Multiple Choice Exam Review

7/24/2019 Multiple Choice Exam Review

1/20


2/20

6. "he function 2205 2 ++= tth describes the height of a baseball ,h- in metres( as afunction of time ,t- in seconds( from the instant the ball is hit. Mar7 solved the e4uation

02205 2 =++ tt and its positive root represents#

a! the initial height of the ballb! the maximum height of the ball

c! the time it ta7es for the ball to reach a maximum height of 2 metresd! the time it ta7es fo the ball to hit the ground.

8. +iven the 4uadratic function23xy= ( which of the following statements is true

a! "he function 9s increasing for all x$valuesb! "he function is decreasing for all x$valuesc! 9ts graph is s)mmetric about the )$axisd! 9ts graph has 2 distinct x$intercepts

:. ;elect the correct graph for the e4uation ( ) ( )nxmxy = ( if m / o and n / 0.

a! b!

c! d!

10. What t)pe of function would best model the data in the table below

a! linearb! 4uadraticc! logarithmicd! exponential

< =

1 21.*

2 *.3

% 62.3

* 102.*

1%


3/20

11. Which of the following se4uences could be generated b) a 4uadratic function

a! >1( 2( %( *( ?@ b! >$( $%( %( 1%( ?@c! >2( *( 8( 12( ?@ d! >2( 3( 18( *( ?@

12. Which of the following is true about a 4uadratic function

a! "he graph alwa)s increasesb! "he graph alwa)s crosses the x$axisc! "he graph is alwa)s s)mmetric about the )$axisd! "he e4uation is alwa)s considered a second degree e4uation

1%. "he graph of the e4uation ( ) 47 2 ++= xy is the image of 2xy= after#

a! a hori5ontal translation of 6 and a vertical translation of *b! a hori5ontal translation of $6 and a vertical translation of *c! a hori5ontal translation of 6 and a vertical translation of $*d! a hori5ontal translation of $6 and a vertical translation of $*

1*. 9f the roots of an e4uation are $2 and *( then the discriminant is#

a! an imaginar) number b! 0c! a positive number d! a negative number

1. Which 4uadratic e4uation best represents the following graph 'a( h( and kare positivereal numbers!.

a! ( ) khxay += 2

b! ( ) khxay += 2

c! ( ) khxay += 2

d! ( ) khxay +=

2

13. When deriving the 4uadratic formula( a student starts with cbxaxy ++= 2 ( then solves

cbxax ++= 20 . Wh)

a! "he student wants to determine the )$intercept of its graphb! "he student wants to determine the x$intercept's! of its graphc! Auadratic e4uations alwa)s e4ual 5erod! Bero is easier to wor7 with than an) other number

16. "he function cbxaxy ++= 2 is represented b) thefollowing graph. Which of the following statements is true

a! a/0 and c/ 0b! a/0 and c0c! a0 and c0d! a0 and c/0


4/20

18. +iven the e4uation ( ) 642 2 += xxxf ( the domain and range can be written as#

a! domain }{ Rx ( range }{ Ryb! domain }1010,{ xRx ( range }{ Ryc! domain }{ Rx ( range },8{ Ryy d! domain }{ Rx ( range },6{ Ryy

1:. avid wants to find the minimum value of the function ( ) xxxf 35 2 += . De should#

a! state the value fora

b

2 b! ma7e ( ) 0=xf ( then factor

c! state the x$coordinate of the vertex d! state the )$coordinate of the vertex

20. Which formula generates the se4uence represented b) the graph below

a! 22 += nntn

b! 122 2 += nntn

c! 122 += nntn

d! 142 2 += nntn

21. "he e4uation of the axis of s)mmetr) of the parabola represented b) the function

( )22= xy is#

a! x $2 b! x 2 c! x $ 0 d! ) 2

22. What is the nature of the roots of a 4uadratic e4uation having a discriminant e4ual to 0

a! two e4ual real roots b! two une4ual real rootsc! two imaginar) roots d! no real roots

2%. +iven the e4uation 0252 =+x ( then ,x- is e4ual to#

a! 5 b! 5 c! i5 d!i5


5/20

2*. Which graph has a vertical stretch factor of2

1when compared to the graph of

2xy=

a! b!

c! d!

