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The Regents High School Examination for Algebra I (Common Core) held in January 2016. The exam includes multiple-choice questions and computational problems covering various topics in algebra, such as functions, equations, inequalities, and graphs.
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The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA I (Common Core)
Thursday, January 28, 2016 - 1:15 to 4:15 p.m., only
Student Name: ______S]""'--~-~-=--c_='---uA=-:::=>..-=-_,.,Q=........,,,~----------
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 3-7 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. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. The formulas that 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 perforated 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 bookl~t. 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 questio~s 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.
Part I
Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial
credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. 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]
I In the function f(x) when xis (1) -
(x - 2) 2 + 4, the minimum value occurs
(4) 4
Use this space for computations. X f.c1-)
::L- - ~ ~"~:>~~. \W~ c___....=_.~:---
2 The graphtelow was created by an employee at a gas station. 50 45 ~ 40 cu 35 0 'Oc 30 =- = 25 -+---t---t- C!J 20 _-I--+------+_ t; 15 -i----+.--- _8_ 10 5 Gas Sales 0 2 4 6 8 10 12 14 16 18 20 Number of Gallons Which statement can be justified by using the graph? _Ji)'_ If 10 gallons of gas was purchased, $35 was paid. - For every gallon of gas purchased, $3.75 was paid. ~For every 2 gallons of gas purchased, $5.00 was paid. '¢"If zero gallons of ga~ were pur~hased, zero miles were driven. ' ' Algebra I (Common Core) - Jan. '16 [2] 6 Michael borrows money from his uncle, who is charging him simple interest using the formula _I_ = _Prt._ To figure out what the interest rate, _r,_ is, Michael rearranges the formula to find _r._ His new formula is _r_ equals (l) _I -P t_ (2) _P-I t_ ## .l_ _Pt_ (4) _Pt I_ Use this space for computations. ### 7 Which equation is equivalent toy - 34 = x(x - 12)? (1) _y_ = _(x_ - 17)(x + 2) (3) _y_ = _(x_ - 6) 2 + 2 ### (2) y = (x - 17)(x - 2) • y = (x - 6) 2 - 2 ## I -3 ~ -= x(~-,z) ## ;,3 ~ = XZ- -\ZX ## y - x.z -\2~~3'-\ _>)_ -ii _-o_ ## P ## -t.· '/... l. _ l 'l )(-\- 3'1 2: ( "?.. ## II :: r , "L ~ -..J 1t' = - 3 '-\ -+-~..J _n x_ -'c....."1.V - ## 8 The equation A = 1300( 1.02)7 is being used to calculate the amount ( 'f.-bJ1- -:: ..+ z. '. of money in a savings account. What does 1.02 represent in this ~ ## equation? [f- ,b) ">. - Z. :: 0 (1) 0.02% decay (2) 0.02% growth (3) 2% decay ## • 2% growth .. ()^ Z.^ =^ Z^ ~o _,._,........- .. ~-·•••• _........, ............... 'i'>'V>~•''"'" -----rr-(~~)--:~~Z~A·~-~~-k 21'. "2- - t...l x - _6 ::..Q_ 9 The zeros of the function _f(x)_ = _2x 2_ - _4x_ - 6 are - 3 and -1 (3) -3 and 1 (2) 3and1 (4) -3 and - ### 10 When (2x - 3) 2 is subtracted from 5x^2 , the result is (1) _x_^2 - 12x - 9 • _x_^2 + 12x - 9 (2) _x_^2 - 12x + 9 (4) _x_^2 + 12x + 9 ## (?. X -=3) &:!- -~ = <f X z._{, A -b;<. + 9 _'1-r._ ~ - _{ 2)< k- 9_ Algebra I (Common Core) - Jan. '16 [4] ~ .,..7- - 'f )( ::: '- ## x'Z-^ -2^ x^ "2. ;;.