Solutions 1F and 2F. 1) correct 12) 2 8 = 4 13) Q = 22 4Q = 13 Q = 13/4 = 3 1/4. 2) correct R 6 S 9. 13) R 6 S -9 or 2) 1 YX YX.

Transcription

1 F F ) ) ) 7 ) Q Q Q Q / / ) correct ) correct ) ) ) R S or R S ) ()P P P ) 0 ) ( 0 ) 0 ) 7) 7 ) A D C ) [ 0 7] ) 7Q( ) ) A B( A B) ) ) ) 0 () () 0 Z() () Z ) [ 0 07C] 000 ) 0 70C 7 70C C 7/70 7/70 7 D D D D 0 0 ) 0) 7 7) 0 7) ) ( ) ( ) ( )( ) ( ) ( ) () () () () ( )( ) 0D D D D / 7) 0AC(B A) ) 0 ) ) ) (C A) 0 / ) 7 0) ( ) 7 7 ) ) [ F 07 0] F 7 0 0F F /0 /0 0) (7) 0 0 / / ) 0) 7 7/ Solutions F and F

2 F ) 0 ) 7 0 ) 0 ) 0 ) ( 0 )( 0 ) ( )(0 0 ) ()(0 ) ) (7 0 )( 0 ) (7 )(0 () ) (7)(0 0 ) (7 0 )(0 0 ) 7 0 ) A B A B A B A B A B ) ) ) AB A B AB AB AB 0 () () () () F ) ( ) ) 7 ) (0) 00 ) ) ) 7) 7 7( ) ) ) ( 0 ) (7 0 ) ) ( 7)(0 () ) 0 ( 0 7 )( 0 0 ) ( 0 ) ( 0 7 )( 0 0 ) 0 0 ) 7D EF D F DF E ) ( 0 ) 0 ( ) 7) ( 0 ) ( 0 ) ( )(0 ) ) Q Q () Q Q() Q ) 0 7) 0A B ) 7 Z ) ( 0 ) ( 0 ) ( )(0 ) ()(0 ) 0 ) ) ) AB A AB 7) ) ) 0) 0) ) ( 0 )( 0 ) ) ( 0 )( 0 ) 0 0 () () () 0 () 0 0 ) /7 0) 0 / Solutions F and F

3 F F ) ( )( ) ) ( )( ) ) ( )( ) ) ( 7)( ) ) ( )( ) ) ( )( ) 7) ( )( ) ) ) ) A B (A) B(A) A A B A B 7 A(B) (B) (B) A(B) 7 A AB B A B AB AB A B AB A B ) () ) 7 ) / ) ( ) ) [ ( ) / ] / ( ) / ) [ () / ] ) ) ( ) ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) 7 ( )( ) 7 7 ) ( )( ) ) 0 ( ) 0 ( 7)( 7) (7) 0 0 (7) 0 0 ) () 7) ) ) [ (0000) / ] / 0 ) [() / ] or ) ( 7)( 7) 7) (7) (7) 7 0 () 7() () () ) / 0 ( /) 0 ) ) 0 / () () (0) /(0) (/) /(/) 0 / / 0 () () () () ( )() ( )( ) ( )() ( )( ) ( ) ( ) 7 ) 0) 7 (7) () (7) () 7 ( 0 7 )( 0 ) ( 0 )( 0 ) ( ) ( )( ) 0) ( )( ) ) ( )( ) ) ( )( ) ) 0 ( )( ) 0 ) 7 0 ( )( ) 0 () () () () 0 0 () 7() 0 0 () 7() 0 0 ) ) 0) ( ( ) ( )( ) ( ) ( ) ( ) ( ) Solutions F and F

4 7F F ) ) 0i ) i ) 0 i ) i i i i ) [ / /] 0 ( )( ) 0 / ) 0 ( )( ) 0 / / (/) (/) 0 / / / 0 () () 0 0 (/) 0 0 (/) 0 0 ) i ) 0 ) i ) / ) ( )( ) ) ( )( ) 0 / / (/) (/) 0 7/ / / 0 (/) (/) 0 / / / 0 ) 0 ( )( ) 0 / / ) i 7) 0i ) i () ) i i i ()() 0) [(0i)][(i)] (0i)(i) 0i 0 ) ()() or ( )( ) 7 7) ) ( 7)( ) ( ) ( ) ( ) ( ) ( ) 7 ( ) ( 7) 0 ) 7) ( )( ) ) ) i 0i i 0) (i)( 0i) 0i 0 (/) (/) 0 7/ / / 0 (/) (/) 0 / 0/ / 0 7) 0 7 ( )( ) ( 7)( ) ( )( ) ( ) 0 ) ) ( )( 0 ) () ) [() / / ] / ) [ () / ] / 7 / or 7 ) ( 0 7 )( 0 )( 0 ) 7 0 0) 7A A A A A ) i i i ) i i i i ) ( / ) ) () / / 0) ) ( ) Solutions 7F and F

