and 25 points * * *).
1 1. Brothers A, B and C each collect some precious stones. Every morning, they get together to redistribute the gems. The distribution rule is: the person with the most gems gives it to the other two people 1. If A, B and C have 10, 7 and 5 gems at the beginning, then
Knowledge points: finding regular problems
Difficulty: ★★★★
Answer: 7.
A: From the first day, the number of gems of three people is: (8, 8, 6)(6, 9, 7)(7, 7, 8)(8, 8, 6)(6, 9, 7)(7, 7, 8). ...
12. Gauss's competition textbook is sold in 25 yuan, and Gauss's thinking training guide is sold in 19 yuan. Students in Class A and Class B have just spent 770 yuan on textbooks and guides. As we all know, students in Class A buy more books than students in Class B, so students in Class A buy more books than students in Class B..
Knowledge point: indefinite equation problem
Difficulty: ★★
Answer: 6.
Answer: 25 yuan and the book with the price of 19 yuan spent 770 yuan. The equation can be listed as follows: the solution of this equation is:, so the two students in the topic only buy books in the above two ways, with a difference of 6 books.
13. Natural numbers include 1 and its own ***8 divisor. If two of the divisors are 6 and 2 1, then the natural number is _ _ _ _ .4.
Knowledge points: number theory problems
Difficulty: ★★★★
Answer: 42.
Answer: From the fact that the two divisors of this natural number are 6 and 2 1, we can know that after this natural number is decomposed into prime factors, it must contain prime factors 2, 3 and 7, so the natural number composed of 2, 3 and 7 is 42, and 42 has exactly 8 divisors.
14. Xiaoming got 20 questions in the first math exam when he entered middle school, and each question got 5 points right, 0 points wrong and 2 points deducted. If Xiao Ming's final score is a prime number, he can answer _ _ _ _ _ _ questions correctly at most in this test.
Knowledge point: the most valuable question
Difficulty: ★★★★
Answer: 17.
Answer: First of all, Xiao Mingcan answers 20 questions correctly at most, but at this time the total score is 100, not a prime number. If Xiao Ming answers 19 correctly, then the total score may be 95 and 93, both of which are not prime numbers. Next, suppose Xiao Ming answers 18 correctly, and the total score may be 90, 88, 86, 84, all of which are not prime numbers.
15. 10
12
12
12
12
As shown in the figure, it is a side development diagram of a three-dimensional figure (unit: cm), so the volume of this three-dimensional figure is _ _ _ cubic cm. (π takes 3.14)1130.4.
Knowledge points: solid geometry
Difficulty: ★★★★★
Answer: 1 130.4.
Answer: First, determine that the three-dimensional figure is a quarter cylinder, the bottom radius is 12 cm, and the height is 10 cm, then the volume of the three-dimensional figure is
Square centimeters.
Four. Fill in the blank 3 (there are 5 small questions in this question, each with 6 points and * * * 30 points)
16. Arrange three squares with sides of 2cm, 3cm and 4cm as shown in the figure. It is known that the area of delta bed is 5cm, so the area of delta △AEC is _ _ _ _ _ _ _ cm2.4..
A
B
C
D
E
Knowledge point: linear area calculation
Difficulty: ★★★★★
Answer: 4.
Answer: According to the picture, the area of triangle ABC is 5 square centimeters, the area of triangle ABD is 6 square centimeters, and the area of triangle ABE obtained by subtracting triangle BED from triangle ABD is 1 square centimeter, so the area of triangle AEC is 4 square centimeters.
17. As we all know, A, B and C represent three different four-digit natural numbers and satisfy the following equation:
, then,
.
Knowledge point: algebraic calculation
Difficulty: ★★★★
Answer: 1.
Answer: Through the formula:
Available:
、
,
, so
,
.
18. Known formula:
, each different Chinese character represents a different number, such as "
"represents a three-digit number, then
The minimum value of is _ _ _ _ _. (243× 1769 = 429867).
Knowledge point: crossword puzzle synthesis
Difficulty: ★★★★★★★
Answer: 429867.
Answer: the sum of two numbers is the same, and the greater the difference between the two numbers, the smaller the product. The situation that satisfies the meaning of the question must be
、
The bigger the difference between these two numbers, the better, so it must be bigger. First, consider that the maximum four digits are 1987, but at this time,
It's not three digits. Considering that the first "high" of three digits can't be 1, the maximum value of four digits is.
The empirical calculation shows that the four digits that meet the meaning of the question are at most 1769, and the three digits are 243, so the minimum product is 243 × 1769 = 429867.
19. On the circular runway, Gao Xiao, Xiao Si and Xiaobei start from point A of the runway at the same time. Gao Xiao advances clockwise, while Xiao Si and Xiaobei advance counterclockwise. When Gao Xiao first met Xiao Si, he advanced 503 meters. After the meeting, Gao Xiao walked on and walked 503 meters to meet Xiaobei for the first time. If Gao Xiao tripled his speed when he left, Gao Xiao would meet Xiaobei for the first time.
Knowledge point: trip problem
Difficulty: ★★★★★★★
Answer: 20 12 meters.
Answer: When Gao Xiao met Xiao Bei for the first time, the distance he walked was 2×503= 1006 meters, and the time was "1". When Gao Xiao met Xiaobei for the second time, he walked 1506 meters, which is equivalent to the time it took to walk 503 meters at the original speed. That is to say, comparing Xiaobei twice, we will find that Xiaobei's time of 1 is 503 meters longer than that of "0.5" and its speed remains unchanged. Xiaobei walked 1006m when he met Gao Xiao for the first time, and the sum of the distances they walked was the runway perimeter 1006+ 1006 = 20656.
20. Define the power of 1, 10, 100, 1000, ... and so on. As a "six-year series". If a number can be written as the sum or difference of one or several different "six-year series", it is called this number.
) is "new grade one number", 1 10 (
) is also a "new junior high school number", but 12 is not a "new junior high school number". We arrange the "new junior high school numbers" from small to large, and the number 120 is _ _ _ _ _ _ _. (All "six-year program" and "new junior high school number" are positive integers)
Knowledge point: counting problem
Difficulty: ★★★★★★★★
Answer:111/kloc-0.
A: 1 can be composed of 1, 1 and 10 can be composed of 1+3, while 1, 10. 1, 10, 100, 1000, 100000 can form1+3+9+27+8. The largest is1111,so 120 is 1 165438.
Five, solve the problem (this question 10)
2 1. A frog jumps straight from point A to play. It is known that it can jump left and right every time, the first jump is 1 cm, the second jump is 3 cm, and the third jump is 5 cm.
A
1
2
three
four
five
six
seven
eight
nine
10
Excuse me:
(1) Can it jump to the left of point A at 100 cm? If yes, how many jumps are required at least; If not, please explain why.
(2) Can you jump to the left of point A at 20 12 cm? If yes, how many jumps are required at least; If not, please explain why.
Knowledge points: combinatorial mathematics problems
Difficulty: ★★★★★
Answer: (1) Yes, there is at least 10 jump.
All the way to the left:1+3+5+7+9+1+kloc-0/3+15+17+19 =/kloc-.
(2) Yes, at least 46 jumps.
First of all, because you jump an odd number of centimeters every time, how many times do you have to jump to the left of 20 12 cm? Because jumping 44 times can only jump to the left of cm at most, it needs at least 46 times.
We can jump 46 times to the right to get 2 1 16, and then adjust 2 1 16, 2116-2012 =12.
So, at least 46 times.