/'

Midyear Review: Week of Jan 23rd, 2017

NAME: _-----"hhl--<>~/.CL-:)u:=--cer~------ Section: MCU504 __

!SECTIONA: MuItipl~ Choice Questions

1. The edges of the graph on the right representthe streets in a residential area.

C D

While on patrol, a police officer takes differentroutes.

A L B ../- ""

,"

'-t' /

E

H G F

Which of the following routes describes a circuit?

A) D, E, F, G, D

B) B, G, F, E, D, C

®B, A, H, G, F, E, B

D) F, E, B, A, H, G, F, E

2. Which of the following statements are FAJ,~E?

1. In a polygon of c~~tJ:ailits, the coordinates of the point farthest from the originmaximize th~Jlaltle of the function to be optimized.

2. In a polygon of constraints, me cooramateS"'~~ lowest point minimize the valueof the function to be optimized.

3. Any optimization problem has one and..~~ymJh-(fl· solution.

G 1 and 2 only

B) 1 and 3 only

C) 2 and 3 only

D) 1,2 and 3

(~

i 'I i 4!

Midyear Review: Week of Jan 23,2017 Review Booklet Page 1

!An optimization situation is represented by the following PO\ygC::4nstraints.

\ Cl, ~ I~\ V ~ ~ 1- +b :f ~t f b,~ 1\. ~ / d-

'1 b~ (j-ttf ~'o('LIY~ b;:.- ~_~[~ ,/

V '\'~:,.J"~Q;;} ~ 7- - 6 r.·/~~ 'Il' ~\"" \ . -? ~ := '-If, -6

~ I1'J' \ 2 ~ 4'" (,1 'b 110 11-Jll~x_:> ~4Y;- y- t)Which of the following coordinates are possible solutions for this situation? ,f- rmJ.' . ,\ -r ,I(hl "zn:JC0 (2,2) and(4, 10) C) (6,2) and(7,5) ~'<}(J

B) (4, 10) and (11,3) D) (7,5) and (11,3)

4. A piping system must be installed to supply water to public buildings in a city. Each edge inthe following graph represents a possible section of this piping system. The number of each edgeindicates the installation cost in thousands of dollars for that section of the system.

What is the minimum cost of installing this system?PS

~ $54000

V $58000

~

C) $72000

D) $88000

tZL-·---

Midyear Review: Week of Jan 23,2017 ReviewBooklet PageZ

5. A future housing development will consist of duplexes (houses with two apartments) andquaFplexes (houses with four apartments). ,

Thel}?~?moters of this development face different constraints. The following polygon representsthe different possible combinations of duplexes and quadruplexes that can be built. -Hr / Lf'Cit 1'1) IN flid/'

i6 (9, 17.5) •Number o~JL ~ &C1'p

quadruPle~er lYJa)<'If: cJvdL '. tJ=.

\~ G,I7)-i'~(1) f 4(n) z: ~} 61f ,IV'" 2(14) f4 (i") '" (,;y1c

4- I-+--+-+---jf---+--+-+--f=~ t-+-l-~t-+-+--+-+-VI-+--+-+-I-+-+-+--f-+4-~~+-~~It-+-l-+-t-+-+--+-+-+4-~-l-+-~~

(4,5)

/-..--.....

The number of apartments (N) that will be available once the project is completed is determinedby the following rule:

N=2x+4y

where x: number of duplexesy: number of quadruplexes

H0'r many duplexes and quadruplexes must the promoters build to maximize the numberof a artments?

9 duplexes and 17 quadruplexes

9 duplexes and 18 quadruplexes

C) 10 duplexes and 16 quadruplexes

D) 14 duplexes and 10 quadruplexes

If··

Page 3Mid~ear Review: Week of Jan 23,2017 Review Booklet

6. The constraints for a situation are represented by the following system of inequalities:

)k~x ~ 0 . CJo::-1I <.

