2.3 pencils 8 ballpoint pens 1 1.9 yuan, 7 pencils 6 ballpoint pens 1 1.3 yuan, a pencil and a pen _ _ _ _ _.

3. Compare the dimensions of the following two products:

A=9.5876× 1.23456, B=9.5875× 1.23457, then a _ _ _ _ b.

The _ _ _ _ th score.

5. From the natural number 1, 2, 3, 4, …, 1997, you can take the number _ _ _ _ _ at most, so that the difference between any two of these numbers is not equal to 8.

6. Use each of the nine numbers 1 to 9 once to form a three-digit number divisible by 9. Require the sum of these three digits to be as large as possible. These three digits are _ _ _ _ _ _.

7. As shown in the figure, AD=DE=EC, F is the midpoint of BC, and G is the midpoint of FC. If the area of triangle ABC is 24 square centimeters, the shaded part is _ _ _ _ square centimeters.

8. In an exam, the average scores of A, B, C, D and E are 90, A and B are 96, C and D are 92.5, A and D are 97.5, and C is less than D 15, so the score of B is _ _.

9. The number of students in a grade is between 200 and 250. If there are 4 people in a row, 1 person, 5 people in a row, 3 people in a row and 6 people in a row, there will be _ _ _ _ students in this grade.

10. The store buys two different kinds of candy A and B at the same price. It is known that candy A is per kilogram 18 yuan and candy B is per kilogram 12 yuan. If these two kinds of candy are mixed together to become assorted candy, then the cost per kilogram of this candy is _ _ _ _ _ _.

Second, answer questions:

1. There is a cube with a side length of 10 cm, and a 3 cm square hole is punched in the center of its upper, left and front three sides until the opposite side. Find the volume of the block after punching.

2. How many are the simplest true fractions * * * with a denominator of 964?

3. The picture shows an urban traffic road, and the number represents the distance (unit: km) of each section. Find the shortest distance from A to F in the picture.

Two athletes are swimming back and forth in a 30-meter swimming pool. The speed of A is 1 m per second, and the speed of B is 0.6 m per second. At the same time, they started from both ends of the swimming pool and swam back and forth for 10 minutes. * * * met several times during this time, if not the turning point?

answer

First, fill in the blanks:

2. 1.8

By 3 pencils +8 ballpoint pens = 1 1.9 yuan 7 pencils +6 ballpoint pens =1/3 yuan.

Get 2 1 pencil +56 ballpoint pen = 83.3 yuan 2 1 pencil+18 ballpoint pen =33.9 yuan.

(56- 18) ballpoint pen =83.3-33.9

1 ballpoint pen = 1.3 yuan.

So 1 pencil = (1 .9-1 .3× 8) ÷ 3 = 0.5 yuan, so the price of1pencil and1pen is1.

3.>

a = 9.5875× 1.23456+0.000 1× 1.23456

b = 9.5875× 1.23456+9.5875×0.0000 1

Because 0.0001×1.23456 > 9.5875 × 0.0005438+0, A > B.

Divide the denominators into one group, the number of 1 group is 1, the number of the second group is 3, the number of the third group is 5, ..., starting from the second group, each group is 2 more than the previous group, and the law of each group of molecules is from 1, adding 1 item by item.

The penultimate in this series is

5. 1000

Every 16 consecutive natural numbers can be 8 at most, so the difference between every two numbers is not equal to 8.

1997÷ 16= 124… 13

The natural numbers from 1 to 1997 are grouped into one group every 16 consecutive natural numbers, and the last number 13 is a group, and * * * constitutes a group of 125. namely

1,2,3,4,…, 16;

17, 18, 19, 20,…, 32;

33,34,35,36,…,48;

…

1969, 1967, 1968,…, 1984;

1985, 1986,…, 1997.

Take the top 8 numbers of each group, * * take 8× 125= 1000 (pieces) so that the difference between any two numbers is not equal to 8.

6.954、873、62 1

1+ 2+ 3+ …+ 9= 45= 9×5, with five 9s. Since the sum of digits of each digit of each three-digit number will not exceed three 9s, the sum of digits of each digit of these three digits can only be 9, 18 and 18 respectively (the sum is five 9s).

In order to make the sum of these three digits as large as possible, the sum of digits on each digit is 9, and the largest three digits are 62 1. The other two digits can only consist of 9, 8, 7, 5, 4 and 3. Obviously, the hundred digits should be as large as possible to get 954 and 873.

So these three numbers are 954,873 and 62 1 respectively.

7. 14

Because AD= DE= EC, so

And because BF=FC, so

Because FG=GC, so

S shadow area =S△ABD+S△DFE+S△GCE

=8+4+2

= 14 (square centimeter)

8.97

E is divided into: 90 × 5-96 × 2-92.5 × 2=73 (minutes);

The score of C is: (92.5×2- 15)÷2=85 (points);

The score of D is: 85+ 15= 100 (minutes);

A is: 97.5×2- 100=95 (minutes);

The score of B is 96×2-95=97 (points).

9.233 people

The natural number of 1 divided by 4 is 5,9, 13,17,21,25, ..., where the natural number of 3 divided by 5 is13,33,53,73, ... The smallest one divided by 6 and the smallest common multiple of 4, 5 and 6 are 60. Any integer that meets the above conditions is written as 60n+53, and n is an integer, so the number of students in this grade is:

N = 3,60× 3+53 = 233 (person)

10. 14.4

The least common multiple of 12 and 18 is 36. In order to solve the problem conveniently, it is assumed that two kinds of candies are purchased from 36 yuan, a candy 36 ÷ 18 = 2kg and b candy 36 ÷ 12 = 3kg, and the total price of the two kinds of candies is 30.

36×2÷(2+3)= 14.4 (yuan)

Second, answer questions:

1. The volume of the wood block after perforation is 784 cubic centimeters. The volume of a hole is 3×3× 10=90 cubic centimeters. When drilling three holes, the volume should be:

90×3-3×3×3×2=2 16 (cubic centimeter)

So the volume of the wood block after perforation is:

10×10×10-216 = 784 (cubic centimeter)

There are 480 simplest true fractions with a denominator of 964.

Because 964=22×24 1, the simplest true fraction with denominator of 964 cannot have even numbers and multiples of 24 1, and even numbers less than 964 have three multiples of 964 2-1= 481,and 24 1.

963-48 1-3+ 1=480 (piece)

The shortest distance from a to f is 13km.

There are many roads from A to F. To determine the shortest route, the longer roads can be eliminated step by step by exclusion method, and finally the shortest route from A to F can be determined. According to the road length given in the figure, some obviously longer roads can be ignored. From a to f, there are three relatively short routes, along the AIHGF route. Its length is:

7+ 1+5+2= 15 (km)

Take the ABCEF route, its length is.

5+2+5+2 =14km

Along the AJKGF route, its length is:

5+4+2+2 =13km

So the shortest distance from A to F is13km.

4. 10 minutes * * * meets 20 times.

It takes 30÷ 1=30 seconds for A to swim 30 meters and 30÷0.6=50 seconds for B to swim 30 meters. 150 seconds later, A and B swim to both ends at the same time and meet again every 150 seconds. As shown in the figure, the solid line represents A and the dotted line represents B. It can be seen that after 150 seconds, A swam five 30 meters, B swam three 30 meters, and * * met five times. Taking 150 seconds as a cycle, 10 minutes is 600 seconds, and 600÷ 150=4, and there are four 6500.