2014 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. The expression 1 + 2 - 3 + 4 + 5 + 6 - 7 - 8 + 9 + 10 equals (A) 0 (B) 1 (C) 10 (D) 11 (E) 19 2. In the diagram on the right, what is the value of x? (A) 80 (B) 70 (C) 60 (D) 50 (E) 40 3. Given p = 9, q = -3, what does p^2 - q^2 equal? (A) 64 (B) 72 (C) 84 (D) 90 (E) 96 4. What number should be filled in the blank to make the equation correct? 2014 ÷ ___ = 100 (A) 0.02014 (B) 0.2014 (C) 2.014 (D) 20.14 (E) 201.4 5. If a certain number multiplied by (\frac{5}{6}) equals 30, then that number multiplied by (\frac{3}{4}) equals (A) 22.5 (B) 24 (C) 25 (D) 27 (E) 40 6. The figure on the right is called a "4th-order infinite square," as its three sides are all equal in length and each side has four nails, with equal intervals between the nails. How many nails are there in total for a "10th-order infinite square"? (A) 26 (B) 27 (C) 28 (D) 30 (E) 32

英文真题

Intermediate Division
Questions 1 to 10, 3 marks each

1. (1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 = ) (A) 0 (B) 1 (C) 10 (D) 11 (E) 19

2. In the diagram the value of (x) is
   (A) 80 (B) 70 (C) 60 (D) 50 (E) 40

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. What value can be placed in the shape to make this statement true?
   (2014 \div __ = 100)
   (A) 0.02014 (B) 0.2014 (C) 2.014 (D) 20.14 (E) 201.4

5. If (\frac{5}{6}) of a number is 30, what is (\frac{3}{4}) of the number?
   (A) 22.5 (B) 24 (C) 25 (D) 27 (E) 40

6. This diagram is called an open square of order 4, since the three sides are all the same length and each side has four posts spaced evenly along it. The total number of posts which would be evenly spaced along an open square of order 10 would be
   (A) 26 (B) 27 (C) 28 (D) 30 (E) 32

真题文字详解(英文)

Intermediate Division
1. 1 + 2 - 3 + 5 + 6 - 7 - 8 + 9 + 10 =
(A) 0
(B) 1
(C) 10
(D) 11
(E) 19

▸ 1 + (2 - 3) + (5 - 4) + (6 - 7) + (9 - 8) + 10 = 1 - 1 + 1 - 1 + 1 + 10 = 11, hence (D).
2. (Also J2) In the diagram the value of x is
(A) 80
(B) 70
(C) 60
(D) 50
(E) 40

▸ Alternative 1
The three interior angles of the triangle are (x^\circ), (50^\circ) and (60^\circ). These add to (180^\circ), so (x + 110 = 180) and (x = 70), hence (B).
▸ Alternative 2
Using the exterior angle formula, (x + 50 = 120), so that (x = 70), hence (B).
3. (Also S3) If (p = 9) and (q = -3) then (p^2 - q^2) is equal to
(A) 64
(B) 72
(C) 84
(D) 90
(E) 96

▸ Now (p^2 = 81) and (q^2 = 9), so (p^2 - q^2 = 81 - 9 = 72), hence (B).
4. What value can be placed in the shape to make this statement true?
2014 ÷ □ = 100
(A) 0.02014
(B) 0.2014
(C) 2.014
(D) 20.14
(E) 201.4

▸ For any (a) and (b), (\frac{a}{b} = 100) only if (a = 100b). So the number in the shape must be (2014 \div 100 = 20.14), hence (D).
5. (Also J6)
If (\frac{5}{6}) of a number is 30, what is (\frac{3}{4}) of the number?
(A) 22.5
(B) 24
(C) 25
(D) 27
(E) 40

2014 AMC – Intermediate Division