2. For the function cbxaxy ++= 2 ( the )$intercept is alwa)s#

a!a

b

2 b! c c!

a

c d!

a

bac

4

4 2

23. "he function representing a parabola with a vertex at '%( 2! and passing through the point'*( *! is#

a! ( ) 232 2 += xy b! ( ) 232 2 += xy

c! ( ) 232

1 2 += xy d! ( ) 232

1 2 += xy

26. "he domain and range of the function represented b) the graph below are#

a! }{ Rx and }{ Ryb! }{ Rx and }2,{ yRyc! }{ Rx and }2,{ yRyd! }1,{ xRx and }2,{ yRy


6/20

28. &n l)mpic diver dives from the high diving board. "he distance( d( in metres( from thesurface of the water varies with the time( t( in seconds( that have passed since she left the

board( according to the e4uation 1032 2 ++= ttd . What is her maximum elevation abovethe water during the dive 'rounded to the nearest unit!

a! % metres b! 10 metres c! 11 metres d! 12 metres

2:. "he function 132 2 += nntn is used to generate a 4uadratic se4uence.

What is the value of 2

a! 1 b! 2 c!4

3 d! *

%0. "he mapping rule that describes how to map2xy= onto ( ) ( )275

2

1+= xy is#

a! ( )

+ 5

2

1,7, yxyx b! ( )

5

2

1,7, yxyx

c! ( ) ( )52,7, + yxyx d! ( ) ( )52,7, + yxyx%1. What are the coordinates of the vertex of the 4uadratic function having a maximum valueof 20 and x$intercepts located at '( 0! and '$1( 0!.

a! '%( 20! b! '2( 0! c! '2( 20! d! '%( 0!

%2. "he graph of a 4uadratic function cbxaxy ++= 2 is given below#When solving for the ,x- in the e4uation

02 =++ cbxax ( the solution 's!

represent#

a! the ,x- coordinate of the vertexof the 4uadratic function

cbxaxy ++= 2 .b! the maximum or minimum value

of ,x-

c! the x$intercepts of cbxaxy ++= 2

d! the ,x- coordinate of the )$intercept

of the 4uadratic function cbxaxy ++= 2


7/20

%%. 9n which of the following 4uadratics is the discriminant e4ual to 5ero

a! b!

c! d!

%*. "he vertex of the parabola represented b) 442 2 = xxy is#

a! '1( $3! b! '1( $! c! '$1( 2! d! '$1( 3!

%. "he axis of s)mmetr) for the parabola defined b) 1282 += xxy #

a! x $* b! x * c! x 8 d! x 12

%*. & cannon ball is shot into the air and its height in meters is represented b)29.41.235.1 tth += where ,t- is time in seconds. Dow high does the cannon ball go

a! 2%.10 m b! *.68 m c! 28.6% m d! 2.%3 m

%. & bas7etball pla)er is tr)ing to increase her shot accurac). ;he sta)s in the same positionon the court and increases the arc of the flight path of the ball.

