January ..51 Uct :l-:s - worksheets, answers, lesson · PDF filequestions or answers prior to...

ALGEBRA I (COMMON CORE)

The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

ALGEBRA I (Common Core) Monday, January 26, 2015- 1:15 to 4:15p.m., only

Student Name: ..51 e L) e... Uct ... :l-:s e:> ..,

' School Name: --------=f.A./~~W=-----=-=t..vl=----.:,:.....___.,'v,..-ll~_~~~__,ft=--=-• ~o~r'--j-=:J-----

The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you.

Print your name and the name of your school on the lines above.

A separate answer sheet for Part I has been provided to you. Follow the instructions from the proctor for completing the student information on your answer sheet.

This examination has four parts, with a total of 37 questions. You must answer all questions in this examination. Record your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet. All work should be written in pen, except graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. The formulas Jhat you may need to answer some questions in this examination are found at the end of the examination. This sheet is perforated so you may remove it from this booklet.

Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this booklet as scrap paper. A perf()rated sheet of scrap graph paper is provided at the end of this booklet for any question for which graphing may be helpful but is not required. You may remove this sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored.

When you have completed the examination, you must sign the statement printed at the end· of the answer sheet, indicating that you had no unlawful knowledge of the questions or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this declaration.

Notice ...

A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination.

DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

(380~ NO~~O~) I 'V8838l'V

Part I

Answer all24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers on your separate answer sheet. [ 48]

Use this space for 1 The owner of a small computer repair business has one employee, computations.

who is paid an. ho.~rly ~at~...9-f j22. The owner estimates his weekly profit using the function P(x) = 8600 - 22x. In this function, x

represents the number of I, ll /) f'./: :: Q f..v <..'""""'-"""'..._,; _ 6 p ~--....,$e. fi'

(1) COmputerS repaired per Week~~ rrc; I ~~ (t k) • h k d k /! t!JI _ jj ?? hr...,./! /(H'~" t..)~4>.

ours wor e per wee I\~U L/,;0 . ,' f -:: 0 <:J00 :f( ~ '- 'I

(3) customers served per week I.,U! l rl (4) days worked per week

2 Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. He converts his speed into miles per hour, as shown below.

40 yd .1__!!_ ~. 60 sec • 60 min 4.5 sec l yd \E) 1 min l hr

Which ratio is incorrectly written to convert his speed?

3ft 60 sec (1) -- (3)

l yd l min

• 5280 ft (4) 60min

l mi 4 1 hr

~~D~~ ~(L

3 Which equation has the same solutions ~s 2x2 + x - 3 = 0? .l_~'"-t'X-X -~ .2X .t-2?< -3 X -3 Ji6 (2x - 1)(x + 3) = 0 (3) (2x - 3~)(x + 1) = 0

(1 (2x + l)(x - 3) = 0 • (2x + 3)(x - 1) = 0

). ·l'-6 X +-X. -3 :2. )<. ... - 2 X + 3 "- -3

Algebra I (Common Core)- Jan. '15 [2]

Use this space for 4 Krystal was given $3000 when she tumed,j_years old. Her parents computations.

invested it at a 2% interest rate compounded annually. No deposits or withdrawals were made. Which expression can be used to determine '2 ::... \ )o how much money Krystal had in the account when she turned 18? --.--)> I (t, - L ,

' - } ol \__$ • e 3000(1 + 0.02)16 (3) 3000(1 + 0.02)18 ~~ ~- eJ \ {o-h~e.s (2) 3000(1 - 0.02)16 (4) 3000(1 - 0.02)18 CbY\1\.. ~ DV.."-J..~

5 Which table of values represents a linear relationship?

9~

,,

(

I I

X

-1

0

1

2

3

X

-1

0

1

2

3

f(x)

-3

-2

1

6

13

(1)

f(x) 1

2 1

2

4

8

(2)

I 3 ? 7

~

2-

'-t

)

I

I

X I

f(x)

-1 -3

0 -1

1 1

2 3

3 5

• X f(x)

-1 -1

0 0

1 1

2 8

3 27 ~--- '-----~-

(4)

t.

2.-

2.

t.

I

7

I~

\)< C9~'(er

e

(~c. E>

t "-.j

~ ~ ~~ _J . .)

J ..

