2013 澳洲 AMC C-Junior 真题 答案 详解

2013 年 C-Junior 真题,中英双语,答案,详解

中英双语真题

Primary Paper

Questions 1-10, 3 points each

1. The expression (1999 + 24) equals:
2. (A) 1923
3. (B) 2003
4. (C) 2013
5. (D) 2023

6. (E) 2113

7. In the diagram, (PQR) is a straight line. Find the value of (x):

8. (A) 40
9. (B) 90
10. (C) 100
11. (D) 110

12. (E) 120

13. Which fraction (\frac{1}{2}) is closest to?

14. (A) 0.45
15. (B) 0.6
16. (C) (\frac{1}{3})
17. (D) (\frac{5}{8})

18. (E) (\frac{2}{5})

19. Which expression equals 20?

20. (A) (3 + 2 \times 4)
21. (B) ((9 + 5) \times 2 - 4 \times 2)
22. (C) (10^2)
23. (D) (20 + 20 \div 2)

24. (E) (10 \div 2)

25. How many minutes are there from 8:37 am to 10:16 am?

26. (A) 39
27. (B) 79
28. (C) 99
29. (D) 141

30. (E) 179

31. Three squares with an area of (25 \text{ cm}^2) are joined side by side to form a rectangle. What is the perimeter of this rectangle?

32. (A) 20
33. (B) 36
34. (C) 40
35. (D) 75

36. (E) 100

37. If a positive integer has digits that can only be 3 or 5, which property always holds true for such numbers?

38. (A) Divisible by 3
39. (B) Divisible by 5
40. (C) Prime number
41. (D) Even number

42. (E) Odd number

43. A point (P) lies at position 0.56 on a scale, while point (Q) is at position 1.2. Where is the midpoint between (P) and (Q)?

44. (A) 0.34
45. (B) 0.64
46. (C) 0.83
47. (D) 0.88
48. (E) 0.93

英文真题

Junior Division
Questions 1 to 10, 3 marks each

1. 1999 + 24 is equal to
   (A) 1923 (B) 2003 (C) 2013 (D) 2023 (E) 2113

2. PQR is a straight line. Find the value of x.
   (A) 40 (B) 90 (C) 100 (D) 110 (E) 120

3. The value of the fraction ( \frac{1}{2} ) is closest to
   (A) 0.45 (B) 0.6 (C) ( \frac{1}{3} ) (D) ( \frac{5}{8} ) (E) ( \frac{2}{5} )

4. Which of the following is equal to 20?
   (A) 3 + 2 × 4 (B) (9 + 5) × 2 − 4 × 2 (C) 10² (D) 20 + 20 ÷ 2 (E) 10 ÷ 2

5. How many minutes are there between 8:37 am and 10:16 am?
   (A) 39 (B) 79 (C) 99 (D) 141 (E) 179

6. Three squares each with an area of 25 cm² are placed side by side to form a rectangle. The perimeter, in centimetres, of the rectangle is
   (A) 20 (B) 36 (C) 40 (D) 75 (E) 100

7. If every digit of a whole number is either a 3 or a 5, the number will always be
   (A) divisible by 3 (B) divisible by 5 (C) prime (D) even (E) odd

8. P is the point at 0.56 and Q is the point at 1.2 on a number line. The point which is halfway between P and Q is at
   (A) 0.34 (B) 0.64 (C) 0.83 (D) 0.88 (E) 0.93

真题文字详解(英文)

SOLUTIONS - JUNIOR DIVISION 1. 1999 + 24 = 2023, hence (D). 2. As the angle on a straight line is 180°, x° = 180° − (10° + 20° + 30°) = 180° − 60° = 120°, hence (E). 3. We know that ( \frac{1}{2} = 0.5 ), so absolute differences are (A) 0.05, (B) 0.1, (C) ( \frac{1}{6} > 0.16 ), (D) ( \frac{1}{8} = 0.125 ) and (E) 0.1. The smallest of these differences is 0.05. Thus, the fraction ( \frac{1}{2} ) is closest to 0.45, hence (A). 4. (A) 3 + 2 × 4 = 11 (B) (9 + 5) × 2 − 4 × 2 = 20 (C) 10² = 100 (D) 20 + 20 ÷ 2 = 30 (E) 10 ÷ 2 = 5 hence (B). 5. From 8:37 am to 9 am is 23 minutes, from 9 am to 10 am is 60 minutes and from 10 am to 10:16 am is 16 minutes: 23 + 60 + 16 = 99 minutes, hence (C). 6. A square with an area of 25 cm² is 5 cm × 5 cm so the rectangle formed from three of these squares will have sides of 5 cm and 15 cm, giving a perimeter of 40 cm, hence (C). 7. (Also I3) If every digit of a whole number is either a 3 or a 5, the number must be odd. Note that 33 is not prime, even or divisible by 5 and 35 is not divisible by 3, showing that odd is the only consistent descriptor, hence (E). 8. The point halfway between P and Q is the average of the two numbers. (0.56 + 1.2) ÷ 2 = 0.88 hence (D).