~!~~ ~ ~-~-JLi1 ~-l'IVsU- ~}kr' 6-M~ 7- r- -(j J L 10f' ~lOx + 8y ::; 80 , r D X-f ;8j L 3 D '\ !i ---_ +g

L--7 -f 0 ~ -/ o)C)-7 'f '3Gp~;gon of constraints represents this Si::tion~ V ~ - ~ ~ + rv

8 87 76 65 54 43 32 21 1

x x1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

B) y D) y10 109 9

8 87 76 65 54 43 32 21 1

x x123 4 5 6 7 8 9 10 123 4 5 6 7 8 9 10

MOOS

Midyear Review: Week of Jan23, 2017 Review Booklet Page 4

· ,

7. iven a polygon of constraints and the corresponding system of inequalities.

Each side of the polygon and its corresponding relation are identified by the same number. flJ.~--'--(2jawfL(D1-=-{IJD

.-f@-> lop -I- 2y ~ / to--:!) -2-/ ~ fro0DO) IQ) Y L J/!)

~~ C C 100) 3 u)

y

CD x~2y

[

(~ x + 2y :::;160

® x:::; 100 /.-7])@) y~10 J

~A ~ -=:10

Which of the following ordered pairs is a vertex of the polygon of constraints?

x

At) ~ (£)(100,30)l~· D)~

8. 1];e following polygon of constraints represents the solution for an optimization situation thatinv Ives minimizing the cost of an order of seafood and steaks.

y(kg)

A

D

c

B

x (kg)

The valu s in the following table were calculated in order to determine the minimum cO~f- JJ1

mi rt ti2 ;48r _,

ynln mJm'fi11~

~ CAJ&O,

Vertex Cost

A $64 ~I..-B $64 1/.

C $128

D $184

In t is situation, how many solutions €imize th~

A No solution C) 2 solutions

B 1 solution D)

Mid ar Review: Week of Jan 23,2017 Review Booklet PageS

9. The solutions for a system of inequalities arerepresented on the right. Points A, B, C, D, E, Fand G are shown on the graph.

rF

x

How many of these points represent a solution for this system of inequalities?

A) :l C) 6U 1'n~h D) 7 ,

" D, ~ {cvV\d~ G- PCI~> c B fr. fVYI.J f ibE 6n ~ j~~~I I I T~ ,/0.. t7\,I\{ nl>/-/"- "",.Jrl~

10. The following table provides information of the distribution of the 500 peo le wofking in acompany.

Men Women TotalFull-Time Workers (210) (j-3> 6) C3.ft;YPart-Time Workers C7P"':) 90 160

Total 280 (2zO) 500

One of these 500 people is chosen at random to take part in a survey on working conditions.

Whatistheprobabilitythat thepersonchosenwillbe-eworkin~~.. _ , '-CVrHL ~

:0 C) ~~ P{jtm (l rJl trAP) -LII 21- --~D1 ~D

B) D)1417

Midyear Review: Week of Jan 23,2017 Review Booklet Page 6

11. e following inequalities represent the constraints for an optimization situation.

x~O ~a+~;!~--?rP- - ZX i-1h ]

~ L~lt~ Y~LJD~ J. 7 //Wh eh graph represents this situation?

) C) yy

1 ~ 11 X 1 X

! ----- Y 0J y

?tulJ~Jtr

11 X

•••••Mid~ear Review: Week of Jan 23, 2017 Review Booklet

1

Page 7

13. Steve wants to install a sprinkler system on his property. The vertices of the following graphrepresent the required sprinklers. Each edge represents a possible water pipe. The number on eachedge indicates the length of the pipe in metres.

Sprinkler C

Steve wants to connect all the sprinklers so as to minimize the total combined length of the pipes.

What is the shortest length of piping required toconnect all the sprinklers?

~ ~ ~;·~~I-¥-ltf~ Z!r~y ~ ~ "-+ IS' +-1, +-{~ = 6o/n_

B14. John wants to form a mixed soccer team for the summer season. The following two constraintslimit the number of players that can be on the team.

• There must be at least 14players . .--7 )L +- Y~ I 'f• There must be It0 more:~ thr~s many boys as girls.

x: number of girls on the t~ 3, ! ~y: number of boys on the team .-? ".(?J,;(What inequalities represent these two constraints?

