Current location - Training Enrollment Network - Mathematics courses - The most difficult math problem in junior high school
The most difficult math problem in junior high school
1. Prove that the remainder obtained by dividing the prime number p by 30 must not be a composite number.

2、

3. A store sells 100 pieces of a commodity every day, and each piece can make a profit in 4 yuan. Now they increase profits by raising prices and reducing purchases. According to experience, for every price increase of 1 yuan, the commodity is sold less 10 pieces every day. How much can I increase the price of each commodity to get the maximum profit? What is the maximum profit?

4、

As shown in figure 1-96, it is known that CB⊥AB, CE bisects ∠BCD, DE bisects ∠CDA, ∠ 1+∠ 2 = 90. Verification: DA⊥AB.

5. Find the integer solution of the equation | xy |-| 2x |+y | = 4.

6、

7、

8、? Pour out 8 liters of liquid pesticide in a bucket, then fill it with water, then pour out 4 liters of mixed liquid and then fill it with water. At this time, the pesticide concentration is 72%, and the capacity of the barrel is calculated.

9. Let p be a point in △ABC. Find the distance range from p to △ABC and the ratio to the perimeter of triangle.

10, Party A and Party B walked out of the East and West Stations at the same time. When they met, Party A walked 24 kilometers more than Party B, it took Party A 9 hours to reach the East Station, and it took Party B 16 hours to reach the distance between the two stops.

Here you are 10. Practice first.