Precalculus Semester Exam
4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebus . .. 1 /1 0 S em este r E xam S ara O sb orn e i s t a k in g t h is a sse ssm en t.
1 . I n , i s a r ig ht a n gle a n d B C = 7 . I f , f in d A C .
( 1 p oin t) 2 . W hic h o f t h e f o llo w in g a n gle s h as a r e fe re n ce a n gle o f ?
( 1 p oin t) 3 . Y our t o w n’s p ublic l ib ra ry i s b uild in g a n ew w heelc h air r a m p t o i ts e n tr a n ce. B y l a w , t h e m ax im um a n gle o f i n clin e f o r t h e r a m p i s 4 .7 6°. T he r a m p w ill h av e a v ertic al r is e o f 1 .5 f t.
W hat i s t h e s h orte st h oriz o nta l d is ta n ce t h at t h e r a m p c an s p an ? ( 1 p oin t) 1 1 .5 f t.
2 .6 f t.
7 .1 f t.
1 8.0 f t. 4 . F in d t h e e x act v alu e o f c sc θ i f a n d t h e t e rm in al s id e o f θ l ie s i n q uad ra n t I I. ( 1 p oin t) 4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebus . .. 2 /1 0 5 . W hic h o f t h e f o llo w in g h as t h e s a m e v alu e a s ? S ele ct a ll t h at a p ply . ( 2 p oin ts ) 6 . W hic h t r ig onom etr ic f u nctio n i s e q uiv ale n t t o ?
( 1 p oin t) 7 . W hic h t r ig onom etr ic f u nctio n r e q uir e s a d om ain r e str ic tio n o f t o m ak e i t i n verta b le ? ( 1 p oin t) 8 . W hat i s t h e h oriz o nta l s h if t o f t h e f u nctio n ?
( 1 p oin t) π u nits t o t h e r ig ht u nits t o t h e r ig ht u nits t o t h e r ig ht u nits t o t h e r ig ht 4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebus . .. 3 /1 0 9 . W hic h i s t h e e x act v alu e o f ?
( 1 p oin t) 1 0. T he s id es o f a t r ia n gle a re 1 3 f t., 1 5 f t., a n d 1 1 f t. F in d t h e m easu re o f t h e a n gle o pposite t h e l o ngest s id e. R ound y our a n sw er t o t h e n eare st d eg re e. ( 1 p oin t) 4 6° 5 8° 7 7° 1 03° 1 1 . F in d a ll s o lu tio ns o f t h e e q uatio n o ver t h e i n te rv al .
( 1 p oin t) 1 2. W hic h p ola r c o ord in ate s r e p re se n t t h e s a m e p oin t a s t h e r e cta n gula r c o ord in ate ? S ele ct a ll t h at a p ply . ( 2 p oin ts ) 1 3. W hic h p ola r e q uatio n r e p re se n ts a n e llip se ? ( 1 p oin t) 4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebus . .. 4 /1 0 1 4. U se D eM oiv re ’s T heo re m t o f in d .
( 1 p oin t) 2 7 i 9 i 1 5. W hic h o f t h e f o llo w in g p oin ts c o uld b e t h e i n itia l p oin t o f v ecto r v i f i t h as a m ag nitu de o f 1 0 a n d t h e t e rm in al p oin t ? ( 1 p oin t) 1 6. G iv en v ecto rs a n d , d ete rm in e i f t h e v ecto rs a re o rth ogonal. I f t h ey a re n ot o rth ogonal, f in d t h e a n gle b etw een t h e t w o v ecto rs . ( 1 p oin t) T he v ecto rs a re o rth ogonal.
T he v ecto rs a re n ot o rth ogonal. T he a n gle b etw een t h e t w o v ecto rs i s 7 2.5 °.
T he v ecto rs a re n ot o rth ogonal. T he a n gle b etw een t h e t w o v ecto rs i s 1 01.3 °.
T he v ecto rs a re n ot o rth ogonal. T he a n gle b etw een t h e t w o v ecto rs i s 1 30.6 °. 4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebus . .. 5 /1 0 U se t h e g ra ph t o a nsw er t h e q uestio n.
1 7. W hic h s ta te m en t m atc h es t h e v ecto r o pera tio n s h ow n o n t h e c o ord in ate g rid ? ( 1 p oin t) v + w = u f o r v = 5 i + 4 j , , a n d u = 3 i + 7 j v + w = u f o r v = 5 i + 4 j , , a n d u = 7 i + j v + u = w f o r v = 5 i + 4 j , u = 7 i + j , a n d w = 1 2 i + 5 j v + u = w f o r v = 5 i + 4 j , u = 7 i + j , a n d 1 8. T w o f o rc es a ct o n a n o bje ct. T he f ir s t f o rc e h as a m ag nitu de o f 3 60 n ew to ns a n d a cts a t a n a n gle o f 3 0° a s m easu re d f ro m t h e h oriz o nta l. T he s e co nd f o rc e h as a m ag nitu de o f 2 40 n ew to ns a n d a cts a t a n a n gle o f 1 35° a s m easu re d f ro m t h e h oriz o nta l. D ete rm in e t h e v ecto r v t h at r e p re se n ts t h e r e su lta n t f o rc e. ( 1 p oin t) 1 9. F or , f in d u nit v ecto r u i n t h e d ir e ctio n o f v .
