2014 澳洲 AMC E-Senior 真题 答案 详解

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中英双语真题

Advanced Test 1-10 questions, each worth 3 points 1. Which expression is equivalent to (9x^{-3})?
(A) (\frac{-9}{x^3})
(B) (\frac{3}{x})
(C) (\frac{1}{9x^3})
(D) (\frac{3}{x^3})
(E) (\frac{9}{x^3})

1. The value of the fraction (\frac{1}{0.04}) is equal to
   (A) 15
   (B) 20
   (C) 25
   (D) 40
   (E) 60

2. Given (p=9), (q=-3), what is (p^2-q^2) equal to?
   (A) 64
   (B) 72
   (C) 84
   (D) 90
   (E) 96

3. A circle has a circumference of π units. What is its area in square units?
   (A) (\frac{\pi}{4})
   (B) (\frac{\pi}{2})
   (C) (\pi)
   (D) (2\pi)
   (E) (4\pi)

4. If (K=L+\frac{6}{R}), (L=4), and (K=7), then (R) equals
   (A) -18
   (B) 1
   (C) 12
   (D) 8
   (E) 2

5. Given that (x), (x^2), (x^3) are positioned on the number line as shown below, which of the following could be the value of (x)?
   (A) -2
   (B) (-\frac{1}{2})
   (C) (\frac{3}{4})
   (D) 1
   (E) (\frac{3}{2})

英文真题

Senior Division
Questions 1 to 10, 3 marks each

1. The expression that has the same meaning as (9x^{-3}) is
   (A) (\frac{-9}{x^3})
   (B) (\frac{3}{x})
   (C) (\frac{1}{9x^3})
   (D) (\frac{3}{x^3})
   (E) (\frac{9}{x^3})

2. The value of (\frac{1}{0.04}) is
   (A) 15
   (B) 20
   (C) 25
   (D) 40
   (E) 60

3. If (p = 9) and (q = -3), then (p^2 - q^2) is equal to
   (A) 64
   (B) 72
   (C) 84
   (D) 90
   (E) 96

4. A circle has circumference (\pi) units. In square units, its area is
   (A) (\frac{\pi}{4})
   (B) (\frac{\pi}{2})
   (C) (\pi)
   (D) (2\pi)
   (E) (4\pi)

5. If (K = L + \frac{6}{R}) and (L = 4) and (K = 7), then (R) equals
   (A) -18
   (B) 1
   (C) 12
   (D) 8
   (E) 2

6. If (x), (x^2), and (x^3) lie on a number line in the order shown below, which of the following could be the value of (x)? (A) -2
   (B) (-\frac{1}{2})
   (C) (\frac{3}{4})
   (D) 1
   (E) (\frac{3}{2})

真题文字详解(英文)

Senior Division
1. The expression that has the same meaning as (9x^{-3}) is
(A) (\frac{-9}{x^3}) (B) (\frac{3}{x}) (C) (\frac{1}{9x^3}) (D) (\frac{3}{x^3}) (E) (\frac{9}{x^3})
(\blacktriangleright) (9x^{-3} = 9 \times \frac{1}{x^3} = \frac{9}{x^3},) hence (E).

1. (Also J5)
   The value of (\frac{1}{0.04}) is
   (A) 15 (B) 20 (C) 25 (D) 40 (E) 60
   (\blacktriangleright) (\frac{1}{0.04} = \frac{1 \times 100}{0.04 \times 100} = \frac{100}{4} = 25,) hence (C).

2. (Also I3)
   If (p=9) and (q=-3) then (p^2 - q^2) is equal to
   (A) 64 (B) 72 (C) 84 (D) 90 (E) 96
   (\blacktriangleright) Now (p^2 = 81) and (q^2 = 9,) so (p^2 - q^2 = 81 - 9 = 72,) hence (B).

3. A circle has circumference (\pi) units. In square units, its area is
   (A) (\frac{\pi}{4}) (B) (\frac{\pi}{2}) (C) (\pi) (D) (2\pi) (E) (4\pi)
   (\blacktriangleright) This circumference is (2\pi r = \pi) so that (r = \frac{1}{2}.) Then (A = \pi r^2 = \frac{\pi}{4},) hence (A).

4. If (K=L+\frac{6}{R}) and (L=4) and (K=7,) then (R) equals
   (A) -18 (B) 1 (C) 12 (D) 8 (E) 2
   (\blacktriangleright) We have (7 = 4 + \frac{6}{R}) so that (\frac{6}{R} = 3) and (R = 2,) hence (E).

5. If (x, x^2,) and (x^3) lie on a number line in the order shown below, which of the following could be the value of (x?)
   (A) -2 (B) (-\frac{1}{2}) (C) (\frac{3}{4}) (D) 1 (E) (\frac{3}{2})

2014 AMC - Senior Division