5 F 0F ) 0 00 ) 0 ) ( ) ) ()( 00 (i)(0 ) 0i ) 0i 0 ) (0000) / 00 ) ) () () () () () ()() () ) 7 ) (7 )( 7) ( 7)( 7) ) ( ) ) (/) (/) (/) / / / ) ( / ) / 7) 7 0 (7 ) 0 7(0) (0) /7 7(/7) (/7) 0 /7 /7 0 ) 0 ) ()( )() ) 0i ( i) ( i)( i) 0i 0 0 ) i i 0i 0i i ) ) ) () () 7 7) () () () () ) (0) (0) ) 7 i 0 0) ( /)( /) A ( ) ( ) ( ) ( i) ( i)( i) A A 7 i 7 i i ) 0 0 ) 0) ( ) ( ) ( )( ) ( )( ) ) 7) ) ()()() () () ()( ) () () ()() 0 ) A A 0) ( /) ) () () (7) ()(7) 7 ) (/0) (/0) (/0) /0 /00 /000 7) ) i i(7)i i 0 () () ) [(0 ) / ] / [0 ] / 0 ) ( )( ) ( )( ) 0) A A A 00 ( ) Solutions F and 0F

6 F F ) / / / ) ) ) / ) / ) 0 7) 0 0 ( ) ( ) ± ± ) ( ) 0( ) ( ) 0( ) ) ( )( ) 0 0) () () () () 0 0 ) () () () () ) 0 ) ) 0/ ) (/) (/) (/) / /7 ) ( ) 7) (0i 0 )(i ) (i )(i ) ) ) i(i i) i(7i) 7i 7 0) i 0 (i ) 0 0i 0 0i 0 i 0 0 0i 0 ( )( ) ( )( ) 0 () (/) (/) ) 0 ( )( ) 0 7) ( / /) ) / ) ( )( ) 0 / ) 0 ( )( ) 0 / ) 0 () ± () ()() () ± 0) / ± ) 0 0 ( )( ) 0 / ) 0 () ± () ( )() () 7 7 ± ± (/ ) ) ( / /) ) [ 0] / / / / ( /) 0/ ( / ) 0 / ± / ± 0 0 ) (/ 0 /) (/ 0 /) 0 (/ 0 / 0/) / 0 / / 0 ) () 0 () 0 () () () ) ) () () () ()() 0 7 ) ( /) 7) ) ) ( ) ( )( ) 0) (/ 0 / 0/) / 0 / / 0 (/ 0 / 0/) / 0 / / 0 (/ 0 /) (/ 0 /) 0 (/ 0 / 0/) / 0 / / 0 (/ ) 0(/)( )() 0/ ( i)i (i)i ( 7 ) 7 ( 7 ) 7 A A A i i i i 7 7 A ( A ) ( A )( A ) 7 Solutions F and F

7 F F ) () ()(7) real rational unequal ) ( 7( ) 0 7 ) 0 ) ) () ()()() real irrational unequal () ± ± () ) 0 () ()()() 7 imaginary () ± 7 () ± i 7 ± ) [ 0] ) () () () () ()() ) / / / / ( /) / / ± ) ) () (A) ()(A) (A) A A A ) ( /) ± ( ) ( ) 0 Other value of works as well 0 0 ) 0 0 price on tag $00 ) price on tag $00 ) price on tag $00 ) 0 07 $ ) 0 $ ) final cost $ ta and tip $ WP % ) ( )( ) 0 ) 0 () ()() 0 ) / imaginary () ± () ()() () ± i ) 0 () ± () ()() () ± i 0 ± i ± i 0 ± 0 7) 0 ) ( )( ) 0 / ) () ()() 0 real rational unequal ± ()() () ± i ± i 0) 0 ± () ± () ()() () ± i ± i ± 7) 0 i 0 0) i 7 0 ( )( ) ) ) subtract from both sides / 7) C 0 ) CO C CO O CO ) (0) ()() real rational unequal 0) ( ) 0 ( )( ) 0 % 7% ) 0 () ()() 0 real rational equal 0) ) 0 ± ()() () ± i 0 7) ( ) 0 0 / ) (0) 0 0 ± i (/) (/) 0 / / 0 ± 0 ) () () () () () () ()( )() 0 Solutions F and F