Der coach graphs the 4uadratic function

( ) ( )21

hxkya

= to model parabolic

ath 9 of the bas7etball. "he coach thenChanges certain values in the givenE4uation to graph path 99. Which value's!id the coach NOTchange

a! a b! hc! 7 d! h and a


8/20

%3. 9f in a se4uence the second difference is constant( then the se4uence is#

a! arithmetic b! linear c! 4uadratic d! cubic

%6. "he e4uation of the axis of s)mmetr) of the parabola represented b) the function

22 = xy is#

a! x 2 b! x $2 c! ) 2 d! x 0

%8. +iven the e4uation 0482 =+x ( then ,x- is e4ual to#

a! 34 b! i34 c! 3.: d! Go possible Halue

%:. Which mapping rule describes how to map function1

y onto the function 2y

a! ( ) ( )52,3, yxyxb! ( ) ( )5,32, + yxyxc! ( ) ( )52,32, yxyx

d! ( )

+ 5

21,3, yxyx

*0. For the function cbxaxy ++= 2 ( the )$intercept is alwa)s#

a!a

b

2 b! c c!

a

cd!

a

bac

4

4 2

*1. 9f the e4uation 0142 2 =+ xkx has two e4ual roots 'double root!( then the value of 7is#

a! 7 0 b! 7 / 0 c! 7 2 d! 7 / 2

*2. Which function has an axis of s)mmetr) atp

qx

4

=

a! kqxpxy ++= 22 b! kqxpxy += 24c! pqxkxy += 42 d! pqxkxy 42 ++=

*%. What value of ,b- ma7es the expression25

362 ++ bxx a perfect s4uare

a!

25

18b!

5

3c!

5

6d!

5

12


9/20

**. & cannon ball is shot into the air and its height( in metres( is represented b) the function29.41.135.1 tth += where ,t- is time in seconds. Which of the following best

approximates how long it will ta7e for the ball to hit the ground

a! 1.%* sec b! 1.0 sec c! 2.68 sec d!10.2 sec

*. 9f the roots of 02 =++ cbxax are10191

i ( then the graph of the function

ycbxax =++2 #a! has no x$intercept b! has no )$interceptc! is not parabolic d! has 2 distince x$intercepts

*3. "he value of ,c- that will ma7e the expression cxx +129 2 a perfect s4uare is#

a! %3 b! * c! 81 d! 13

*6. +iven 044 2 =++ kxx ( for what values of ,7- will there be no real roots

a! 71 b! 7/1 c! 7 0 d! 7/ $1

*8. 227 has the same value as#

a! 227 b! 63 c!4

9

1

d!

3

3

1

*:. What is half of 202

a! 102 b! 201 c! 192 d! 101

0. ;elect a graph that best represents the following situation#

,& car depreciates at a rate of %0I per )ear-

a! b!

c! d!


10/20

1. Marla is tr)ing to determine the value for x in the e4uation 227 =x . Which one of thefollowing will she use to obtain the value of x

a!

=

7

22logx b! 22loglog 7 =x c! 7log

22log=x d!

22log

7log=x

2. Which e4uation is the same as ( )

x

y 24=

a!xy 24 = b! 22 += xy c! xy 22= d! xy 8=

%. "he price of a particular product doubles ever) % )ears. 9f the price of the product wasJ13.*0 on Kanuar) 1( 1::3( then the price of the product will be J%3.0 in the )ear#

a! 2028 b! 20%1 c! 20%3 d! 20*0

*. 3 2x can be expressed as#

a! 23

xb! 3

2

xc!

3

2xd! ( )32x

. 3log7log9log2 333 + expressed as a single logarithm is#

a! 13log2 3 b! 21log2 3 c! 42log 3 d! 189log 3

3. 9f5

664log =x then x is e4ual to#

a! 0.0* b! %2 c! 3.53 d! 1*6

6. Which of the following table of values is an exponential function

a! b!

< 2 % *

= : 13 2 %3

c! d!

< 2 * 3 8

= 1 6 1% 1:

8. Koe) has been collecting anti4ue to) cars as an investment. "he value ,H-( in dollars( of a

to) car with respect to its age ,t- in )ears( can be modeled using the function ( ) 432t

V = .

Which of the following is true

a! "he carLs initial value was 2 dollars and it tripled in value ever) * )ears.b! "he carLs initial value was % dollars and it doubled in value ever) * )ears.c! "he carLs initial value was * dollars and it tripled in value ever) 2 )ears.d! "he carLs initial value was 2 dollars and it 4uadrupled in value ever) % )ears.

