2015 澳洲 AMC D-Intermediate 真题 答案 详解

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中英双语真题

Intermediate Paper 1-10 questions, each worth 3 points
1. What is the area of the right triangle shown in the diagram?
(A) 10 (B) 12 (C) 14 (D) 7 (E) 6

1. A movie is 2 hours and 20 minutes long. It is divided into two equal parts. How many minutes are there in each part?
   (A) 85 (B) 70 (C) 80 (D) 65 (E) 75

2. Given p = 11, q = -4, what is the value of (p^2 - q^2) ?
   (A) 105 (B) 137 (C) 117 (D) 115 (E) 94

3. The expression 2015 - 20.15 equals
   (A) 1984.85 (B) 1995.15 (C) 1994.85 (D) 1995.85 (E) 2035.15

4. What is the total value of 2015 twenty-cent coins?
   (A) 2015 yuan (B) 107.50 yuan (C) 17.50 yuan (D) 403 yuan (E) 43 yuan

5. A, B, C, D, E sit around a round table in order. A starts by saying 1, then B says 2, then C says 3, and so on. When someone says a number that is a multiple of 7, they must leave immediately. Who will be the last one left at the table?
   (A) A (B) B (C) C (D) D (E) E

6. In a farm, the ratio of horses to cows is 3:2, and the ratio of cows to sheep is 4:3. What is the ratio of sheep to horses?
   (A) 5:7 (B) 3:8 (C) 3:5 (D) 5:18 (E) 1:2

英文真题

Intermediate Division
Questions 1 to 10, 3 marks each

1. What is the area of this triangle in square centimetres?
   (A) 10 (B) 12 (C) 14 (D) 7 (E) 6

2. A movie lasts for (2\frac{1}{3}) hours. The movie is shown in two equal sessions. For how many minutes does each session last?
   (A) 85 (B) 70 (C) 80 (D) 65 (E) 75

3. If (p = 11) and (q = -4), then (p^2 - q^2) equals
   (A) 105 (B) 137 (C) 117 (D) 115 (E) 94

4. (2015 - 20.15) equals
   (A) 1984.85 (B) 1995.15 (C) 1994.85 (D) 1995.85 (E) 2035.15

5. What is the value of 2015 twenty-cent coins?
   (A) $2015 (B) $107.50 (C) $17.50 (D) $403 (E) $43

6. Ana, Ben, Con, Dan and Eve are sitting around a table in that order. Ana calls out the number 1, then Ben calls out the number 2, then Con calls out the number 3, and so on. After a person calls out a number, the next person around the table calls out the next number. Anyone who calls out a multiple of 7 must immediately leave the table. Who is the last person remaining at the table?
   (A) Ana (B) Ben (C) Con (D) Dan (E) Eve

真题文字详解(英文)

Solutions – Intermediate Division
1. (Also J5) The area is ( \frac{1}{2} \times 12 \times 2 = 12 \text{ cm}^2 ), hence (B).
2. (Also J7) The movie lasts for (120 + 20 = 140) minutes, so each half is (140 \div 2 = 70) minutes, hence (B).
3. ( p^2 = 121 ) and ( q^2 = 16 ), so ( p^2 - q^2 = 105 ), hence (A).
4. (2015 - 20.15 = 1994.85), hence (C).
5. There are 5 twenty-cent coins for every dollar, and (2015 \div 5 = 403), hence (D).
6. (Also J10) The table below shows that Ben leaves after calling out the number 7, Eve leaves after calling out the number 14, Ana leaves after calling out the number 21, and Con leaves after calling out the number 28. Therefore, Dan is the last person remaining at the table.

1	2	3	4	5	6	7	8	9	10	11	12	13	14
A	B	C	D	E	A	B	C	D	E	A	C	D	E
15	16	17	18	19	20	21	22	23	24	25	26	27	28
A	C	D	A	C	D	A	C	D	C	D	C	D	C

hence (D).
7. For every 4 cows there are 6 horses and 3 goats, so the ratio of goats to horses is (1:2), hence (E).
8. Since (141 \div 12 = 11r9), Warren has completed 11 floors and 9 windows. Since he moves down after each completed floor, he has moved down 11 floors to floor number (38-11=27), hence (D).
9. The 20 blue and yellow lollies are ( \frac{2}{3} ) of the packet, so there are 30 lollies in the packet. Of these 15 are yellow, which is ( \frac{1}{2} ) of the total, hence (C).

2015 AMC – Intermediate Solutions
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