CST 11 Math - September 16 th, 2016 Test: Linear equations and Linear inequalities NAME: At!$fJJ' ~ Section: MCU504: -- - 86 1100 1. Solve the equations below: (4 marks) 2 5 a) 3("3 x -"3) = - x + 4 /{J1:x - ~(~)==- X+lf dt~ - 5 = -7C +4 + re -t~ -+>< 1- )_ '3 X - 9 3>X ~ ~ - 3 t. \,X ::: 3J b) 3(2y - 5) = 21y 3l2y)-"3{S") ~y_/5 =- 21 Y ::;::.,2/y' b Y. -6 Y I -15 ~ 15 f --/1) ĪS IS-V - Īs -/ Y,., [~== -I ] 2. By finding the x and y intercepts, graph each of the following. (6marks) r-r-.,.-r--:r.rr b) -3x + 7y = 21 I x intercept =- 7 y intercept = ~ '1:1 3 "7 f\l (It z: --=-3 ==- - 7 MCUS04Test: Linear equations and linear inequalities, September 16, 2016 Page 1
3. Write in slope-intercept form then graph each of the following linear equations. (8 marks) Slope = _3_- 1 Slope = ~;z(.--- yintercept = _-_- _2.._ y intercept = 4 'Xcnt -:;, - 1- := _ l>s g Slope intercept form: Y -:::;..5j.- 2. Slope intercept form: y-:; i.tli 4. Write a linear equation in slope-intercept form given the following information (6 marks) a) Slope = 2, Yintercept = 3 Cl=-:< )- 0 z: ax;.+b k~3 y The equation is:hi,--- _-_L_-_X_'_+_3 The equation </-3X+18 is: -Jr'--------- =.!(x- 'f The equation is: L.. Y..s- _ MCUS04Test: Linear equations and linear inequalities, September 16, 2016 Page 2
5. Paul pays a membership flat fee of $240 plus $$41.60 per day at the Larimack for each use of the golf course. (4 marks) If x represents the number of days and y represents Paul's total cost in dollars, a) Write a linear equation (in slope-intercept form) that represents Paul's expenses for the use of Larimack Golf course. ~/al1ra e~ ~ Y==- 11.60)< +210 The equation is:c7 15 ) U=--a~+ b) If Paul spent $1280 this year how many days did he play? (f ~ ::=- 4Uo;t +;14 D Lt 1~ /J:8() -r:k, /d go ~ 4(.' off ;j4~ _ 2A.41:> -:tlt /OqD ::: 4/ 60 ~ (j'.6 D ~1) ~ X rafad at 4(.6 D Y d5' datra's Ff' li"1 Cl ek: Paul had played for cl S- days MCUS04Test: Linear equations and linear inequalities, September 16, 2016 Page 3
y >CllCtb~ a=-~ b=-b 6. a) Graph: Y > - 3x - 6 (5 marks) slope = -0 I y-intercept =... b x-intercept = -:?- choose:(dottevor solid I I! i \r I I 110 L--- I i I! i,llil}l: ~ 1...-1: I I I '\ X 8 -==W I i!!,\ " 7...-v! j I I.Y! I I I v 6 I,',..., I I! I ~!! i I I \"i I I 5_...-Vl i,! J.-- J I 1'1;4...-/ /,..-Yil I I I I ~ ~ 1...-/ I i! tj 1 I I 1-'\1 2 ---"~V! I' / I r-i!! t I 1 _7 j I ','!/ I 1, t ~ I ~ ---. I ~ : choose: (Shade above) or shade below ~f db-; ca'ntj!/1 AlLut,';. ItU,~ -7 ftp 1% ~, [l)rrnjht!)/'t'tj- 0-".! i ' ~ I i i -f;o!! I H b) Graet:"-:y~-0 flfr. (5 marks)' ~!rr: ~ i I i: I I I I I i-i I! j _ -,2- t ~ f.y" ~ _ 2 \/1.. f 1 i l..,...r I I ~ i I 7 I I I I! I ~.-,. /'. I I/o I 12]\ T 6 I i! s ope = -, I Id1 I \ I 5 I J l+-!! y-intercept == 0 e r ~! i/ l I r\ I 4 I!I i -t--tl-+- 1 la"" I i..v-1 ~ 3! 'I I I x-intercept = 0 I!! /f f T~ "H-H' [ I \/~-2v. +0! I yt! i IAT " r, I I, I, / -. r: " L.;9f-S! -7i -6-5'X3 1-2j -11 0\ 11 2 31 4\ 51 61 71 Si 9110ix choose: dotted or @I~d).> I1 L.-1I! j/f-l)"!! 1 I I LJ L..--ri 1.Yf T-2"'~ I i! I' L..! I ::::Ll i.),a _JID choose: shade above or ~adebel~ L',I; I -,[:7 T -4 I \: I. 1 : I I I I! I H--J...-r1! -5V' "' i I I I [J I Y I i vr -6 =x I I I I i...y1 I i y i -7 Y-1 ~!, I! 1 I LI J-'1!! 1...;Jl f! I ~ j I I lij/ I I Y 1-9 i--f V I " i [-I ~ C/ MCU504Test: Linear equations and linear inequalities, September 16, 2016 Page 4
7. For each inequality, identify the slope, the V-intercept and the X-intercept, then graph it. a) y - 4 + 2x ~0 (4 marks) +4 2'f.. -+4 -lr< IT i -2X+4- ] 'ltnf 4.- - - i" rj/~t -4-2- -2- y~ -7 50UcL AA d ajbov'l b) 4x -itx 9y<45-4x (4 marks) MCUS04 Test: Linear equations and linear inequalities, September 16, 2016 Page 5