< 2 3 8 1= 3 12 2* *8

< 2 8 11

= 2* 12 3 %


11/20

:. +iven 1log 3 =x ( the value of ,x- is#

a!2

1=x b!3

1=x c! 1=x d! 3=x

30. Which of the following is e4ual to 54

a

a! 5 4a b!

5

4

1

a c! ( )54a d!

4

51

a

31. "he expression ( ) ( ) ( )9log5log3log3 222 + is e4uivalent to#

a!

9

15log3 2 b! ( )1log3 2 c! ( )5log 2 d! ( )15log 2

32.3

3120

is e4ual to#

a! 1203 b! 1193 c! 1201 d!

1173

3%. 9f219log =x ( then x is e4ual to#

a! % b! *. c! 18 d! 81

3*. Which graph best describes the growth of bacteria that doubles ever) three hours 't istime in hours( & is amount of bacteria per s4uare mm!.

a! b!

c! d!


12/20

3. "wo exponential functions(1

y and y ( of the form xaby= are graphed. Dow do thetwo values of ,a- compare in the two functions

a! "he value of ,a- for1

y is greater that the

Halue of ,a- for 2y .

b! "he value of ,a- for 1y is less than the valuef ,a- for 2y

c! "he value of ,a- for1

y is e4ual to the value of

,a- for 2y .

d! For the function1

y ( 10


13/20

61. 9f a person earns an annual interest if 6I compounded annuall) on an investment ofJ0.00( which functions shows how much mone) the investor has at time t( in )ears

a! ( ) ( )ttP 07.150= b! ( ) ( ) ttP 7.150= c! ( ) 5007.1t

tP = d! ( ) ( )t

tP 07.050=

62. "he function ( ) 325 += xy has a hori5ontal as)mptote at#

a! ) $ b! ) $% c! ) % d! )

6%. &n exponential e4uation that is e4uivalent to3

24log 8 = is#

a!48 3

2

= b! 84 32

= c! 832

4

=

d!3

284 =

6*. "he table given shows how two dollars invested over a period of )ears grows in valuewhen interest is compound annuall). What is the approximate annual interest rate

a! 1.0%Ib! %Ic! 3Id! :.6I

6. Which one of the following tables of values was generated b) an exponential function

a! b!

c! d!

63. "he value of ( ) 320 36 + is#

a!1000

1b!

10

1c! 1000 d!

729

1

66. Which of the following is e4ual to 32

b

if 0b

a! 3 2b b! 3 21

bc! 3b d! 3

1

b

< )ears 1 2 % *

= J 2.03 2.12 2.18 2.2

< $1 2 %

=

2

1 1 2 *< $1 1 %

= 1 % : 26

< $1 0 1 2

=

3

1

3

2 1

3

4

< 1 2 % *

= 1 * : 13


14/20

68. Which graph representsxbay = ( where 0>a and 10


15/20

8.Which of the following expressions is e4uivalent to 23

2

x

a!2

3

2

1

xb!

3

2

2

1

xc!

2

3

2

xd!

3 2

2

x

83. 9f2

3

64

1log =

x then ,x- is e4ual to#

a! 13 b! 8 c!8

1d!16

1

86. Which of the following relationships cannotbe modeled as an exponential function

a! +rowth of a opulation b! Compound 9nterestc! Dalf$life of radioactive elements d! tidal c)cles

88. Which of the following is FALSE

a! NMNM

aa

a

a loglogloglog = b! c

aa McM

1

loglog =

c!M

NNM

log

loglog = d! ( ) xMxMN N

x

N += loglog

8:. "he value of ,x- in the e4uation3

532log =x is#

a! * b!5

3c! 8 d!13

:0. Choose the converse of the following statement#

,9f two chords on a circle are e4uidistant from the centre of the circle( then the) arecongruent.-

a! "herefore chords on a circle are e4uidistant from the centre of the circle.b! 9f the centre of a circle is e4uidistant from two chords( then the) are congruent.c! 9f two chords on a circle are congruent( then the) are e4uidistant from the centre of

the circle.d! "wo chords on a circle are congruent if the) are e4uidistant from the centre.