8 F F ) ) ) ) ) V L WH S A L N S L A N A H H B L A D L A D A H ) I(R r) E B C (F ) (N )D D N S N A L A (B B ) (B B ) H C F L A D (N ) C F ) S % CS 7 ) 0 () ()() imaginary ) () ± () ()() ± i ) 0 ± i () ()() real rational unequal ) ( )( ) 0 (/ ) 7) 0 ± ()() ( ) ± ) ) ) ) ) ) G G HO G HO C M C C H M C g H M H C H C C H H C HO M H g G HO H C H We need to know HO and we are given G HO () 0 HO 0 trains 0 HO 0) S(I R) A RL ) SI SR A RL RL SR A SI R(L S) A SI A SI R L S ) S(I R) A RL S(I R) RL A ) % savings so % of the bill is $ % B B $07 for previous bill ) increase is ) ) WP 0 WP 0 0% Na Na PO () % P % Na PO O % Na PO 7) b ac () ()() 7 imaginary 7) of 0 ) of 0 ) 0% 0f 0 0 0% 0 0% 0) 0% of 0 ) C S CS 7 C % CS 7 ) 0 ± ()() ) multiply each term by ) multiply each term by 7 7 / ± 7 7) ) ) C CF C F 7 C CF F 7 CF 7 M C M C g M F M F g F 7 CF ) () ± 7 () i 7 ) multiply all terms by 0 ( ) ( ) ( ) 0) multiply all terms by () () () () 0 7 i 7 ( ) 7 ( ) Solutions F and F

9 7F ) ) ) ) gal qts gal C CS 7 C S qts 7 m 000 mm 70 mm m yd yd yd ) ) ) 7) ) ) 0) ft 7 ft km ft 7 in ft 70 cm cm m 00 cm in cm in 00 oz m 0 gal mi km in ft ft yd cm mi in ft ft yd S CS 7 in ft ft yd m m 07 m 00 cm 00 cm g oz yd m qt gal m 00 cm kg 000 g in yd l qt m kg 7 in 0 l ) ) ) ) given mocha looking for total so M ) ) (R P)(S Q) 0) M C 7 M C M S 7 M S M Other M O M ) (S Q)(R P) ) S Q R P S Q R P g g N NF ()() F 7 0% NF 7 7 7% F ) D R ) D R D m/h / / mi ) D R ) 7) ) ) lbs in yd oz 7 oz lb ) 70 cm m 70 cm 00 cm 0) D mi R m/h R D S D A D in R S S R A A (7)(7 /) (R A )( A ) 7 A mi 7 hr / A :00 PM :0 :0 PM D 7 7 / 7 mi D A D S R A A R S S (0)(0) (7)( S ) 00 7 S S D mi or D 7 00 mi m m 0 mm m yd in R S 7 / hrs mph R A 7 S :0 :00 7:0 hrs or 7 / hrs R A 0 A 0 hrs R S mm m 000 mm 000 mm m m yd in lbs kg ) 7 kg lbs ) ) ) ) 7) B ) ) 0 l M NM NM M 0 qts l M given M and looking for M 7 A ( ) B gal qts boats ( ) A Cl 0 % FeCl 0 gal Fe FeCl 0 % 0) (A) (A) () (A) () () A A A Solutions 7F and F

10 F 0F ) Situps R 0 0 situps ) S R R S ) S R ) ) ) m D H D S R H H R S S R H (0) (R H 0)() 0R H R H 0 R H 0 R H 0 R S R H D J D J D C m S R 00 0 mi R J J R C C (R C )() (R C )() R C R C R C R C ) R J R C R J 7 D R D R D mi R R R R D C ( /)() (R )() 7 R R R mph D ()() D R ( /)() 7 D or 0 cm 0 per day days R S R H 0 S H 0 J C R J R C R R / R R m 00 cm 00 cm 00 cm m m m ) ) 000 mm 7 l ) 00 yds ) 7) ) mm 0 qts 7 qts l m yd mm cm cm cm 0 mm 0 mm 0 mm cm S SP SP S 0 m S given strikes looking for total S M 0 M ) A 0A 0 A 0A 0 0 Marks A 0A (A ) A ± A ± 0) B B 0 ± ()() () ± ± i ± 0 ± i ) negative up over ) b if m b then ) b () () b b b ) ) ) on the graph 7) m 0 () / b () / () b b b ) / ) [ / ] 0) on the graph ) D J D J D E 0 0 R J J R E E 0 ()( E ) (0)( E ) 0 E 0 E 0 7 E E J D E R J D J ()() 0 D E (0)() 0 R E 0 J E #0 ) ) 7) ) ) 0) D U D R U U R D D yd ft yd D U D D ()() ()( D ) D R D (R U ) 7 D () D (7)() or ()() miles 7 mi M S 0 M P 0 M O 0 yd ft yd 0 yds # ft yd yd R U U 7 ft 0 mi yd (7)(0) mi ft (0) M S 7 g (0) M P g (0) M O 70 g Solutions F and 0F