^^3 \\ -i.- -;... _Z-_ zy.. _*-\)_ ~ 3-(:-\; 0-)) "2. ::: _t.f_ ### ')( .. \ ::: d: 2- x _=_ \ ..::i: 2. /.., _=_ '4Z. _:: J_ ## > x; \-2.. ~ -\ ## ''-----------^ ,. ## 5 ;<. l- Jr 01' +^0 ## l ~)( 2. - \'2-1' -\- q) - ## ---17- + \2X - 1w~a- ~ Use this space for 11 Joe has a rectangular patio that measures 10 feet by 12 feet. He wants computations. to)ncrease the area by 50% and plans to increase each dimension by _I Z_ fJ _(_ /· _5) ::.-_ / _8 O_ equal lengths, _x._ Which equation could be used to determine _x?_ faf (10 + x)(l2 + _x)_ = 120 (3) (15 + x)(l8 + _x)_ = 180 _IJD_ + _t)IJ_ z.+ _x) = 180_ **fl** (10 + x)(l2 + _x)_ = 180 (4) (15)(18) = l=.20::_+~x^2 ____~---~------- 12 When factored completely, _x 3_ - 13x2 - _30x_ is X 3_ rsX _z_ - _501'_ y (x~ -\.3 _/{-Jo)_ (1) _x(x_ + _3)(x_ - 10) • _x(x_ + _2)(x_ - 15) x (_x+2)U-1~) ## (2) x(x - 3)(x - 10) (4) x(x - 2)(x + 15) 13 The table below shows the cost of mailing a postcard in different years. During which time interval did the cost increase at the greatest average rate? **Year** 1898 1971 1985 2006 2012 Cos~·(¢) 1 6 14 24 35 (2) 1971-1985 • 2006-2012 _= 2._ t.f - _I_ c./ - / _lJ_ --- _Z.I_ ~ - I :: _s--_ (;?) rA _Zoo&_ - l _9_ 05"'" ~) IV\.:: 1971-/898 73 wiz.-zt>Ok:. _ __iz_ f 9 )_ _ _ftj-6.,_ - ~ (_4) ~:: 3S-Z~ - /( ## ~ ('('\ - 196>5"-l 97 I - I 'f 14 When solving the equation _x_^2 - _Bx_ - 7 = 0 by completing the square, which equation is a step in the process? X 2._ ~ _X_ - 7 _=-_ 0 (1) _(x_ - 4) 2 = 9 (3) _(x_ - 8) 2 = 9 z _g 'f., =-_ 7 -i... - _(x_ - 4)^2 = 23 (4) _(x_ - 8)^2 = 23 _)\_ - _f_ if)7.. - _"{_ + l:. _'-\)_ ### 15 A construction company uses the function f(p), where p is the number of people ~orking on a project, to model the amount of money it spends to complete a project. A reasonable domain for this function would be X _z.._& "I._ +c - (0-~) "2- _=-_ 2. 3 - positive integers ) (^) _/_ _z."/ 3 _J <-/ 1 C::-_ , • • · \ , (2) positive real numbers ·- " o "- e_e.f;_ _q..,... Pr~ 0 ~~ 'f, ~ ~ (3) both positive and negative integers - '1\:.0 _(\_ e cc..~ +?o,... (\es~. ...,(...,.. l "\ _:,) e_ \ (4) both positive and negative real numbers -V'\.-o^ _I\_^ ~t1^ _'\"'Orn_^ ,,^ ~Q..."'\\_...,L. _J_^ r~^ "~b-L~~ Algebra I (Common Core) -Jan. '16 [5]^ [OVER] 20 The graph of _y_ = _f(x)_ is shown below. ## t2, \) (-\J z) (z..,3) _(};_ 4) y What is the graph of _y_ = _f(x_ + 1) - 2? y (^) y ### x y ### x Algebra I (Common Core) - Jan. ' ### x y #### [7] Use this space for computations. ## (1+0 ---? MO-'~ I i-o le-~ -2- _-7_ MOVL 2. do~..-. ### x #### [OVER] 21 Which pair of equations could _not_ be used to solve the following ### equations for x and y? _4x_ + _2y_ = 22 _-2x_ + _2y_ = - ( 1) _4x_ + _2y_ = 22 / _2x_ - _2y_ = 8 / (3) 12x + _6y_ = 66 _{; 6x-6y=24 v_ (2) _4x_ + _2y_ = 22 ii"' ,/' _-4x_ + _4y_ = - - _8x_ + _4y_ = 44/ _-8x_ + _8y_ = - 22 The graph representing a function is shown below. y ## x Which function has a minimum that is _less_ than the one shown in the graph? uvt~; _(J,_ -Z) u<Vie..,c.::: ~J -11) (1) _y_ = _x_^2 - _6x_ + 7 8) _y_ = _x 2_ - _2x_ - 10 (2) _y_ = Ix+ 31 - 6 (4) _y·=_ Ix - 81 + 2 _E5)_ -6) (BJ 2) Algebra I (Common Core) -Jan. '16 [8] Use this space for computations. 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. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. 