:1. What are the coordinates of the centre of the circle that has the points 'a( b! and 'c( d! asendpoints of a diameter

a!

2,

2

dbcab!

++

2,

2

dcba

c!

2,

2

bdacd!

++

2,

2

dbca


16/20

:2. +iven PQ with midpoint M'2( $%! and endpoint A'$( 1!( what are the coordinates of

a! '$1.( $1! b! '$1( $*! c! '%.( $2! d! ':( $6!

:%. "he segment below is to be cut into * e4ual pieces. What are the coordinates of

a! '2( 1! b! '$1( 2!

c!

2

1,1 d! '$1( %!

:*. 9f two chords of a circle intersect( then their perpendicular bisectors#

a! donLt intersect b! are parallelc! bisect each other d! intersect at the center of the circle

:. +iven the following figure#

a! & C

b! "he midpoint of AD is

2

1,1

c! "he diagonals ACand BD&re of e4ual lengths

d! "he diagonals AC and BD

bisect each other

:3. +iven the points & and on the diagram as indicated( & is e4ual to#

a! ( ) ( )22 2561 ++

b! ( ) ( )22 2651 ++

c! ( ) ( )22 2651 ++

d! ( ) ( )22 5216 +++

:6. "o prove that a 4uadrilateral &C is a rectangle( Kohn showed that the opposite sides arecongruent. Which of the following statements would complete his proof

a! pposite sides are parallel. b! "he diagonals bisect each other.c! AB and BCare perpendicular d! BCDABC

(5,-2)

(1,6)


17/20

:8. & chord in a circle is 10 cm long. 9f the radius is 6 cm( what is the distance between thechord and the centre of the circle.

a! 6 b! 51 c! 62 d! 74

::. 9n which diagram is there enough evidence to conclude that the segment & passesthrough the centre of the circle

100. "wo dice are tossed. What is the probabilit) that the will land on different numbers

a!36

30b!

36

6c!

36

5d!

36

2

101. & bag contains 12 green marbles( 10 red marbles and 18 white marbles. ill removes 1

marble from a bag. "he probabilit) that ill removes a red marble from the bag is#

a!4

1b!

10

1c!3

1d!

40

1

102. 9f an event can succeed in ,s- wa)s and fail in ,f- wa)s( then the probabilit) of successis#

a!f

sb!

sf

s

+c! fs d! f1

10%. 9n a school of 200 students( 80 have blood t)pe . 9f students are chosen at random(what is the probabilit) of selecting five students with t)pe blood

a!76

1

77

1

78

1

79

1

80

1 b!

580

5

Cc!

510

5

Pd!

5200

580

C

C


18/20

10*. Consider the following Henn diagram. Which of the following is correct

a! 'N or O! 'N! P 'O!b! 'N and O! 'N! P 'O!c! 'N or O! 'N! x 'O!d! 'N and O! 'N! x 'O!

10. =our math teacher gives )our class a list of eight 4uestions to stud). Five of the eight4uestions will be randoml) selected for the next test. 9f )ou stud) onl) the first five 4uestionsfrom the list( the probabilit) that all of those five 4uestions will be on the test is#

a!58

1

Cb!

58

1

Pc!8

5d!

8

1

103. "he value of!499

!500is#

a! 1 b! 1.002 c! 00 d! undefined

106. & bag contains : marbles( * of which are red. What expression represents the probabilit)of selecting three red marbles when three marbles are drawn at random

a!39

1

Cb!

39

4

Cc!

39

4

Pd!