( 1 p oin t) 4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebus . .. 6 /1 0 2 0. W hic h o f t h e f o llo w in g i s a p oin t o n t h e p la n e c u rv e d efin ed b y t h e p ara m etr ic e q uatio ns? x = 3 t ( 1 p oin t) 2 1. W rite t h e f o llo w in g p ara m etr ic e q uatio ns a s a p ola r e q uatio n. x = 4 t ( 1 p oin t) r = 4 c o t θ c sc θ r = 4 t a n θ s e c θ r = 1 6 c o t θ c sc θ r = 1 6 t a n θ s e c θ 2 2. A b ase b all p la y er h its a b all a t a n a n gle o f 5 6° a n d a t a h eig ht o f 4 .2 f t. I f t h e b all’s i n itia l v elo city a fte r b ein g h it i s 1 54 f t./ s a n d i f n o o ne c atc h es t h e b all, w hen w ill i t h it t h e g ro und?
R em em ber t h at t h e a ccele ra tio n d ue t o g ra v ity i s 3 2 . ( 1 p oin t) 8 .0 1 s e co nds 7 .9 8 s e co nds 5 .4 3 s e co nds 5 .3 8 s e co nds 2 3. W hic h s e t o f p ara m etr ic e q uatio ns r e p re se n ts t h e f u nctio n ?
( 1 p oin t) x = 2 t 4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebus . .. 7 /1 0 x = t + 5 x = t + 3 2 4. W hic h i s a p ola r f o rm o f t h e f o llo w in g p ara m etr ic e q uatio ns? y = 7 c o s θ s in θ ( 1 p oin t) r = 7 c o s θ 2 5. F in d .
( 1 p oin t) 1 8 0 5 2 6. W hat i s t h e e q uatio n o f t h e l in e t a n gen t t o t h e f u nctio n a t t h e p oin t ?
( 1 p oin t) y = 8 x + 5 2 7. D ete rm in e i f t h ere a re z ero , o ne, o r t w o t r ia n gle s f o r t h e f o llo w in g: a = 1 0 m b = 1 2 m ( 4 p oin ts ) 4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebus . .. 8 /1 0 2 8. W hat t y pe o f l im aço n i s g ra p hed b y t h e p ola r e q uatio n ? I d en tif y t h e a x is o f s y m metr y a n d h oriz o nta l a n d v ertic al i n te rc ep ts . ( 4 p oin ts ) 2 9. N ote : R em em ber t o s h ow a ll o f t h e s te p s t h at y o u u se t o s o lv e t h e p ro ble m . B e s u re t o u se t h e t e xt b ox w here t h e q uestio n m ark ( ? ) f ir st a ppea rs t o s h ow y o ur m ath em atic a l w ork . Y o u c a n u se t h e c o m men ts f ie ld t o e xp la in y o ur w ork . Y o ur t e a ch er w ill r e vie w e a ch s te p o f y o ur r e sp onse t o e n su re y o u r e ceiv e p ro per c re d it f o r y o ur a nsw er. W rite t h e c o m pose d t r ig onom etr ic f u nctio n i n t e rm s o f x . E xpla in y our s te p s a n d/o r s h ow y our w ork . R em em ber t o r a tio naliz e t h e d en om in ato r i f n ecessa ry . ( 4 p oin ts ) 4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebus . .. 9 /1 0 3 0. S ele ct a tta ch m en t o r d ra g a nd d ro p a file in to th is a re a 2 0 M B lim it 4 /2 5/2 017 S em este r E xam h ttp s://w ww.c onnexus.c om /c onte nt/r e nder.a spx?dis able A ssessm ent= tr u e& prin tp re vie w =tr u e& prin tp opup= tr u e& id S ectio n= 764036& id C ours e= 45360& id W ebu . .. 1 0/1 0 N ote : R em em ber t o s h ow a ll o f t h e s te p s t h at y o u u se t o s o lv e t h e p ro ble m . B e s u re t o u se t h e t e xt b ox w here t h e q uestio n m ark ( ? ) f ir st a ppea rs t o s h ow y o ur m ath em atic a l w ork . Y o u c a n u se t h e c o m men ts f ie ld t o e xp la in y o ur w ork . Y o ur t e a ch er w ill r e vie w e a ch s te p o f y o ur r e sp onse t o e n su re y o u r e ceiv e p ro per c re d it f o r y o ur a nsw er. V erif y t h e i d en tity : ( 3 p oin ts ) S ele ct a tta ch m en t o r d ra g a nd d ro p a file in to th is a re a 2 0 M B lim it