Pre-Calculus 12 Practice Exam 2 MULTIPLE-CHOICE (Calculator permitted )

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Jerome Hancock
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Pre-alculus Practice Eam MULTIPLE-HOIE (alculator permitted ). Solve cos = si, 0 0.9 0.40,.5 c. 0.79 d. 0.79,.8.

1 Pre-alculus Practice Eam MULTIPLE-HOIE (alculator permitted ). Solve cos = si, ,.5 c d. 0.79,.8. Determie the equatio of a circle with cetre ( 0,0) passig through the poit P (,5) + = c. + = + = 9 d. + = 9. Determie the measure of the stadard positio agle θ if the poit P ( 4,) is o the termial arm of agleθ, where 0 θ < c. 7 d Epress as a sigle logarithm: loga logb logc a log bc a log b c c. ac ac log d. log b b 5. Determie the itercept of 5 = c. 0.6 d A ivestmet ears.5% per aum compouded dail. How ma ears would be required for a ivestmet to triple i value? Assume all ears have 65 das c d Determie the umber of differet arragemets of all the letters i the word TRIGONOMETRY. Notice that there are area codes for British olumbia: 50, 604 ad 778. It will be ecessar to add aother area code as the populatio icreases. The ew area code caot be the same as a eistig code, it must begi with a ad ed i a eve umber. Determie the umber of possible area codes to choose from c. 49 d I a stadard deck of 5 cards, determie the umber of 5-card hads that must cotai at least quees c d A dace group has twelve people from which five eed to be chose to compete i a atioal competitio. Bob ad Nac are i the group of twelve ad have recetl obtaied gold at a regioal competitio. The are therefore required to be amog the five selected for the atioal competitio. Give this requiremet, how ma differet fivemember teams are possible? 0 0 c. 5 d. 79. Determie the 5 th term i the epasio of ( ), + where 6 ( ) 4 ( ) 4 4 ( ) 5 ( ) c. ( ) ( ) d. ( ) ( ) 5. A sheet of metal cm cm will be used to make a ope-top bo b removig a square of legth i each corer ad turig up the sides as show i the diagram c d A area code is the first digits i a phoe umber ad idicates the locatio of either the provice or the cit. I aada, the followig area codes eist: What is the volume of the bo as a fuctio of? V = c. V V = 44 4 = ( ) d. = ( ) V. Determie all solutios to the equatio + 4 = -0.6, c. 0.7 d..

2 4. Which equatio represets the graph of f () is horizotall stretched b a factor of? = f ( ) c. = f ( ) = f ( ) d. = f ( ) after it MULTIPLE-HOIE (alculator NOT permitted) 5. Determie the equivalet epressio for 8 cscθ + secθ. hatal simplified the epressio as siθ + cosθ show below. I which step is hatal s first error? c. d c. 4 d. P The graph of = asibis show. Determie the values of aad b.. Determie all o-permissible values for the sec epressio, i the iterval 0 < si + a =, b = a =, b = c. a =, b = d. a =, b = =, c. 7 =, 6 6 d. 7 = 0,,, =,,, The termial arm of agle θ i stadard positio itersects the circle at the poit (, ). Which epressio represets cotθ? c. d. 8. Which epressio represets the measure of all agles i radias that are cotermial with agle θ? + θ, Z c. θ +, Z θ +, Z d. θ +, Z 9. Determie the rage of the fuctio = 5si 8 c d Determie the geeral solutio for si4 = = +, Z 8 = +, Z 8 c. = +, Z 8 d. = +, Z 8. The fuctio h 5 cos t + 6gives assadra s 60 height, hmetres, above the groud whe she is ridig a Ferris wheel after t secods. Determie the legth of time for oe rotatio ad the lowest poit o the Ferris wheel. 60 sec, 6 m c. 0 sec, 6 m 60 sec, m d. 0 sec, m 4. Determie the umber of solutios for si ( csc + ) = 0i the iterval 0 < with the correct reasoig. There are three solutios because si = 0 has two solutios ad csc + = 0has oe solutio i the iterval 0 < There are three solutios because si = 0 has oe solutio ad csc + = 0has two solutios i the iterval 0 < c. There is oe solutio because si = 0 has to be rejected ad csc + = 0has oe solutio i the iterval 0 < d. There is oe solutio because si = 0 has oe solutio ad csc + = 0has to be rejected i the iterval 0 <

5. Two studets, Yuri ad Rubi, solved the epoetial + equatio = as show below.. For which of the followig does f ( ) = f ( )? I, III ol I, IV ol c. II, III ol d. II, IV ol P is o the graph = f ().

