1. At 6: 45 on the clock face, the hour hand is _ _ _ _ _ _ _ degrees behind the minute hand. Hang Shunqing's sixth grade Olympic Mathematics course P 13 1_8.

Answer: 67.5 degrees.

Solution: At 6: 45, the minute hand points to the word 9, and the hour hand rotates 0.5×45=22.5 degrees from the position of the word 6.

The hour hand lags the minute hand: 90-22.5 = 67.5 degrees.

Li Ying and Huang Ming scrambled to climb the stairs. When Li Ying takes three stairs, Huang Ming can take five. There are 20 stairs between every two floors in this building, so when Huang Ming walks to the sixth floor, Li Ying walks to _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

Answer: the fourth floor.

Solution: 20× (6-1)× 3/5 ÷ 20+1= 4 layers.

3. There are 12 scores that make up the arithmetic progression, and the sum of the sixth and seventh items is, so the sum of these 12 scores is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

Answer: 3+ 1/5.

Solution: (8/15) × (12 ÷ 2) = 3+1/5.

4. The radius of the big circle is 6 cm, and the radius of the small circle is 4 cm. The difference between the shaded areas in two circles is equal to _ _ _ _ _. P365_ 12。

Answer: 62.8.

Solution: Yin Da 3.14× 62-x; Silver: 3. 14×42-x

Subtraction: 3. 14×20=62.8.

5. After the price of a commodity is reduced by 10% for two consecutive times, the price is 8 1 yuan. Then the original price of this item is _ _ _ _ _.

Hu Xinghu's class is at P28 1_ Question 2205.

Answer: 100 yuan.

Solution: if the original price is X, then X× (1-10% )× (1-kloc-0/0%) = 81,and x = 100.

2. Calculation problems:

1. Teacher Counseling Sixth Grade Zhou Xianglin P25 Development III

Answer: 1.

Solution:19901990 =1990×10001,199065438 =/kloc-0.

1989 1989= 1989× 1000 1, 1989 1989 1989= 1989× 1000 1000 1.

So, the original formula =

== 1.

2. Knowledge Publishing House's Chinese Olympiad Mathematics Textbook 6 P 1 1_ Example 4

Answer: 1.

Solution: Original Style =

3. Geometric problems:

1. The following figure consists of six equal circles, and the overlapping area of every two adjacent circles is 2 square centimeters, accounting for the area of each circle. What is the total area of this figure? Problem solving skills P367_2

Answer: 87+5/6.

Solution: the area of each circle:17/6 ÷1/6 =17.

17×6- 17/6×5=87+5/6.

2. As shown in the figure, A and B are the centers of two quarter circles. So, how many square centimeters is the area difference between the two shaded parts? Sixth grade P65_ 16 of Hangzhou Shunqing Olympic Mathematics Course

Answer: 1.42.

Solution:1/4× 3.14× 42-2× 4-1/4× 3.14× 22 =1.42.

4. Answer questions:

1.(7 points) A monkey picked a bunch of peaches, ate 1/7 peaches on the first day, ate the remaining 1/6 the next day, and ate the remaining 1/5 and 65438+ every day on the third, fourth and sixth days. Hang Shunqing Olympic Mathematics Course Grade 6 P 164_ Example 5

Answer: 84.

Solution:12.

=84.

2.(8 points) If a commodity is priced at a profit of 20% and then sold at a discount of 18%, the profit of * * * is 16.8 yuan. What is the cost of this commodity? Zhou Zhou exercises grade six P200_ Example 3.

Answer: 300 yuan.

Solution:16.8 ÷ [(1+20%) × 88%-1] =16.8 ÷ 5.6% = 300.

3.(7 points) There is a reservoir with a water inlet pipe and a drainage pipe. It takes 5 hours to fill a pool of water and 2 hours to drain it. Now there is a pool full of water, which is opened by one person in the order of drainage, water intake and drainage 1 hour. Zhou Zhou practices grade six P 103_ 14.

Answer: 4+4/5 hours.

Solution: There is water after 1 hour:1-1/2 =1/2;

There is water after 2 hours:1/2+1/5 = 7/10;

There is water after 3 hours: 7/10-1/2 =1/5;

There is water after 4 hours: 1/5+ 1/5=2/5.

2/5( 1/2)= 4/5 hours.

Therefore, the water is discharged after 4+4/5 hours.