6 Which domain would be the most appropriate set to use for a ......_ ? A function that predicts the number of household online-deyj,ces in ~ "i terms of the number of peoP.l~ in the household? 1\ j){ integers _;;r( irrational numbers ..-..:; Uc... _&e~~ ,

{4!( v-.~ ,...-r~o-alS • whole numbers F' rational numbers -

(_ LJ(_ Jo ~+ ne..a.J. Pr~~ o ~ we_ J..--..~ "~ 1\"-j j:," .... ~.s


;::# ~ IL"f\~ I" J,..g \j v ~-::>

[OVER]

7 The inequality 7 - ~ x < x - 8 is equivalent to Use th" IS space for

• X> 9 (3) X< 9 7-~ f.. <: )<, _ 6 computations .

< E'A- 2~ 3 3 (2) X > -- (4) X < --5 5 t.,l - 2 X

'2..~ ..trz. ~

4-~ t./5' ~

~,2.)( -\""" z. ~ <= <;;"X

L'f_

8 The value in dollars, v(x), of a certain car after x years is represented 81

by the equation v(x) = 25,000(0.86)x. To the nearest dollar, how much more is the car worth after 2 years than after 3 years? . ( O ·86) 2...

• 2589 (3) 15,901 V l 1-) : 2. 'S'1 COD .

(2) 6510 (4) 18,490 \}(_ :::.. I ~J '+ ~ D 3 Z? ( 8b)

~-~ = /(/,<!90·/s;?o/~)2~ VI.!):= 2S: 000 o. \I :. I~, 90 ) v (3)

9 Which function has the same y-intercept as the graph below?

y

X \ \-

-z.-.--1_;~~ ;; ~3

Y=- 3 -+~ Y- - ')(. - -r+ 3 rJ1' 12- 6x /~l y = 4

. (;/( 27 + 3y = 6x

/-' 3 t :::: f> X - 2 7

'I -:_ )..."f. - ?

)Z) 6y +X= 18

.y+3=6x '/ ~{,X-3 X ~ -:)

t \ \Jr-q.)< i .... '-,..


10 Fred is given a rectangular piece of paper. If the length of Fred's piece of paper is represented by 2x - 6 and the width is represented by 3x - 5, then the paper has a total area represented by

(1) 5x - 11 (3) lOx - 22

• 6x2 - 28x + 30 (4) 6x2 - 6x - 11

(; x-b)(J x-s--) t >< L - /6 X -~~X + 3 0

6 '~> Z-- zex -r3o 11 The graph of a linear equation contains the points (3,11) and ( -2 1).

Which point also lies on the graph? X y

(1) (2,1)

(2) (2,4)

(3) (2,6)

• (2,9)

~--- z -----l ~3 . "0 s ____ 1 __ ,..... 7

~ ·--r-==r(:-~ 12 How does the graph ofj(x) = 3(x - 2)2 + 1 compare to the graph

of g(x) = x2?

J5! The graph ofj(x) i~an the graph of g(x), and its vertex is moved to the left 2 units and up 1 unit .

• The graph ofj(x) is narrower than the graph of g(x), and its vertex is moved to the right 2 units and up 1 unit.

y.fi The graph ofj(x~arrower than the graph of g(x), and its vertex is moved to th~ units and up 1 unit.

)#f' The graph ofj(x) is@an the graph of g(x), and its vertex is moved to the right 2 units and up 1 unit.

13 Connor wants to attend the town carnival. The price of admission to the carnival is $4.50, and each ride costs an additional 79 cents. If he can spend at most $16.00 at the carnival, which inequality can be used to solve for r, the number of rides Connor can go on, and what is the maximum number of rides he can go on?

~· 79 + 4.50r :::; 16.00; 3 rides

~0. 79 + 4.50r:::; 16.00; 4 rides

• 4.50 + 0.79r:::; 16.00; 14 rides

~ 4.50 + 0. 79r :::; 16.00; 15 rides


Use this space for computations.

[OVER]

14 Corinne is planning a beach vacation in July and is analyzing the daily high temperatures for her potential destination. She would like to choose a destination with a high medi~n temperature and a~ i!.!!::~tile range. She constructed box plots shown in the diagram belOW:

i X()z_LBD


~n Beach ~ores

Whi~pering Palms ~~ P~tican Beach / (JD \:\ <-

/(1.-z-1'~ I >1 I Ji,;.:}-1_.,.. ~ ()?- ~ ,~\;.-tr,-~' •I I l I I I I• •I I I I I I I• ~~ 70 75 80 85 90 95 100 70 75 80 85 90 95 100

Which destination has a median temperature above 80 degrees and the smallest interquartile range? , c

)if) Ocean Beach jZ} Serene Shores

(2) Whispering Palms • Pelican Beach

15 Some banks charge a fee on savings accounts that are left inactive for an extended period of time. The equation y = 5000(0.98)x represents the value, y, of one account that was left inactive for a period of x years.