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 The function, _t(x),_ is shown in the table below. x t(x) -3 10 -1 7. 1 5 3 2. 5 0 -\ _z,S-_ Algebra I (Common Core) - Jan. '16 [ 26 Marcel claims that the graph below represents a function. y -4 -3 -2 - -1~~+----- 1 - ### I 1- State whether Marcel is correct. Justify your answer. Algebra I (Common Core) -Jan. '16 [11]^ [OVER] 28 The graph below shows the variation in the average temperature of Earth's surface from 1950-2000, according to one source. - ... **::::s cu** ... **Q.** Q) **E** ~ **c 0 +:I cu ·c** ~ Q) **C>** ~ Q) **Variation of Earth's Surface Temperature Over 50 Years** **Year** co CX> 0 During which years did the temperature variation change the most per unit time? Explain how you determined your answer. -rl.__ +"-""f~r<- U _a_;'_ j..,· o ~ .._l.,_..._J ~.!._ f<-.-_ VV\..•.s(\ .Cro- \ lf _60_ ~ \9~ $'", It_._ lr.1.,_ S ~~ _Cr_ $,c~ ,juuJ is Y~ *--'---- .(?.,,. _OJ>./_ o~ ~,__\e_rvJ., Algebra I (Common Core) - Jan. '16 [13]^ [OVER] 29 The cost of belonging to a gym can be modeled by C(m) = 50m + 79.50, where C(m) is the total ### cost for m months of membership. State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership. , ~ t-" _s)o~ Y-1~ ~ _Y=M 1' -r_ ~ Algebra I (Common Core) -Jan. '16 [14] 79.~ W 'h-t--l r~r~e.....b "~ _II $""'03._ _II-,?._ ~o, _w_ ~, J. _fee_._ ## 31 Given that a > b, solve for x in terms of a and b: Algebra I (Common Core) -Jan. '16 [16] 32 Jacob and Jessica are studying the spread of dandelions. Jacob discovers that the growth over ### t weeks can be defined by the functionf(t) = (8) • 2t. Jessica finds that the growth function over ### t weeks is g(t) = 2t + 3. Calculate the number of dandelions that Jacob and Jessica will each have after 5 weeks. ~ _2(s-+3)_ ~ _B ( z)_ ::J _(?)_ - _11_ - _8(32-)_ sc~) _2_ - 2s~ 3 _lrj,_^ ~^ _zc;;;-_ Based on the growth from both functions, explain the relationship _betweenf(t)_ and _g(t)._ _Q_ ~ _0-{_ / _U_ J ~e-s e _P_ £ Algebra I (Common Core) - Jan. '16 [17]^ [OVER] 34 Fred's teacher gave the class the quadratic functionf(x) = _4x 2_ + 16x + 9. a) State two different methods Fred could use to solve the equationf(x) = 0. rf)~o-~r~· c... ~,..- ---\~ {}_o~ \~\-e.... ~ S ~Q..C-0.... b) Using one of the methods stated in part _a,_ solve _f(x)_ = 0 for _x,_ to the _nearest tenth._ (!_O~f(\e__~ ~. S<t.:_v.c f""~ _l/_ X _z__ +- _/6X -1-_ 9 _:=.O_ _--_ - ### x+~ _X=_ _z Algebra I (Common Core) -Jan. '16 [19]^ [OVER] 35 Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee sales. Data from nine days this past fall are shown in the table below. Day 1 Day2 Day3 Day4 Day 5 Day6 Day7 Daya Day High Temperature, t 54 50 62 67 70 58 52 46 48 Coffee Sales, f(t) $2900 (^) $3080 $2500 $2380 $2200 $2700 $3000 $3620 $ State the linear regression function, _f(t),_ that estipiates th,e day's coffee sales with a high temperature _Mt._ Round all values to the _nearest integer._ y::: o.......~ +-b _(i. =_ - ~B b :::: _6 I (f'_ 2. y; -~ex ~t1ez., (i?@Y-5fS~ .+- _6 IB_ z_ \ State the correlation coefficient, _r,_ of the data to the _nearest hundredth._ Does _r_ indicate a strong linear relationship between the variables? Explain your reasoning. - ,. 9 _q tf I .50 q_ z _I_ 8 -. 91 \ S~r.. ~ re_\~o~ l:'() \ '\ \$ c\^ oc;.e-^ \.c^ \^ • Algebra I (Common Core) - Jan. '16 [20]