11 F F ) / m / (negative reciprocal) ) / ) [ / ] ) on the graph ) / / ) (0 0) (0 ) 7) / / (0) / (0) / 0 / no ) on the graph solid line ) 0) / / ) [/ /] ) on the graph / b () /() b b / / () > / (0) / 0 yes () m m ) / b () /() b / / b / b D R R R R W R D W R R R R W W (R W )() (R W )() ) 7) ) total time R R W 0 R W ) W 7 7R W R W W 7 W R R 0 0) given line 000 mm mm cm cm 0 mm 0 mm cm M C M H M Cl in cm in # # # mm cm 0 mm cm () M C g () M H 0 g () M Cl 0 g ) on the graph # ) (see graph) ) EC 00 EC 00 EC 0 ) DB DB DB 7) AE AE AE 7 ) DE ) 0) ) ) DE ( ) ( ) ( () ( ) ( ) ( m () 0 ) ) / b () /() b / / b b / / / ) on the graph ) / b () / () b / / b b 7/ / 7/ ) on the graph ) ( ) ( ) ( m / so perpendicular is / / b () / () b / b / / 7) on the graph ) on the graph ) (0) (0) 0 no 0) solid on the graph ) () () yes # # #7 #0 A E B C D given line parallel line given line perpendicular line Solutions F and F

12 F F ) ( 0) ( ) 7 C (0 ) R 7 ) on the graph ) ( ) ( ) C ( ) R () ) on the graph # & ) see graph ) 0 see graph # & ) ( 0) ( 0) ( ) C (0 ) R ) on the graph 7) ( 0) ) If term 0 ± ) If 0 term 0 () ± 0 0) on the graph ) AC 0 AC 0 # & 0 # given 0 ) ) 7) ) ) 0 ( ) ( ) C ( ) R 0) on the graph ) ( ) ( 0) ( ) ) on the graph # #0& 0 B A ) BC ) ) ) BC 7 ( ) ( ) ( / b () () b b ) on the graph 7) / / m / so perpendicular is / / b (0) /() b / b / / ) on the graph [ > ] > / ) (0) > /(0) 0 > no 7 7 0) dotted on the graph ) ( ) ( ) ( ) () > / (0) > yes perpendicular # # & 0 parallel given ) ( 0) ) term 0 ± ) AB ( ) [ ()] AB ) AC [ ] [ ()] 0 7) ) term 0 AC 0 ( ) ( ) ( ) ( ) ( ) ( ) 0) / / (0) /(0) / 0 / no ) / m / so perpendicular is / / b () /() b / b / b / / () / (0) / / yes # #0 Solutions F and F

13 F F ) 0 B A () () ) (/) (/) 7 / ) on the graph ) () ) (/) (/) / # # ) 0 7) see graph (/) ) see graph ) 0 7 see graph # # ) on the graph ) / () () / 7) ) on the graph ) B A B A ( ) A B B A C ( ) 0) Area ( ) B A () A () () Dimensions: ) (on the graph) /( ) # 0) [ ] 0 0 ) [ 0 ] ) [( ) ( ) ] () ( ) ( ) C ( ) R # ) (on the graph) ) ( ) ( 0) 7 ( ) ) [( ) ( ) ] ( ) ( ) C ( ) R # ) ( 0) ( ) C (0 ) R #0 ) ( 0) ( 0) ) 0 ( ) ( ) C ( ) R 7) AB ( 0) (0 ) ) AB 0 ( ) ( 0 ) ( ) ) [ > / /] () < / / 0) on the graph (0) < /(0) / 0 < / no () < /(0) / < / yes #0 ) AD ( ) [ ()] 7 7) ( AD 7 ) C ( ) 0) on the graph with new center ) ( ) ) / m / so perpendicular is / / b () / () b / b / / 0 0 #0 0 Solutions F and F