What is they-intercept of this equation and what does it represent?

(1) 0.98, the percent of money in the account initially

(2) 0.98, the percent of money in the account after x years

• 5000, the amount of money in the account initially

(4) 5000, the amount of money in the account after x years

= s-ooo


16 The equation for the volume of a cylinder is V = nr'2h. The positive value of r, in terms ofh and V, is


• r = tv f-;J;

(2) r = .Jvnh

(3) r = 2Vrth

(4) r = _.Y_ 2Jt

\) - 1\ (2 ~

v ;:r~ ~ \ '1.-

r-J-" - -~-· J~ - \

~-17 Which equation has the same solutions as x2 + 6x - 7 = 0? X 2- -\-- b X ~ 7 { ~ "2....

(1) (x + 3)2 = 2 (3) (x - 3)2 =. 16 / 0' -\- ~) z_ == 7 k '(?) (2) (x - 3)2 = 2 II (x + 3)2 = 16 · ·- \... ""2-- .,., 7 -\-- '1

~- (__'!..+"3) -(1,...f\~s ~.... 0_-<-3) .... ~I~..

18 Two functions, y = lx - 31 and 3x + 3y = 27, are graphed on the same set of axes. Which statement is true about the solution to the system of equations?

(1) (3,0) is the solution to the system because it satisfies the equation y = lx- 31.

(2) (9,0) is the solution to the system because it satisfies the equation 3x + 3y = 27 .

• (6,3) is the solution to the system becauseit sa~!sfiesJ;wth.,rsuatipn§,:. ·-(4) (3,0), (9,0), and (6,3) are the solutions to the system of equations because they all satisfy at least one of the equations.

y-=/X,3) ~ j = -3 'A --r?... "7

1 ~ -"'A+q

---0 \

2..

3

2-\

1 z_

cr ~ 7

3 0 \ !:> ~ I <5' / 2 ~

_:;!~~---~.-··~·· ~----~~----- ·-( ~ 3 \3 J ''--------------·· --. -·- ... -- .. -\ ~-- . ___ ,...,

\

\_ Algebra I (Common Core)- Jan. '15 [7] [OVER]

Use this space for 19 Miriam and Jessica are growing bacteria in a labor.atory. Miriam uses ... \ -~mputations.

the growth function f(t) = n2t while Jessica uses the function ~-g\t) = n~t, w~ere n repres~~ts the initi~ number of_bacteria and X 1 'J_~.,.-.. ·· tIS the time, m hours. If Mmam starts With 16 bactena, how many .._,- -·

time? I (_2 X !.J1__ _ _,_. . bacteria should Jessica start with to achieve the sa. m.e growth over ) ~· 0 .. ·-

(1) 32 (3) 8 \ y :;; 16 ~ .b ':S'J'S 5 (.

(2) ;~ IH • 4 >.. o)v - --"···--() ::: t\ l h - f\ _ (4 x) '!- Y __ _

2-t _ (#"' L\ <.-1::' JiL ~ f\ . y - 4 () \ (\ - \[\ J ffi ;~ z_Sb

20 If a sequence is defined recursJve!y 7 ) ~ 2 and I .,-.: :53 b f(n + 1) = -2f(n) + 3 for n ~ 0, thenf(2) is equal to Z- b :> )

( 1) 1 • .5 ---·--····-··-·-·-- ·-· (2) -11 ( 4) 17

skt 1 £ J(p-~-Q = -z !!-(o) +3 ~~ 2 ~-olv~t-.R.,.. Po) == -2 (_z) ~5 Sol-H.[:.,..

{J(S) .(! (j) :::. -I {J ( ~

.P ~+1) == -2 fu) -+3 ~ ( ?.-) = -2 (- \) ~ 3 ~ {z..) = 2. +3

21 An astronaut drops a rock off the edge of a cliff on the Moon. The distance, d(t), in meters, the rock travels after t seconds can be modeled by the function d(t) = 0.8t2. What is the !lverage speed, in ~eters £_er secon.$ of the rock between 5 and to seconds after

it was dropped? 'j == o. eX 2-

• 12 (3) 60 ..,., ~') (2) 20 (4) 8o \~ zO\

: 10 8D ,

sf~~.) ' J_.'..~~ ~.{: ----+,·~.,(..

