2022 澳洲 AMC D-Intermediate 真题 答案 详解

中英双语真题

Intermediate Questions
1-10 题，每题 3 分

1. 算式 (2220 - 2022 =)
   (A) 18 (B) 188 (C) 198 (D) 200 (E) 202

2. 右侧图案是由29个(1cm \times 1cm)的正方形组成的。请问它的周长是多少 cm?
   (A) 52 (B) 58 (C) 60 (D) 68 (E) 72

3. 右侧数码时钟显示的时间为20:22。请问再过多少分钟才是午夜?
   (A) 158 (B) 218 (C) 258 (D) 278 (E) 378

4. 算式(\frac{1^2 + 2^2}{3^2 + 4^2})之值等於什麼？
   (A)(\frac{1}{5}) (B)(\frac{3}{7}) (C)(\frac{9}{49}) (D) 4 (E) 5

5. 在右图所示的三角形PQR中，(PQ = PR) 且 (\angle QPR = 48^\circ)。请问(\angle PQR)是多少？
   (A) (60^\circ) (B) (66^\circ) (C) (72^\circ) (D) (78^\circ) (E) (84^\circ)

英文真题

2022 AMC Intermediate Questions 21 Intermediate Questions 1. 2220 - 2022 = (A) 18 (B) 188 (C) 198 (D) 200 (E) 202 2. This shape is built from 29 squares, each 1 cm × 1 cm. What is its perimeter in centimetres? (A) 52 (B) 58 (C) 60 (D) 68 (E) 72 3. A digital clock shows the time as 20:22. In how many minutes will it be midnight? (A) 158 (B) 218 (C) 258 (D) 278 (E) 378 4. The value of 1² + 2² / 3² + 4² is (A) 1/5 (B) 3/7 (C) 9/49 (D) 4 (E) 5 5. In the triangle PQR shown, PQ = PR and ∠QPR = 48°. What is ∠PQR? (A) 60° (B) 66° (C) 72° (D) 78° (E) 84° 6. What fraction of this rectangle is shaded? (A) 1/2 (B) 5/8 (C) 5/6 (D) 2/3 (E) 7/12 7. (0.4)² + (0.1)² = (A) 0.25 (B) 1.7 (C) 0.17 (D) 1 (E) 0.26 www.amt.edu.au

真题文字详解(英文)

2022 AMC Intermediate Solutions 55 Intermediate Solutions 1. (Also UP3) 2220 - 2022 = 198, hence (C). 2. (Also UP6) Alternative 1 Out of the 29 squares, there are 12 squares that have 3 edges on the perimeter, 4 squares that have 2 opposite edges on the perimeter and 4 squares that have 2 adjacent edges on the perimeter. This accounts for all 12 × 3 + 4 × 2 + 4 × 2 = 52 edges on the shape, hence (A). Alternative 2 Start with the central 3 x 3 square, with perimeter P = 12. Join the remaining 20 squares one-by-one. Each join increases P by 2: an increase of 4 from the new square but then a decrease of 2 from the join. After joining 20 squares, P = 12 + 20 × 2 = 52, hence (A). 3. From 20:22 through to 21:00 is 38 minutes. From 21:00 through to 00:00 is 180 minutes. Then the total time is 218 minutes, hence (B). 4. \frac{1+4}{9+16}=\frac{5}{25}=\frac{1}{5}, hence (A). 5. (Also J9) Since △PQR is isosceles, ∠PQR = ∠PRQ. Also ∠PQR + ∠PRQ = 180° - 48° = 132°. Consequently ∠PQR = ∠PRQ = 132 ÷ 2 = 66°, hence (B). 6. The rectangle has area 7 × 12 = 84 and the shaded trapezium has area \frac{7(8+12)}{2}=70 so the fraction shaded is \frac{70}{84}=\frac{5}{6}, hence (C). 7. (0.4)^2 + (0.1)^2 = 0.16 + 0.01 = 0.17, hence (C). 8. (Also J13) Australia needs to buy enough petrol for another 30 days. This is 30 × 160 million = 4800 million litres, hence (E). www.amt.edu.au