SOLUTIONS OF THE END OF THE YEAR MAJOR ASSIGNMENT …

SOLUTIONS OF THE END-OF-THE YEAR

C2 MAJOR ASSIGNMENT (JUNE 2ND, 2017)

Part A

QUESTIONS 1 TO 6: 4 marks for each correct answer.

1. A

4

0

2. D

4

0

3. D

4

0

4. D

4

0

5. B

4

0

6. C

4

0

4

2

0

4

0

Part B

QUESTIONS 7 TO 10: 4 marks for each correct answer.

7. The inequalities that represent the constraints are:

x + y ? 1000

and

x ? y + 100

2 marks for each correct constraint.

8. The measure of angle C is 93¡ã

92¡ã and 94¡ã are also accepted.

Solutions of the End-of-the-Year C2 Major Assignment ¨C June 2nd, 2017

Page 1

9. Corey¡¯s initial capital was: $2128

10. Given that a student signed up for more than one sports, the

probability that he/she plays soccer is

??

??

or

?

??

4

0

4

0

or 72.7%

Solutions of the End-of-the-Year C2 Major Assignment ¨C June 2nd, 2017

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Part C: QUESTIONS 11 TO 19, each is worth 10 marks.

? 11. Sarah¡¯s Caf¨¦

y

220

Example of an appropriate solution:

? Optimizing Function: Profit = 3x + 1.25y

? where x = number of coffees sold each day

and y = number of muffins sold each day

200

180

160

140

x?0

y?0

x ? 70

120

(200, 100) C

(70, 100) B

100

80

y ? 50

y ? 100

60

(70, 50) A

D (100, 50)

40

x

x ? 2 y or y ?

2

20

Polygon of constraints: ?

20

40

60

80

100

120 140

160

180

200 220 x

? Vertices of the polygon of constraints:

(can be read from the graph or determined from solving systems of equations)

A (70, 50)

B (70, 100)

C (200, 100)

D (100, 50)

? Value of the objective function at the vertices:

Vertex

3x + 1.25y

A (70, 50)

$272.50

B (70, 100)

$335

C (200, 100)

$725

D (100, 50)

$362.50

Answer:

The maximum profit that Sarah can earn each day is $725

Solutions of the End-of-the-Year C2 Major Assignment ¨C June 2nd, 2017

Page 3

? 12. MJ¡¯s Candles

The three candles contain the same amount of wax, i.e., they have the same volume :

, ? they are equivalent

Volume of conic candle = Volume of cylindrical candle = Volume of spherical candle

Volume of the cone =

???? ?? ????¡Á??????

3

=

?102 ¡Á30

3

Finding the height (h) of the cylinder:

Volume of the cylinder = Volume of the cone

? ?10

??

2

=

¡Á? =

?102 ¡Á30

?102 ¡Á30

?102 (3)

3

by dividing by ?102 on both sides?

h=

30

3

= 10 cm

Finding the radius (r) of the sphere:

Volume of the sphere = Volume of the cone

4?? 3

3

=

?102 ¡Á30

3

Solutions of the End-of-the-Year C2 Major Assignment ¨C June 2nd, 2017

Page 4

By dividing by 4? and by multiplying by 3 on both sides:

3

? =

?102 ¡Á30

4?

?

3

? =

102 ¡Á30

4

3

? ?= ¡Ì

102 ¡Á30

4

= 9 cm

Therefore, the radius of the sphere is 9 cm.

Finding the total surface area, ???? ,of the cylinder (r = 10 cm; h = 10 cm):

______________________________________________________________

???? = 2 ¡Á ???? ?? ???? + ??????? ????, where lateral area = ? ¡Á ???????? ¡Á

??????

? ???? = 2(?102 ) + ?(2 ¡Á 10) ¡Á 10 = 1257 cm?

Finding the total surface area, ????? , of the cone (r = 10 cm; h = 10 cm; s = ¡Ì??? + ??? )

__________________________________________________________________________

s is the slanted height of the cone

????? = ???? ?? ???? + ??????? ????

????? = (?? 2 ) + ? ¡Á ? ¡Á ?

? ????? = (?102 ) + ? ¡Á 10 ¡Á ¡Ì102 + 302

? ?????

= ???? ??2

Finding the surface area ??????? of the sphere (r = 9 cm):

__________________________________________________

??????? = 4 ¡Á ? ¡Á ?????? 2

? ??????? = 4 ¡Á ? ¡Á 92

? ??????? = ???? ??2

Margot and Jim decided to make 100 units of each type. The total wrapping cost of all the

candles given that 1cm? of golden thin foil sheet costs 0.5 cents is:

Total Cost ($) = (1257 x 0.005 x 100) + (1308 x 0.005 x 100) + (1018 x 0.005 x 100)

Total Cost ($) = $1791.50

Answer: The total cost of wrapping all the candles is $1791.50

Solutions of the End-of-the-Year C2 Major Assignment ¨C June 2nd, 2017

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