5fee;l 8 0 '~''· e}"' I')

--.e.:~""""~ .. ~ <"''•' \0"".'

--22 When factored completely, the expression p4 - 81 is equivalent to

(1) (p2 + 9)(p2 - 9) ' i ,f-/ ~ ~ u ~ 9) (2) (p2- 9)(p2 - 9) Re'Peff f. L- ~ ~. P, /. . . • (p2 + 9)(p + 3)(p- 3) ~ e;r_~te-> .. J::.. ~ t--· (4) (p + 3)(p - 3)(p + 3)(p - 3) · ;)e/ ~ .,.p/.e..>

u ~cc

{!~ ~v (f;} $Cr-3)


23 In 2013, the United States Postal Service charged $0.46 to mail a letter weighing up to 1 oz. and $0.20 per ounce for each additional ounce. Which function would determine the cost, in dollars, c(z), of mailing a letter weighing z ounces where z is an integer greater than 1?

(1) c(z) = 0.46z + 0.20

(2) c(z) = 0.20z + 0.46

(3) c(z) = 0.46(z - 1) + 0.20 Q-


• c(z) = 0.20(z - 1) + 0.46 Cf)c;.\r- 9

f 1 1\ {tr>\' ~ eorl"- ji o~,t ,._, __-

""';"'.,.> ~"'~ 24 A polynomial function contains the factors eX - 2, and X + 5.

Which graph(s) below could represent the graph of this function?

~I

• I, only

(2) II, only

X

X D

Algebra I (Common Core) -Jan. '15

X

(3) I and III

( 4) I, II, and III

[9]

III y

X

[OVER]

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [ 16]

25 Ms. Fox asked her class "Is the sum of 4.2 and J2 rational or irrational?" Patrick answered that the sum would be irrational.

State whether Patrick is correct or incorrect. Justify your reasoning.


26 The school newspaper surveyed the student body for an article about club membership. The table below shows the number of students in each grade level who belong to one or more clubs.

1 Club 2 Clubs 3 or More Clubs gth 90 33 12 1oth 125 12 15 11th 87 22 18 12th 75 27 23

If there are 180 students in ninth grade, what percentage of the ninth grade students belong to more than one club?

~~·~ 10

oc_\~;

ll?'

\ Cl~ go

zct~~~ .33

3o ,. tl\ 'I) re. Cl-kr ( z .

45" bel·~J ~ M~~ :~t.r.~ I c..l-.1

Lj) ___:-:;---} eo L\ s-oD

X. -~ .... ~ ,oo

-:::: \ 8 0 )<..

'f<5'0 0 ~ ~

~

::: 18

~'A ('1\~e-~~ I c..IJ . 2~

1~)o 'j \.o

Algebra I (Common Core)- Jan. '15 [11] [OVER]

2 7 A function is shown in the table below.

X f(x)

-4 2

-1 -4 {_-If J ;)

0 -2

3 16

If included in the table, which ordered pair, ( -4,1) or (1, -4), would result in a relation thatjs no longer a function? Explain your answer. ~-

-f 1

t- Lf; 0 (2 fl_Al·D "j !2/ e-U<!? \JI..J~

X ) ~.e... ~ be..... or>.e_ a..~ """}

---_J_f\

v J~e_ of f (x). :rJ' .fk oi'Je/dJ J,

0~€.-

po.. ·, r

-f.,_\Je_

(-~) 1) i ~ ~-~ d..J.eJ ~"- ~ ft~ WI) J j ~,_ -i-.._.j D

u a.-l""' ~ .


28 Subtract 5x2 + 2x - 11 from 3x2 + 8x - 7. Express the result as a trinomial.

3Xz_ +-B - 7 t:5 X~ 1"

"')

""" - I \

~--.. __.. -----·

3~1.- -r6:X -7 -5'A'l.- -2'A k\\


29 Solve the equation 4x2 - 12x = 7 algebraically for x.

Q_ ~4

'b ::: - \Z ..

~xz_-12x =-7

4 X -z- - 12 X - 7 ::::::0 - C- = -7


30 Graph the following function on the set of axes below.

f(x) = ( jxj, -3::::; x· < l . 1, ~.::::;X::::; 8

f(x)

... : 1 i I ! I I I ! ¥ I l i I I '· '· I '• X

..


31 A gardener is planting two types of trees:

Type A is three feet tall and grows at a rate of 15 inches per year.

Type B is four feet tall and grows at a rate of 10 inches per year.

