HYC_Mock_1112_P2

Alex

2015-01-11 11:50 pm

A right circular cylinder and a hemisphere with equal base radii and equal heights. If the total surface area of the cylinder is A, then the total surface area of the heimsphere is
A. 3A/4
B. A
C. 5A/4
D. 3A/2

In the figure, ABCD is a //gram. EF and AC intersect at P. If AE:ED=3:1 and BF:FC=1:4, then AP:PC=
https://www.flickr.com/photos/130230543@N06/15632131
A. 1:1
B. 3:4
C. 4:5
D. 15:16

In the figure, ABCD is a //gram. Find the slope of AC
https://www.flickr.com/photos/130230543@N06/16252008865/
A. 1
B. 5/3
C. 5/7
D. -7/5

Two perpendicular lines x+y-1=0 and bx+y+3=0 intersect at the point (a,b). Find a and b
A. a=0 b=1
B. a=-2 b=1
C. a=2 b=-1
D. a=3 b=-1

The % of the graduates entering the local u of a school is 90% this year and was 85% last year. Which of the follow is/are correct?
1. Compare with last year, the % of graduates entering the local u this year is increased by 5%
2. Compare with last year, the % of graduates entering the local u this year rises by 5 percentage points
3. The number of graduates entering the local u is 5 more than last year

Find the maximum area of the rectangle shown in the figure
https://www.flickr.com/photos/130230543@N06/16252017155/
A. 11/2 cm2
B. 11/4 cm2
C. 1/8 cm2
D. 1/4 cm2

回答 (1)

Pak Wai

2015-01-12 12:34 am

✔ 最佳答案

A = 2πrh + 2πr^2 = 2πr^2 + 2πr^2 = 4πr^2 (as h = r)
Total surface area of the hemisphere
= πr^2 + 2πr^2
= 3πr^2
= 3A/4

Triangle AGE ~ Triangle CFG (AAA)
AE:FC = 3/4 : 4:5 = 15 : 16
i.e. AG : GC = 15 : 16

L1: x + y - 1 = 0
L2: bx + y + 3 = 0
L1 perpendicular to L2
=> Slope of L2 = -1/Slope of L1
-b = -1/-1, b = -1
L2: -x + y + 3 = 0
When L1 and L2 intersect at (a,b)
a + b - 1 = -a + b + 3
2a = 4
a = 2
Hence, a = 2, b = -1

Compare with last year, the % of graduates entering the local u this year rises by 5 percentage points.
It rises by (90% - 85%)/85% x 100% = 0.0588%.
Since the number of graduates are not given, we could not find out the exact number of graduates, as well as the difference between these 2 years.

Area of rectangle
= (3 - x)(2x - 5)
= -2x^2 + 11x - 15)
= -2(x - 11/4)^2 + 121/8 - 15
= -2(x - 11/4)^2 + 1/8
Maximum area = 1/8 cm^2

2015-01-11 18:41:12 補充：
Oops... I've skipped one question.

In the figure, ABCD is a //gram. Find the slope of AC

Let A be (a, b),
4 - a = 6 - (-1) and -1 - b = 7 - 6
we have A(-3, -2)
slope of AC = [7 - (-2)]/[6 - (-3)] = 1

參考: Myself, Myself

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