Today we are going to take a look at five typical questions from the 2009 AMC8 competition. You are welcome to check out the historical article for the analysis of past past past papers, and this series will continue to be updated until you have participated in the 2024 competition. You can ask me any questions you have about the AMC8 competition, and you can also communicate about the analysis of the questions.
【Recommended】Selected documents, **and** past question sets to improve the efficiency of the last 20 days of preparation, please go to the end of the article to understand.
The test point of this question is the number sequence: number sequence.
The first 8 items are as follows: 1, 2, 3, 6, 11, 20, 37, 68. So choose D.
The test point of this question is probability.
The board has a total of 8*8=64 squares. The squares located on the four edges have 8*2+6*2=28, and the squares that are not on the edges have a total of 64-28=36. So the probability of choosing one of the squares that is not on the edge is: 36 64 = 9 16. So choose D.
The test point for this question is still probability.
Let's start by listing all the possible sums of the two turntables:
Observing the above 9 results, only and 9 are not prime numbers, there are 2 total, and the remaining 7 results are all prime numbers, so the probability is 7 9, choose d.
The test points of this question are: plane geometry + classification discussion.
The isosceles triangle is characterized by the fact that the two base angles are equal, and there are three possible situations depending on the title:
If 70° is the top angle, then x is one of the bottom angles, which is x=(180-70) 2=55
If 70° is one of the bottom angles and x is the other bottom angle, then x=70
If 70° is one of the bottom angles and x is the top angle, then x=180-70 2=40
To sum up, the sum of the three possible values of x is 55 + 70 + 40 = 165, and d is chosen.
Six-point growth reminder: The question stem here clearly tells us that there are three possible scenarios, so pay attention to the analysis. If the stem tells us that an angle is 100 degrees, find the sum of the possible values of x, or if you don't tell us that there are concentrated cases, find the sum of all possible cases. The difficulty increases a bit, and you need to take into account all possible scenarios.
The test point of this question is permutations and combinations.
These integers are at most 3 digits, excluding 1, then each digit may take one of the three numbers 0, 2, and 9, a total of 9 possibilities, so the three digits may form a total of 9 9 9 = 729 numbers(Note: This already includes 1 digit, 2 digits and 3 digits: for example, if the 1st digit takes 0, the 2nd digit takes 3, and the 3rd digit takes 4, it means 034, which is a two-digit number).。However, if all three of them take 0, that is, 0 does not meet the requirements and needs to be deducted, so a total of 728 numbers meet the topic. Pick D.
Six-point growth reminder: This question can also find the number of 1 digit, 2 digits, and 3 digits respectively, and add them by classification, but the above method is the easiest and fastest, please experience it repeatedly.
In order to help children better review and prepare for the AMC8 competition, Six Points Growth has exclusively produced a wealth of practice question sets, exam preparation documents, and materials. Whether the child participates in an institutional training course as a supplementary learning resource or is fully self-taught (which has been proven to be possible), there is a significant increase in efficiency. If you are interested, welcome to communicate and exchange.
Prepare for the exam scientifically, use the fragmented time to sprint for more than 20 days, and get good results!
Come on!