1011_F5MATH_NORMAL_P2(ALL)

Alex

2015-01-04 10:19 pm

If a:b = 2:3, which of the following is /are also equal to 2:3?
(1) b:a
(2) 1/a:1/b
(3) 2a:3b
A. None of them
B. (1)
C. (2)
D. (2) and (3)

By offering a discount of 10%, the profit on selling an article will be reduced by half. What is the profit % if the article is sold without the discount?
A. 5%
B. 10%
C. 20%
D. 25%

By what percentage must the radius of a sphere decrease so that its volume will be decreased by 20%? (Correct the answer to 2 decimal places)
A. 6.27%
B. 6.67%
C. 7.17%
D. 10.56%

Cones A and B are similar. If the base area of A is 4 times the base area of B. Which of the following must be true?
(1) The slant height of A is twice the slant height of B
(2) The curved surface area of A is 4 times the curved surface area of B
(3) The volume of A is 8 times the volume ofB
A. (1) and (2)
B. (1) and (3)
C. (2) and (3)
D. (1), (2) and (3)
(Answer is A right?!)

The sum of the exterior angles of a convex hexagon is
A. 180o
B. 360o
C. 540o
D. 720o

A solid has 8 verticles and 16 edges. How many faces does it have?
A. 8
B. 10
C. 12
D. 24

ABCD is a square and AC is the diagonal. E is a point on AC such that EA=2, EC=4, find EB
A. 3
B. sqt10
C. sqt12
D. sqt20

回答 (1)

用戶26240

2015-01-05 12:13 am

✔ 最佳答案

1.
Answer : A. None of them

Let 2k and 3k be a and b respectively.

(1) false
b : a = 3k : 2k = 3 : 2

(2) false
(1/a) : (1/b) = (1/2k) : (1/3k) = (3/6k) : (2/6k) = 3 : 2

(3) false
2a : 3b = 2(2k) : 3(3k) = 4k : 9k = 4 : 9

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2.
Answer : D. 25%

Let c be the cost, and s be the marked price.

s × (1 - 10%) - c = (1/2) × (s - c)
0.9s - c = 0.5s - 0.5c
0.4s = 0.5c
s = 1.25c

Profit % without the discount
= [(1.25c - c)/c] × 100%
= 25%

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3.
Answer : C. 7.17%

The original sphere and the smaller sphere are similar.
Original radius : New radius
= 1 : ³√(1 - 0.2)
= 1 : 0.9283

% decrease in radius
= (1 - 0.9283) × 100%
= 7.17%

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4.
Answer : D. (1), (2) and (3)

(1) true
(Slant height of A) : (Slant height of B) = √4 : √1 = 2 : 1

(2) true
(Curved surface area of A) : (Curved surface area of B) = 2² : 1² =4 : 1

(3) true
(Volume of A) : (Volume of B) = 2³ : 1³ = 8: 1

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5.
Answer : B. 360°

The sum of exterior angles of a convex polygon is 360°, no matter how many sides that the polygon has.

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6.
Answer : B. 10

F + V - E = 2
F + 8 - 16 = 2
F = 10

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7.
Answer : B. √10

Join diagonal BD, and the two diagonals meet at F.

BD = AC = 2 + 4 = 6
BF = AF = (1/2)(6) = 3
EF = 3 - 2 = 1

The two diagonal⊥each other.
In ΔBEF :
EB² = BF² +EF²
EB² = 3² + 1²
EB = √10

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