14 7F F ) line and ellipse ) on the graph ) ( ) ) () ± () (7)(0) (7) ( 7 ) 7 7) parabola line ) on the graph ) 7 ( ) ( ) ) 7 ( ) ( ) ) and / 7 [/ ] 0 0 # # ) [D N 7] D N 00[0D 0N 0] 0D N 0 D 70 D ) N check: (0) (0) 0 0 ) N N N (N ) (N ) N N N N N N N ) 0 check: () (0) () ) N N N (N ) 7(N ) N 0 7N N N ) 0 check: (0) 7() 0 0 # ) line and parabola ) on the graph ) ( ) substitution 0) ) ) 7 ± 7 ( ) 7 7 (from quadratic formula) 0 0 ( ) ( ) 7 ( ) # 7) N N N (N) (N ) (N ) N N N 0 7N N 0 N N ) check: () () () ) 0 ( )( ) 0 7) () () ) hyperbola ellipse ) ellipse C (0 0) ± ± ) ( ) ) 7) ± /7 ± ± 7 ± ( ) ( ) ( ) ) ( ) ( ) hyperbola ± ± 0 ) CD [ ()] [ ()] 0) ( CD ) ( / ) ) G S 7% G F 0% G FF % [G S G F ] (0) 0G S 0G F 0 [7G S 0G F ()] (00) 7G S 0G F 0 G S oz 0) G 0% oz (G S G F ) ) W % W S 0% W F % ) W S W G S 0 [W W S ] () W W S 700 [W 0W S ()] (00) W 0W S 0 W S W okay W S 0 ) ( ) ( ) Solutions 7F and F

15 F 0F ) (F 0) / (J 0) (F 0) J 0 F 0 J 0 F 0 J ) (J 0) (F 0) ) [ (F 0) 0] (F 0) F F 0 F 0 F ) F 0 J () 0 J 0 J ) B / D or B D ) [Q H ] Q H 00[Q 0H 7] Q 0H 7 H ) (Q H ) Q 7 check: (0) 7() ) (N ) (N ) 7(N) N N 7N N 0 N N N H 0 Numbers A Z 7 B Z C Z Numbers 7 A Z B Z C Z A B D Eliminate Z A C E Put in D D () A B D Eliminate A [ Z 7]() Z 7 B [ Z ]() Z D A [ Z 7]() Z 7 C [ Z ] () Z E 0 A [ Z ]() Z B [ Z ]() Z D Z Eliminate ( ) () 0 Put & in A A () () Z 7 Z 7 Eliminate Z Z ) (D ) (B ) 7) (B) (B ) B B B B ) B D () D D ) 7 check: () (7) 7() 7) (N ) 0 (N) (N ) N 0 N 0 N Numbers A C E A [ Z ]() Z C [ Z ] () Z E Z Put Z in D D () 0 0 (D ) (B ) D (B ) D B () Z () Z 7Z 7 Z Put Z & 0 in A A (0) () ) D D R D D R D R D 7 B W 0) D U R U U R U 7 R U B W ) B W 7 B W B 0 B ) 7 B W 7 () W W ) 0 check: () 0 (0) () ) P S 0% P 0% 0 [P S P ] 0P S 0P 0 00[0P S 0P 0()] 0P S 0P 0 P S oz 0) P oz oz 0P S 0 Numbers 70 (D ) (B ) D (B 0) D B D D R D D 70 R D () D U R U U 0 R U () B B B so B and D () D R D B W R U B W B B W W Solutions F and 0F

16 F F Numbers Check () () () () 7 0 Z 7 ()()()()()()(7)()()()()(7)()()()()()() ()()()()()()()()()()()()()()()()()() (70)()()()()() ()()()(0)()() Numbers Check () (0) () (0) 0 0 ( Z) ( ) Numbers 7 A Z B Z C Z Numbers 7 Checḵ (0) () (0) () () () 0 0 () () ()()()()()()()()()()()()()()()()()() ()()()()()()()()()()()()()()()()()() (0)(7)(0)(0)()() ()()()(0)()() Numbers 0 A Z 7 B Z C Z 7 7 (7)()()()()()()()()()()()()()(7)()()() ()()()()()()()()()()()()()()()()()() (0)()()(0)()() 7 ()()()(0)()() 7 7 ()()()(7)()()()()()()()()()()()()()(7) ()()()()()()()()()()()()()()()()()() ()()()()()() ()()()(0)()() Z ()()()()()()()()()()()()()()()()()() ()()()()()()()()()()()()()()()()()() ()(7)()(0)()() ()()()(0)()() 0 0 ( Z) ( 0 ) ()()()()()()()()()()()()()()()()()() ()()()()()()()()()()()()()()()()()() ()(0)()(0)(0)() ()()()(0)()() Solutions F