miscellaneous exercise 16
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Solutions to Miscellaneous Exercise 16 (Ho Soo Thong & Khor Nyak Hiong’s Panpac Additional Mathematics)
Solved by: Dr Lee Chu Keong ([email protected])
Dr Lee Chu Keong (http://ascklee.org/)
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Miscellaneous Exercise 16
Question 1
At stationary points,
At :
is a minimum point.
At :
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is also a minimum point.
Question 2
At stationary points,
At
:
(
)
( )
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is a minimum point.
Question 3
√
[
] [√ ]
√ √
√
√
√
At stationary points,
√
√
√
Question 4
At ,
:
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At , :
When :
When :
Question 5
(
)
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( )
Question 6(a)
Question 6(b)
Question 6(c)
Question 7(a)
Question 7(b)
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Question 7(c)
At stationary values,
:
Therefore, the stationary value is a minimum.
Question 8(a)
For this question, similar triangles will have to be used.
First, note that is an isosceles triangle.
Divide into two right angle triangles and .
√
√
√
√
Label the foot of h, S. is similar to :
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Question 8(b)
Question 8(c)
Question 9
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(
)
Question 10
(
) (
)
(
)
(
)
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(
)
Question 11
This question involves similar triangles again.
, and are all similar to each other.
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Question 12
(
)
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(
)
Question 13(a)
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√
√ ( )( )( )
√
√
√
√
√
√
√
At the maximum area, `
:
√
√
√
√
√ √
Question 14
Let the length of two parallel sides be x each.
The other two sides will be of length
.
(
)
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At the maximum area,
:
When
, the figure is a square!
Question 15
√
√
√
√
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Question 16
Question 17
√
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√
√
√
√
√
√
√
√
√
Squaring both sides of the equation:
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√
√
√
Question 18
Equation of the curve:
Coordinate of a general point on the curve:
√
√
√
√
By long division:
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