3 5. Two studets, Yuri ad Rubi, solved the epoetial + equatio = as show below.. For which of the followig does f ( ) = f ( )? I, III ol I, IV ol c. II, III ol d. II, IV ol P is o the graph = f (). Which poit must be o the graph of = f ( 5)?. The poit (, 8) Which statemet is true? Yuri is icorrect, Rubi is icorrect. Yuri is icorrect, Rubi is correct. c. Yuri is correct, Rubi is icorrect. d. Yuri is correct, Rubi is correct. ( 8, 8) ( 8,8) c. (,8) d. ( 8, 8). The graph of = f () is show below. Which graph represets = f ( 4)? 6. Which is the best estimatio of log 0?..4 c..6 d Solve for : log = log 8 c. d. c. 8. Determie the Richter scale readig for a earthquake that is 5 times more itese tha aother earthquake that measures 4.0 o the Richter scale. 9 0 c. 4 + log5 d. 5 + log4 9. Determie the domai of the fuctio = log ( 4 ) d. < < c. <, > d., 0. Eplai how the graph of 5 = f ( ) is related to the graph of = f () It is the graph of = f () traslated 5 uits up. It is the graph of = f () traslated 5 uits dow. c. It is the graph of = f () traslated 5 uits to the left. d. It is the graph of = f () traslated 5 uits to the right. 4. A cubic polomial fuctio f has zeros {, 0, }. Which restrictio o the domai of f will allow its iverse to be a fuctio? > > 0 c. < 0 d. >

4 5. Raj used sthetic divisio to divide a polomial f () b as show below. 40. Give f ( ) = ad g( ) =, which graph best represets = f ( ) + g( )? c. Determie the value of k that will give a remaider of - as show i the table. 4 c. 5 d ompare the graphs of the two fuctios at = f ( ) = ( ) ( + ) ad g ( ) = ( ) ( + ) The graph of f () crosses the -ais at = ad the graph of g() just touches the -ais at = but does ot cross it. The graph of f () just touches the -ais at = but does ot cross it ad the graph of g () crosses the -ais at =. c. The graph of f () crosses the -ais at = ad the graph of g() crosses the -ais at =. d. The graph of f () just touches the -ais at = but does ot cross it ad the graph of g() just touches the -ais at = but does ot cross it. d. 4. The graphs of f () ad g() are show below. Determie ( g( ) ) f. 7. Give the fuctios f ( ) = + ad g ( ) = 4, determie the value of ( f + g)( ). 0 c. d For which of the followig fuctios is f ( f ( ) ) =, for all values of i the domai of f? I ad II ol I ad III ol c. II ad III ol d. I, II, ad III 9. A polomial fuctio f has zeroes, -, ad. + Give the fuctio g ( ) =, determie the f ( ) domai of the fuctio h ( ) =. g( ) -6 - c. 0 d. 4. Determie the equatios of all asmptotes of the graph of + = =, = c. =, = =, = d. =, = 4. Which of the followig best represets the graph of the ratioal fuctio =? 4 R c. R, R, d. R,,

5 c.. Give si α =, where α is i quadrat I ad 5 cos β =, where β is i quadrat IV, determie the si α β. eact value of ( ) d.. Prove algebraicall: cosθ = secθ + secθ cscθ cotθ siθ 4. The graph of = f () is sketched below. Determie the domai ad rage of = f () ad eplai how it was determied For the fuctio f ( ) =, which of the followig statemets eplai the behaviour of the graph of f for the values of a variable ear a opermissible value? Whe is close to o either side, f is close to. Whe is just to the right of 0, f is a large positive value. Whe is just to the left of 0, f is a large egative value. Whe is close to o either side, f is close to 4. Whe is just to the right of 0, f is a large positive value. Whe is just to the left of 0, f is a large egative value. c. Whe is close to o either side, f is close to. Whe is just to the right of 0, f is a large egative value Whe is just to the left of 0, f is a large positive value. WRITTEN-RESPONSE QUESTIONS (alculator NOT permitted). Determie a equatio for the cubic polomial fuctio graphed below. Leave aswer i factored form. d. Whe is close to o either side, f is close to 4. Whe is just to the right of 0, f is a large egative value Whe is just to the left of 0, f is a large positive value. WRITTEN-RESPONSE QUESTIONS (alculator permitted). A food sample cotais 00 bacteri The doublig time for bacteria left at room temperature is 0 miutes. How ma miutes will it take to reach a usafe level of bacteria? Solve algebraicall usig logarithms. Aswer must be writte as a decimal accurate to at least decimal places.. Eplai the relatioship betwee the epoetial fuctio f ( ) + ad its iverse. Provide a aswer that icludes a algebraic aalsis ad describes graphical characteristics. You will be evaluated o the cocepts epressed, the orgaizatio ad accurac of our work, ad our use of laguage. =

6 Aswers MULTIPLE-HOIE. a. d. d 4. d. d. c 4. c 5. b. d 4. a 5. d 6. a 4. a 5. c 6. a 7. b 5. d 6. c 7. b 8. d 6. c 7. b 8. c 9. d 7. b 8. d 9. a 40. c 8. c 9. a 0. a 4. c 9. b 0. b. d 4. c 0. a. b. c 4. b. a. d. b 44. a WRITTEN-RESPONSE (alculator permitted).. 4. WRITTEN-RESPONSE (No calculators)...

CALCULUS BASIC SUMMER REVIEW

CALCULUS BASIC SUMMER REVIEW NAME rise y y y Slope of a o vertical lie: m ru Poit Slope Equatio: y y m( ) The slope is m ad a poit o your lie is, ). ( y Slope-Itercept Equatio: y m b slope= m y-itercept=