2021 澳洲 AMC D-Intermediate 真题 答案 详解

中英双语真题

1. 正方形 ABCD 的中心为点 O。 已知阴影区域的面积为 16 个平方单位，请问这个正方形的边长是多少个长度单位？ Square ABCD has centre O. The shaded area is 16 square units. What is the length of the side of the square?
   (A) 4 (B) 8 (C) 16 (D) 32 (E) 64

2. 数轴上位于 (10^2) 和 (10^4) 正中间的点表示的数是多少？ On the number line, which number is halfway between (10^2) and (10^4)?
   (A) 500 (B) 550 (C) 1010 (D) 2021 (E) 5050

3. 小金将三袋燕麦干草与一袋含 20% 苜蓿、80% 燕麦的干草混合起来作为马饲料。 如果所有袋子的体积都相同，请问这个混合饲料中苜蓿占百分之多少？ To feed a horse, Kim mixes three bags of oats with one bag containing 20% lucerne and 80% oats. If all the bags have the same volume, what percentage of the combined feed mixture is lucerne?
   (A) 3 (B) 5 (C) 6 (D) 20 (E) 60

4. 我有一块圆柱形的实心木块。木块顶部及底部都与侧曲面相交成直角。假如我用一个平面将这个圆柱体截成两个较小的木块，请问下列哪一个选项的图形不可能是切面的形状？ I have a solid block of wood in the shape of a cylinder. The top and bottom faces meet the curved side at right angles. Suppose that I slice the cylinder along a plane to create two smaller blocks of wood. Which of the following could not be the shape of the resulting faces created by the slice?
   (A) (B) (C) (D) (E)

英文真题

1. On the number line, which number is halfway between (10^2) and (10^4)?
   (A) 500
   (B) 550
   (C) 1010
   (D) 2021
   (E) 5050

2. To feed a horse, Kim mixes three bags of oats with one bag containing 20% lucerne and 80% oats. If all the bags have the same volume, what percentage of the combined feed mixture is lucerne?
   (A) 3
   (B) 5
   (C) 6
   (D) 20
   (E) 60

3. I have a solid block of wood in the shape of a cylinder. The top and bottom faces meet the curved side at right angles. Suppose that I slice the cylinder along a plane to create two smaller blocks of wood. Which of the following could not be the shape of the resulting faces created by the slice?
   (A) Square
   (B) Triangle
   (C) Circle
   (D) Ellipse
   (E) Irregular oval

4. Diya timed herself cycling laps around her suburb. After five laps, her stopwatch indicated a time of 18 minutes and 15 seconds. What was Diya's average time per lap?
   (A) 3 minutes and 3 seconds
   (B) 3 minutes and 15 seconds
   (C) 3 minutes and 27 seconds
   (D) 3 minutes and 39 seconds
   (E) 3 minutes and 51 seconds

Questions 11 to 20, 4 marks each
11. I have four consecutive odd numbers. The largest is one less than twice the smallest. Which of the following is the largest of the four numbers?
(A) 9
(B) 11
(C) 13
(D) 15
(E) 21

1. On a compact disc, uncompressed music data is stored as 44,100 samples for each second of music, where each sample requires 4 bytes of data. Which of the following is closest to the number of bytes required to store 5 minutes of music on the disc?
   (A) 1 million
   (B) 5 million
   (C) 10 million
   (D) 50 million
   (E) 100 million

真题文字详解(英文)

2021 AMC Intermediate Solutions 55 Intermediate Solutions 1. There are 10 edges, each 2 cm long, so the total perimeter is $2 \times 10 = 20$ cm, hence (D). 2. $2000 - 200 + 20 - 2 = 1800 + 20 - 2 = 1820 - 2 = 1818$, hence (C). 3. The angle marked $a^{\circ}$ is coterior to the $145^{\circ}$ angle. Since coterior angles add to $180^{\circ}, a=180-145=35$, hence (A). 4. $50\%$ of $\frac{1}{2}$ is $\frac{1}{4}$. So $50\%$ more than $\frac{1}{2}$ is $\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$, hence (D). 5. $\frac{1+3+5+7+9}{2+4+6+8+10}=\frac{25}{30}=\frac{5}{6}$, hence (B). 6. The shaded area is one-quarter of the square's area. So the square has area 64 square units and side 8 units, hence (B). 7. The midpoint corresponds to the average of 100 and 10000, which is $\frac{1}{2}(100+10000)=5050$, hence (E). 8. (Also J11) Alternative 1 There are four bags, and one-fifth of a bag is lucerne. Let the lucerne be one unit, then one bag has 5 units and four bags has 20 units. So the lucerne is 1 part in 20 in the total mix, which is 5%, hence (B). Alternative 2 Each bag is one-quarter or 25% of the mix. The lucerne is one-fifth of one bag, which is 5% of the mix, hence (B). 9. Consider possible faces from cuts at different angles. These are • a circle, if the cut is horizontal • a rectangle, if the cut is vertical • an oval (ellipse) possibly with one or two segments removed, if the cut is slanted Looking at the shapes in the question, the triangle (B) is the only shape that isn't one of these shapes. Checking, shapes (A), (C), (D) and (E) can be found as shown. Therefore the triangle is the only shape that can't be the shape of the cut face, hence (B). www.amt.edu.au