2024 AMC amc8 真题 答案 详解

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中英双语真题

2024 MAA AMC 8

1. What is the ones digit of the value of the below expression? 下面表达式计算结果的个位数字是几?

$$222,222 - 22,222 - 2,222 - 222 - 22 - 2$$

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

1. What is the value of the below expression in decimal form?
   下面表达式计算结果的小数表示是什么？

$$\frac{44}{11} + \frac{110}{44} + \frac{44}{1100}$$

(A) 6.4
(B) 6.504
(C) 6.54
(D) 6.9
(E) 6.94

1. Four squares of side length 4, 7, 9, and 10 units are arranged in increasing size order so that their left edges and bottom edges align. The squares alternate in color white-gray-white-gray, respectively, as shown in the figure. What is the area of the visible gray region in square units?
   四个边长为4、7、9和10个单位的正方形按尺寸递增的顺序排列，使它们的左边缘和底边缘对齐。如图所示，正方形的颜色交替分别为白-灰-白-灰。问可见的灰色区域的面积是多少平方单位？

(A) 42
(B) 45
(C) 49
(D) 50
(E) 52

英文真题

The image contains text related to the MAA AMC 8 competition. Here's a transcription of the visible text:

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MAA AMC

1. You will have 40 minutes to complete the competition once you receive your competition manager's instructions.
2. Elevation are not necessarily drawn to scale.
3. The competition will reduce the use of a calculator.
4. Answer sheets must be filled out completely with a #2 pencil.
5. Only blank scratch paper, rulers, and erasers are allowed as aids. Prohibited materials include: calculators, watches, phones, computing devices, compasses, protractors, and graph paper. No electronic devices are permitted.
6. Points for each incorrect answer:
7. 2 points for each correct answer.
8. 0 points for each problem left blank or answered incorrectly.

AMC 8 36th Annual MAA American Mathematics Competitions

The MAA AMC office reserves the right to disqualify scores from a school if it determines that the rules or the required security procedures were not followed.

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Note: Some parts of the text appear to be mirrored or rotated, which may affect their readability.

真题文字详解(英文)

Problem 1 What is the unit digit of: 222,222 - 22,222 - 2,222 - 222 - 22 - 2? (A) 0 (B) 2 (C) 4 (D) 8 (E) 10 Solution 1 We can rewrite the expression as 222,222 - (22,222 + 2,222 + 222 + 22 + 2). We note that the units digit of 22,222 + 2,222 + 222 + 22 + 2 is 0 because all the units digits of the five numbers are 2 and 5 · 2 = 10, which has a units digit of 0. Now we have something with a units digit of 0 subtracted from 222,222, and so the units digit of this expression is (B) 2 Solution 2 222,222 - 22,222 = 200,000 200,000 - 2,222 = 197778 197778 - 222 = 197556 197556 - 22 = 197534 197534 - 2 = 197532 So our answer is (B) 2 Solution 3 We only care about the units digits. Thus, 2 - 2 ends in 0, 0 - 2 after regrouping(10-2) ends in 8, 8 - 2 ends in 6, 6 - 2 ends in 4, and 4 - 2 ends in (B) 2 Solution 4 We just take the units digit of each and subtract, adding an extra ten to the first number so we don't get a negative number: (12 - 2) - (2 + 2 + 2 + 2) = 10 - 8 = (B) 2 Solution 5 222,222 - 22,222 - 2,222 - 222 - 22 - 2 ≡ 2 - 2 - 2 - 2 - 2 - 2 ≡ -8 ≡ (B) 2 (mod 10) Solution 6 We can ignore the other digits and just do 22 - 2 - 2 - 2 - 2 - 2. Because you are subtracting five 2s and 2 · 5 = 10, you subtract 10 from 22. This gives us 12, so the last digit is (B) 2

真题文字详解(中英双语)

Problem 1 What is the unit digit of: 222,222 - 22,222 - 2,222 - 222 - 22 - 2? (A) 0 (B) 2 (C) 4 (D) 8 (E) 10 This number's unit digit is how many: (A) 0 (B) 2 (C) 4 (D) 8 (E) 10 Solution 1 We can rewrite the expression as 222,222 - (22,222 + 2,222 + 222 + 22 + 2). We note that the units digit of 22,222 + 2,222 + 222 + 22 + 2 is 0 because all the units digits of the five numbers are 2 and 5 · 2 = 10, which has a units digit of 0. Now we have something with a units digit of 0 subtracted from 222,222, and so the units digit of this expression is (B) 2 Solution 2 222,222 - 22,222 = 200,000 200,000 - 2,222 = 197778 197778 - 222 = 197556 197556 - 22 = 197534 197534 - 2 = 197532 So our answer is (B) 2 Solution 3 We only care about the units digits. Thus, 2 - 2 ends in 0, 0 - 2 after regrouping (10-2) ends in 8, 8 - 2 ends in 6, 6 - 2 ends in 4, and 4 - 2 ends in (B) 2 Solution 4