39

1

P

108. ;ome students were as7ed whether the)watch hoc7e) or football. "he results are shownin the following Henn iagram. What is the probabilit)that a person chosen at random watches hoc7e)

a!5

2b!

2

1c!

5

4d!

10

3

10: +iven the following tree diagram.What is the probabilit) of sta)ing homeand inviting friends

a! 0.0b! 0.60c! 0.:0

d! 0.3


19/20

110. "im and Rebecca are the first and second students in a line of 6 students waiting to bu)tic7ets for a concert. "he number of different orders in which the remainder of the studentscan line up behind them is#

a! Q b! 6Q c! 'Q!'2Q! d!!2

!7

111. "wo coins and one die are simultaneousl) tossed on a table. What is the probabilit) ofobtaining two heads and a 3

a!12

5b!

24

1c!5

1d!

8

1

112. 9f we shuffle a standard dec7 of 2 cards and randoml) select one card( what is theprobabilit) of selecting a 7ing or a 4ueen

a!52

1b!

26

1c!13

1d!

13

2

11%. "wo boxes contain marbles. "he first contains five red marbles and three white marbles."he second box contains four blac7 marbles and seven green marbles. ne marble is chosenat random from each box. What is the probabilit) that a white and a blac7 marble will bechosen

a!22

3b!

32

33c!

12

1d!

35

12

11*. Mr. ;mith has % pairs of blac7 pants and 2 pairs of gre) pants in the first drawer of hisdresser. 9n the second drawer( he has 1 white shirt and * multi$colored shirts. De gets up lateone morning and without loo7ing 4uic7l) grabs a pair of pants from the first drawer and a shirtfrom the second drawer. What is the probabilit) that he grabs a pair of blac7 pants and awhite shirt

a!25

3b!

25

4c!

5

4d!

5

2

11. =ou want to put 8 different boo7s on a shelf( side b) side. 9n how man) wa)s can theseboo7s be arranged

a! 8Q b!!2

!8c! 18 P d! 88C

113. eter( Mar)( and ;usan are part of a group of 10 people. &n executive consisting of eteras the resident( Mar) as the "reasurer( and ;usan as the ;ecretar) could be formed from thisgroup. What is the probabilit) this executive will be formed

a!310

1

Pb!

310

1

Cc!

310

3

Pd!

310

!3

C


20/20

116. *0 people were surve)ed and as7ed whether the) use a mechanical pencil or a woodenpencil when writing a test. "he results are shown in the Henn iagram below. 9f one person israndoml) chosen( what is the probabilit) that this person does not use a wooden pencil whenwriting a test

a!

20

9 b!

5

4

c!10

7 d!

20

11

&nswers# 1! d 2! a %! d *! b ! b 3! a 6! d 8! c :! c 10! b 11! b 12! d 1%! b 1*! c 1! a 13! b16! d 18! c 1:! d 20! c 21! b 22! a 2%! c 2*! d 2! b 23! a 26! b 28! c 2:! d %0! d %1! c %2! c%%! b %*! a %! b %*! c %! b %3! c %6! d %8! b %:! a *0! b *1! c *2! a *%! c **! c *! a *3! b*6! b *8! b *:! c 0! d 1! c 2! b %! c *! b ! d 3! b 6! d 8! a :! b 30! a 31! d 32!b 3%! a 3*! b 3! b 33! a 36! b 38! c 3:! b 60! d 61! a 62! c 6%! a 6*! b 6! b 63! a 66! b68! b 6:! d 80! b 81! d 82! c 8%! a 8*! d 8! c 83! a 86! d 88! a 8:! c :0! c :1! d :2! d :%! d:*! d :! c :3! c :6! c :8! c ::! d 100! a 101! a 102! b 10%! d 10*! a 10! a 103! c 106! b108! b 10:! d 110! a 111! b 112! d 11%! a 11*! a 11! a 113! a 116! d

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Multiple Choice Exam Review