How can I improve my middle and high school math scores through self-study? What are the math competitions that can be participated in in middle and high school now? Are there any math competitions that are moderately difficult and fun? What are the ?.. of junior high and high school mathematics with a large number of participants?
If you are also concerned about the above questions, you may wish to take a look at the AMC10 American Mathematics Competition, you can first systematically study the past questions of AMC10, even if you do not participate in the AMC10 Competition, and thoroughly understand the 1250 past questions and the knowledge system behind them, then junior high school and high school mathematics will definitely learn very easily and easily. If you want to participate in the AMC10 competition in the future (once a year, you can compete at home, Chinese and English questions), you can also get a good ranking by thoroughly understanding these real questions.
In order to help you, I have compiled a total of 1250 real questions from all AMC10 papers A and B from 2000 to 2023, and have exclusively produced a variety of ** exercises, using fragmented time, one year is enough to achieve good results in the 2024 AMC10 competition through self-study.
Today, we will continue to take a look at 5 random AMC10 past papers and a detailed analysis, which are from the complete official AMC10 question bank of 1250 past years.
The test point of this question is the operation of powers, and the answer is E.
n 4 = 8 2022 4 = 2 6066 2 2 = 2 6064 = 4 3032, so choose e.
The test point of this question is Algebra (Column Equation Solving Problems), and the answer is d.
Assuming that the original cost of dinner is x USD, then the tip is 15%x and the tax is 10%x, so x+15%x+10%x=275, solution, x=22. Pick D.
The test point of this question is algebra (column equation solving application problem), and the answer is d.
Suppose the chipmunk hides x acorns, then list the equation according to the title: x 3-x 4 = 4, solve, x = 48, choose d.
The test point of this question is arithmetic, and the answer is C.
There are a total of 11 rows from the 12th to the 22nd row, and each row has 33 seats, so there are a total of 11 seats 33 = 363, choose C.
The difficulty of this question is not high, but some candidates directly use 22-12 to get 10 rows when they do the question, and finally choose the wrong one. Question ** is now similar to how many rows, how many steps, how many floors, etc., taking into account whether the first and last ones are counted.
The test point of this question is permutation and combination, and the answer is B, and there is only one way. We use y, r, g, b, and o to represent yellow, red, green, blue, and orange, respectively. According to the title:
The 5 nails in the first column are all of different colors, y, r, g, b, o
The 4 nails in the second column are all of different colors, but there are no orange nails to arrange at this time, so the nails in the second column can only be y, r, g, b.
Similarly, the 3 nails in column 3 are all different colors, but there are no blue nails to choose from, so the nails in column 3 are colored y, r, g....And so on, the last column can only be y.
Because the single nail in the last column can only be y, and the nail in column 4 can only be y and r, and the yellow nail cannot be placed in row 5 of column 4 (otherwise there will be 2 yellow nails in the same row), so the y of column 4 can only be in row 4. In the same way, the other 3 yellow nails can only be in the 3rd row of the 3rd column, the 2nd row of the 2nd column, and the 1st row of the 1st column. Row 5 of column 4 is r, while the r of column 3 can only be placed in row 4 (because row 5 already has r, and row 3 already has y).
Similarly, the r of the other columns can only uniquely determine the placement position. In the same way, all other colored nails can only be placed in the only way.
To sum up, there is only one way, so choose B.
Here's how to place it:
Tips: From the above questions, you can feel that although AMC10 is a mathematics competition for grade 10 (high school one and below), many questions can be answered with junior high school knowledge, and even many primary school students have participated in the training of Olympiad mathematics, or most of the AMC10 questions can be solved after the study of AMC8.
The above-mentioned six-point growth exclusive production of ** practice questions, in line with learning and cognitive psychology, ** in the complete calendar year AMC8 and AMC10 past questions, and will continue to update. AMC8 and AMC10 exam preparation are available, and repeated practice is also conducive to the improvement of mathematics ability in primary and junior high schools.