Answer: __ X_'+_Y_2_7_1--'.1f__ and __ y_~~3_1__ are the inequalities that

represent these two constraints.

"Midyear Review: Week of Jan 23, 2017 Review Booklet Page 9

~SECTION C: Long Answer Questions

15. A map of a larger region is shown below. The vertices are towns or villages and the edges are theroads. The weights on the edges are measured in kilometers.

a) Determine the chromatic number of the diagram below.

c) Identify a Hamiltonian circuitfJ--B- 1-1- C-- F-C - £. -1>-#

d) Find a circuit of length 5

l3-fl-(}-f-C-8e) Determine the distance d(A, F) .:::: Z-

M?iMiI.

Midyear Review: Week of Jan 23,2017 Review Booklet Page 10

16. The following table provides information on the distribution of the 400 employees in acompany.

Production Sales Shipping Total

Part-Time Employees lOO tX..=~o b~,;;...O ;K-:=.- /40Full-Time Employees Z :=220 15 25 (260)

Total 'i-=- :SW 3S- LIS- 400

The following information can be used to complete the table above.

f~~) -7 I. The probability of choosing a part-time employee at random is 35%.140.-7 0·3s;<400 = (if/)

~ . 2. The probability of choosing a production department employee at random is 80%.1 9-00 ~-. 1'+0/. I /) 3. The probability that an employee works part -time in the sales department is equal to ) -:52-0f~1\frJiJ-UIAt\.... the probability that an employee works part-time in the shipping department. /-:!J 4. .:::..£

. a +b -::;./ 'f D- too - 2- 6v - (15"+IS)An employee IS chosen at random, It +b =- 41) -;z - c: 2- Z 0

---7 a. Z-104'' 20a) What is the probability that the emplOYee chosen works part-time in the sales

department?

P(f'aJ-r~~n sA) z: 20 o-rqoo

b) Given that an employee works full time, what is the probability that he/she worksin the production department

Midyear Reriew: Week of Jan23, 2017 ReviewBooklet Page 11

MCUS04 Math Name: _ Section:

At 0' Arcy McGee HighSchool a group of 40 students is surveyed on three sports activities,volley-ball, basketball, and soccer. The following are the results.

If

C: • lesJii;le/1 /; ~ .~cur" AlJl 'B ~ I1 It- ~t ~~ kOkUVI I _dA 1/

A~ if A- ~r flcar VDU ey_VfWL. . #.-C::: I-~

U:-A = f&-It-A-() ~ (J c= ~

A student is chosen at random from this group. The following are 3 possible events:A: choosing a student who plays volley-ballB: choosing a student who plays basketballC: choosing a student who plays soccer 5(2.1

14 students play soccer.16 students play volley-ball.4 students play all three sports.6 students play soccer and volley-ball.9 students play basketball and volley-ball.7 students play basketball and soccer.Only 5 students do not participate in any of the three sports

a) Represent this situation using a Venn diagram.

~qlA-::.C; -? ;X ~ (, - 4- ==- L¥ 80A.:: q -,) W z: q-4=s-'\l:: 1£ _ (' 2 + 4- 1-5)

-M- C. (\ B.::::- 7 -;> 'j, =- 7 - 4;:: 3~u:. 1'+:....l2-t'?f"4)=~ ._

.:\f-(C OB UA ) I:::; s- -;> Z z: 40 - C~ct~.t 4 ·f Lt-} -+ s:+r)-z: If -:9 #-U:=- 2Jb) Determine the probability of choosing a student who plays soccer given that he/she

pays at least two sports:P ( c I If f-&f evt ~f 3 LJfj)cr1s il): : 3 + lft z-. =- :1.. ~ G+2

vv (2+J+4+r) 14 '

d} Calculate P{AIB}

P(All3).:=:. q or 3q ~~3

e) Calculate the probability of choosing a student who does not play volley-ball GIVEIJ l'HAT~/SH£ 'PLII'/S G-/:i#+~ BA-5~E-TBA-t.L- oR SOU,GR,

P (A'lsuc):= P(A' n(BuC)P(BUC)