For children who want to understand or add to the AMC8 American Mathematics Competition, it is one of the most scientific and effective ways to prepare for the AMC8 past questions.
In order to help children prepare for the exam more efficiently, I have compiled all the AMC8 past papers from 2000 to 2004, and exclusively produced a variety of ** exercises, using fragmented time, one year is enough to achieve good results in the 2025 AMC8 competition through self-study. See the end of this article for details.
This question is about probability and permutations.
According to the title, we just need to find out how many types of license plates are possible. The first letter has 5 choices (because it has to be a vowel, i.e. the reason), the second letter has 21 choices (because it has to be a consonant), the third letter has 20 choices (because it has to be a consonant and different from the second letter), and the fourth is a number with 10 choices. So the overall probability is 5 * 21 * 20 * 10 = 21,000 licenses. So what is shown on the license is:"amc8"The probability is 1 21000, choose B.
This kind of question should be carefully examined, and the difficulty itself is not high.
The test point for this question is permutations and combinations (recursive method or other).
Answer: Assuming that there are a total of n steps, there are f(n) ways to climb according to the rules. We categorized the number of steps that JO climbed for the first time.
1. If JO climbs 1 ladder for the first time, there are F(N-1) ways to climb N-1 ladder later.
2. If JO climbs 2 steps for the first time, there are F(N-2) ways to climb N-2 steps later.
3. If JO climbs 3 steps for the first time, there are F(N-3) ways to climb N-3 steps later.
Thus, we get the recursive formula: f(n) = f(n-1) + f(n-2) + f(n-3).
Let's calculate the initial conditions. If there is a total of 1 staircase, there is only 1 way to climb, i.e. f(1)=1.
If there are a total of 2 steps, there are 2 ways to climb, i.e. f(2)=2;
If there are a total of 3 steps, there are 4 ways to climb, 1, 1, 1 or 1, 2 or 2, 1 or 3, i.e. f(3)=4.
According to the recursive formula, f(4)=f(1)+f(2)+f(3)=1+2+4=7, f(5)=f(2)+f(3)+f(4)=2+4+7=13, f(6)=f(3)+f(4)+f(5)=4+7+13=24, so when there are a total of 6 steps and 24 ways to climb, choose e.
The test focus for this question is arithmetic. Analyzing this diagram, we can get that 15 feet of floor white bricks have (15+1) 2=8 rows, and each row has (15+1) 2=8 white tiles, so a total of 8*8=64 white tiles are needed. Choose C.
The test points of this question are arithmetic and percentages, and the difficulty is low. According to the title, SHEA's height is 60 inches after 20% increase, so the height before the increase is 60 (1+20%)=50 inches, which is also the original height of ARA. SHEA has increased by 10 inches, so ARA has increased by 5 inches, so ARA is now 50 + 5 = 55 inches, choose E.
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 exam preparation is available, and repeated practice is also conducive to the improvement of mathematics ability in primary and junior high schools.