8. Write the inequality represented by each graph below (8 marks) a. c. 6'.".-0".-.-.-.-."."."."."'''' 1------:-------:------f------~------ ~:::::::::::::::::::::::::::: (.:.:.:.:.:.:.:.:.:.:.:.:.:.:. sbft:: 4=- it ~'nt:= -2- ~ e~wa~ djm-v<- I:::::::::::::::::::::::::::::::::::::::::::::::::::::::,.""",,",,",,",,",,,,",,""''',,'',,'',,'',,'',,'',,'' ~"..",,",,",,",,",,",,",,",,",,". Inequality: _Y_<_4_X_f_2_ I:.:.: :.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:. {:::::"::::::::::::::::::::::::::::::::::::::::: Inequality: _y_<_4_x_-_2_ b. d. Inequality: Y>4/-2 rn - -4.~~-.... Inequality: ~. Y«.2)<-4 "" """ ",,"",,""""",,",,"" I MCU504 Test: Linear equations and linear inequalities, September 16, 2016 Page 6
9. Which of the inequalities is illustrated in the diagram below? (Circle your answer) (4 marks) a) y < -x + 4 b) y > -3x + 1.5 C:<-3~ d) Y < -1.5x + 4. /)- 3 -? c,l-.-, - T f)rq=-3 ",.. ef), TJv... ~M AAAid& )J ; :::::::::::::::::::::::::::::::::::::::::..:::::::::::::::::::::\ YZ::-3X+ 4 ~ 1:/ ~if,'$ c) MCUS04Test: Linear equations and linear inequalities, September 16, 2016 Page 7
11. a) Write an inequality whose solution set is shaded above its solid boundary line. That line -3 has a slope of - and passes through the point (-6, 2). (4 marks) 2 '1>- -.::..- z 3 x+b 6::: Jj - :f)t.) :=: cj-c-:,.. l-{) b ~-7 The inequality is: _ b)-write an inequality whose solution set is shaded below its dotted boundary line. That 1 line is perpendicular toy = - 4. x -10 and passes through the point (2,0). (4 marks) i';5!4::=c a,)(t b 2- ;twl f:.4<> T,.{f\~ (2,0) (] I C'" - - I -)7 Cl - -=--.::. 4 Mn(Jl Q, - -) 2- -I. ~ et I '. y = 41(+ b b ::: y - tl;x ~ = _ Lt (2.)~~ r,~{-(.2,g) ~ 10:::::- 2 The inequaiity is: _y_<:_4_x_' _- 8 MCUS04 Test: Linear equations and linear inequalities, September 16, 2016 Page 8
12. Juanita has at most $17.50 to spend on soft drinks. A can of orange juice costs $1.25 each and a bottle of apple juice costs $2.50 each. x: number of cans of orange juice Y: number of bottles of apple juice f,:() X+ ; 50y -/.2.5"X a. Write and graph the inequality that shows the number of cans of orange juice and bottles of apple juice Juanita can buy. (4 marks) <I J,~O -- 1 yc~) J I 14 { 12 -/~~sx - 'I '/ 10 ". I )X+17,~ --- ~ ~.S7) +7 Jo. ~>,., h, JP v I1 IlL./ ~ 7 z I1 (0 I I Ill' I(". / " '''j I 7~ 1 I j.., ~,I J it if 1/ J.fI',.,." ~,.. 'j j v,,., / / / 'J j ~.d ~ 'l -14-2 -'()I 8 -'fi - / I j /1-4 2 0. / 4 8 0 7"! 12 iiio.. A tt (XI 12 +7J h, 7 Iq.' ""11, \ - 1~ - - I,. 'f 14- -, c I, if ~, ~ b. Give two examples of a possible combination of the number of soft drinks Juanita can buy within her budget. (2 marks) ~ ~LJWL~J ~ ~.Q,e- J 1/11'" G~ ~)... s..t"1 t'~ Jv: oed S-~JWCJ.4 MCUS04Test: Linear equations and linear inequalities, September 16, 2016 Page 9
13. Translate the following sentences into inequalities. Write your answer under the "inequality" column. (10 marks) Sentences Variables Inequality a) Mary earns at least three times as X: Mary's earnings ($) X)3y much money as Nancy Y: Nancy's earnings ($) b) Lebron is at least 30 cm taller than X: Lebron's height (cm) Curry Y: Curry's height (cm) X;? if 30 c) The students must sell a maximum X: number of T-shirts of 500 T-shirts for the fundraiser d) Motor vehicles can drive at a X: speed (km/h) maximum of 40 km/h in school zones X"~500 X~4D e) Sophie can type at least q5 words X: Time (in minutes),/~5~x' per minute..> Y: numbers of typed words MCUS04Test: Linear equations and linear inequalities, September 16, 2016 Page 10