Algebraical~y determ .. ine exac.tly,~o':' n;any years it will take for these trees to be the same height. tQf '1\ r~~r~~"~ ft-.,, -:::Jr s. f: I 4:-'s La..-.f-- j r~f'"&-'-C-~ ~ ~,;;, ::::,\....~ \.._ \-..._ c.k.s.

t\QY\c

Y. = Jb ,.:ek~ -+' l~{l-) 4

113 y~,;L +- ID x.

3b +- js-- X -:::: ~ 6 r (D ;x -31> -10 f.. -3b .-,JQ,.X

-------------------s-x = IZ-

x

/r. = 3.£ -1- I 5" { z. 4)

if.- ;. 7 Z l~e~> 'J{53 :;; L\ 8 -r VD {z. ~ '1-B ::: '1. 2-- 1 :.-J--->

~


32 Write an exponential equation for the graph shown below.

y

----~

Algebra I (Common Core) -Jan. '15 [17]

X

\ z_

•

'I z.s • '5' / \

'2.. ./

/ I

[OVER]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which sh<!uld be done in pencil. [16]

33 Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50 for four bags of popcorn and two drinks.

Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.

't:b I J -e-o l,

~;s't 2-r.-'J_&-7

Using these equations, determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.


34 The graph of an inequality is shown below.

y

..J ~\.[j ~ ~{I'"'

'~ 3 < s>k>V'> .. : t:'tl '.,..... / ' ' l \,...::;.

,~X '() ~ -;, z., tf' ~ ~

a) Write the inequality represented by the graph.

Y?..'2X-3

b) On the same set of axes, graph the inequality x + 2y < 4.

;_yz-X t--4 y < - .J.;:., x ~ 2-

c) The two inequalities graphed on the set of axes form a system. Oscar thinks that the point (2,1) is in the solution set for this system of inequalities. Determine and state whether you agree with Oscar. ~xplain your reasoning.

I~

Jt__. f'':' ...... + t!-1 I) I. 5 _!!! -r- 0-

-tl ~· 5 e.c.o .J e.-t ~...1- ., "'- , X + Z-j <:: <..f

(?;f) -2 .y z( ,) L q . 4 ~ ~ is .-o\-- },.-..._£. ---


sJ~-h::, ~ o..C

[OVER]

35 A nutritionist collected information about different brands of beef hot dogs. She made a table showing the number of Calories and the amount of sodium in each hot dog.

y -;:: ~-\-~ Calories per Milligrams of Sodium Beef Hot Dog per Beef Hot Dog

CJ._ ~ ~ I c;--p 186 495

181 477

b :: -s~b. b

(~:::.'B~t£l ( :::: .Cfl.J \'2-'Z-33

176 425

149 322

184 482

190 587

158 370

139 322 -------~

a) Write the correlation coefficient for the line of best fit. Round your answer to the nearest hundredth.

[ \ ~ ;:: ~ ~ ~:1 b) Explain what the correlation coefficient suggests in the context of this problem.

lt_.__ c_ 0 /f J J;"' ~ CP p, ~ -~.Y. . 5 -::'::l J U 6

U ~.Q.J~ \ ~ (L v e.r1 ~+-r =" j ~e.\ a-·~-~ o "'- S. "'-. ; ~ k e.~.«Le...""' -\l ~ f\ ~'k .<!i"

o ~ c...a.-\ o r·,e~ ~e.,...- bee.. Q ~ ~t.J j ~ -\-l e- ~ ~ \\ ; J en..- ~ o 0 So j ·, "'-"'--

' ~ ~ 'r; e...rc...C. ~ o \-~ D :r A f u ~~-t-c..c r r e..\ o-\-~ o "'"' ~ 0 __\g \oe_ c :::.... \ . 0 ,


36 a) Given the functionf(x) = -x2 + 8x + 9, state whether the vertex represents a maximum or minimum point for the function. Explain your answer.

b) Rewrite j(x) in vertex form by completing the square.

-A.'&.+-BX %..

-X. ------)

Algebra I (Common Core) -Jan. '15 [21] [OVER]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be written in pencil. [ 6]

37 New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that one side is doubled in length, while the other side is decreased by three meters.

The new rectangular garden will have an area that is 25% more than the original square garden. Write an equation that could be used to determine the length of a side of the original square

,- \ ~- .-garden. dJ . A..e...'--'. ~

l£__5 '9 . s~z:>) 5 _3 z_

> (2 s)~ -3):::: /,2:) S Explain how your equation models the situation.

2S7--b5 -1."2-0"&.- . .J-t>

"2..-

., 75" s 0 75 5>

5


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