Six olympiad math problems

Sixth grade Olympic mathematics examination questions and answers

I. Calculation: (4 points for each small question, ***20 points)

1, calculation: 0.8÷3÷9/20×3/2÷0.64×27.9=.

2. Calculation: 8/25 ÷ [(53/12-85/24) × 4/7+(55/18-3112) ÷/kl.

3. Divide the six scores 8/35, 3/8, 1/45,120, 4/9, 5/2 1 into three groups, so that the sum of the two scores in each group is equal.

4. Calculation:

5. Calculation:

Fill in the blanks: (6 points for each small question, ***60 points)

1. The bus and truck leave from A and B at the same time and meet in 4 hours. It is known that the speed ratio of passenger car to truck is 7: 5, so the truck will arrive at A one hour after the meeting.

There are nearly 65,438+000 chairs in the auditorium. Parents' meeting will be held in grade three. The original chairs were not enough, so the same number of chairs were moved from the classroom. The result is that 65,438+0/65,438+02 chairs are unoccupied. This time, a parent will come to the parents' meeting.

There are 85 students in Class A and Class B in a certain grade. Now111of the number of students in class B is transferred to class A. If the ratio of the number of students in class A to class B is 9: 8, there are students in class A. ..

Xiao Ming walks a distance at a constant speed. If he walks more than 0.5 kilometers per hour, he will save 1/5 time. If he doesn't walk to zero every hour. 5 kilometers, it took 2.5 hours more, so this journey is kilometers?

5. Four numbers ABCD, one number at a time, and the remaining three numbers are averaged. This is done four times, and the following four numbers are obtained: 36.4, 47.8, 46.2, 4 1.6. Then the average of the original four numbers is.

6. Two candles of the same length, one can light for 3 hours and the other can light for 4 hours. If the remaining length of one candle is twice that of the other at 10 in the evening, then these two candles should be lit at 8 o'clock?

7. In a class, 70% students scored above 90 points in the first practice, 75% students scored above 90 points in the second practice, and 85% students scored above 90 points in the third practice, so the number of students who scored above 90 points in three exercises accounts for at least% of the class.

8. The current time is between 10 and 1 1 point. If the minute hand of a watch is just opposite to the clockwise hand three minutes ago after six minutes, then the accurate time now is minutes.

9. After a commodity is reduced by 20%, it can still get a profit of 12% (profit = selling price-cost price). Then the profit rate (profit as a percentage of cost) of the commodity before price reduction is.

10. A triangle can be divided into three vertices and a small non-overlapping triangle with nine vertices inside the triangle.

Three. Fill in the blanks (8 points for each small question, * * * 40 points)

1 1, Xiao Zhang walked down the escalator moving at a constant speed, one step at a time, * * * walked 50 steps to the bottom, then he walked down the escalator, one step at a time, the speed was five times that of his descent, * * * walked125th to the top, the escalator stopped, and he saw one.

12, the sum of two natural numbers is 667, and the quotient obtained by dividing their least common multiple by their greatest common factor is 120, and the greater the difference between these two numbers, the better, so these two numbers are.

13. A natural number is three digits when expressed in hexadecimal, three digits when expressed in hexadecimal, and its number happens to be the reverse number when expressed in hexadecimal, so this natural number is.

In 14 and ⊿ABC, g is the midpoint of AC, DEF is the quartering point on the side of BC, AD and BG intersect at m, AF and BG intersect at n, and it is known that the area of ⊿ABM is larger than that of quadrilateral FCGN by 1.2 cm2, so the area of ⊿ABC is square cm?

The length of each side of 15 and pentagonal ABCDE is100m. A starts from A and walks in the direction of A→B→C→D→… at a speed of 70 meters per minute. B starts from E and walks in the direction of E → A → B → … at a speed of 55 meters per minute. Then they walk on the same side for the first time in minutes.

answer

I. Calculation: (4 points for each small question, ***20 points)

The Hua Song scores of 1 and 155/4 are calculated by multiplication.

2、 32/ 125

3,7/154/9 and 1/45,1120 and 3/8, 5/2 1 and 8/35.

4、 1 1/ 16

The numerator and denominator of 5, 18 are calculated simultaneously respectively.

Fill in the blanks (6 points for each question, 60 points for * * *)

1, 5.6 hours

2、 176

34 1 person

415km