Evans, Lipson, Wallace, Greenwood

Transcription

1 Camrig Snior Mathmatial Mthos AC/VCE Units 1& Chaptr Quaratis: Skillsht C 1 Solv ah o th ollowing or x: a (x )(x + 1) = 0 x(5x 1) = 0 x(1 x) = 0 x = 9x Solv ah o th ollowing or x: a x + x 10 = 0 x 8x + 15 = 0 x 1x + 7 = 0 x + x 99 = 0 x 4x 1 = 0 x x 15 = 0 Solv ah o th ollowing or x: a x + 1x 99 = 0 4x 4x = 0 x + 7x + = 0 6x + x = 0 6x 1x + 5 = 0 x + 5 = 6x g x + 4x = 1 4 Th ara o th shap low is 4 m. Fin th valu o x. x m x m x m m 5 A rtangl has primtr 40 m an th ara is 51 m. Fin th imnsions o th rtangl. 6 A group o popl ook out a untion ntr or $1500. Fiv popl withraw rom th group. Th rmaining popl hav to pay $5 mor ah to ovr th ost. How many popl wr in th original group? Evans, Lipson, Walla, Grnwoo 016 1

2 Camrig Snior Mathmatial Mthos AC/VCE Units 1& Chaptr Quaratis: Skillsht C Answrs 1 a or 1 0 or or 1 0 or 9 a 5 or 5 or 9 or 11 or 9 6 or 5 or a 9 or 11 1 or 1 or 1 1 or 5 g 7 or 1 5 or 1 or , 6 0 popl in th group Evans, Lipson, Walla, Grnwoo 016

3 Camrig Snior Mathmatial Mthos AC/VCE Units 1& Chaptr Quaratis: Skillsht E 1 Expan ah o th ollowing: a (x ) (x + ) ( x + 4) x 4 Fatoris ah o th ollowing: a x 6x + 9 x 10x + 5 x x x 5x x 66x + 11 Solv ah o th ollowing y omplting th squar: a x + 4x 11 = 0 x + 8x 5 = 0 x + 8x + = 0 x 8x + 4 = 0 x 9x + 8 = 0 4 Exprss ah o th ollowing in th orm y = a(x h) + k. Hn stat th oorinats o th vrtx: a y = x + x + 8 y = x + x 8 y = x + 4x 1 y = x x + 10 y = x + x y = x x g y = x + x + 9 Evans, Lipson, Walla, Grnwoo 016 1

4 Camrig Snior Mathmatial Mthos AC/VCE Units 1& Chaptr Quaratis: Skillsht E Answrs 1 a x 6x + 9 x + 6x + 9 x 8x + 16 x x a (x ) (x 5) x (x 11) 5 x a 15 or or or or or a y = (x + 1) + 7; ( 1, 7) y = (x + 1) 9; ( 1, 9) y = (x + ) 16; (, 16) y = (x 1) + 9; (1, 9) y = y = g y = 1 1 x ; ( 1 4, 1 4 ) 1 1 x ; ( 1 4, 1 4 ) 7 x ; ( 4, 7 4 ) Evans, Lipson, Walla, Grnwoo 016

5 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht G 1 Solv ah o th ollowing inqualitis: a ( x )( x ) 0 ( x 5)( x 1) 0 (x )( x 4) 0 ( x 1)( x 1) 0 ( x)( x ) 0 ( x 4)(x 1) 0 g (x )(x ) 0 h (x 1)( 4 x) 0 Solv ah o th ollowing inqualitis: a g h x x 8 0 x 5x 4 0 x 4x 0 x x 9 0 x x x x x x 1 10x 7x 1 Us a Graphis Display Calulator to solv ah o th ollowing inqualitis: a x x 5 0 x x 4 0 x 4x 1 0 x 7x 8 Evans, Lipson, Walla, Grnwoo 016 1

6 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht G Answrs 1 a { x : x } { x : x } { x: 5 x 1} { x: x 4} 1 { x : x 1} { x : x } { x : x } { x : x } 1 { x : x } { x : x 4} g { x: x } h 1 { x : x } { x : x } 4 a { x : x } { x : x 4} { x: 8 x } { x:1 x } { x : x } { x : x } { x: 5 x 1} { x: 4 x } g 4 { x : x } { x : x } h 1 1 { x: x } 5 a { x: 1.19 x 4.19} { x : x.56} { x : x 1.56} { x : x 0.68} { x : x.7} { x : x 0.84} { x : x.17} Evans, Lipson, Walla, Grnwoo 016

7 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht I 1 Dtrmin th isriminant o ah o th ollowing quaratis: a x x x + 6x + 9 x x 4 x 5x x x 1 6x x Without skthing th graphs o th ollowing quaratis, trmin whthr thy ross or touh th x-axis: a y x 5x y x x 1 y x 10x 5 y 4 4x x y = x x + 5 y x x By xamining th isriminant, in th numr o roots o: a x 8x 5 0 7x x 1 0 1x x 7 0 x x 0 x 7x 8 0 x 6x 0 4 By xamining th isriminant, stat th natur an numr o roots or ah o th ollowing: a x 4x 1 0 x x 7 0 x x 4 0 Evans, Lipson, Walla, Grnwoo 016 1

8 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht I x 10x 0 x x 0 8x 16x 8 0 Evans, Lipson, Walla, Grnwoo 016

9 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht I Answrs 1 a a Crosss Nithr Touhs Touhs Nithr Crosss a Two Non Two On Non Two 4 a Non Two Irrational Two Irrational Two Rational Non On Rational Evans, Lipson, Walla, Grnwoo 016

10 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht K 1 A amily o paraolas hav ruls o th orm y = ax. For th paraola in this amily that passs through th point (, 1). Fin th valu o a. A amily o paraolas hav ruls o th orm y = ax +. For th paraola in this amily that passs through th points ( 1,4) an (0, 8), in th valus o a an. A amily o paraolas hav ruls o th orm y = ax + x. For th paraola in this amily that passs through th point (1, 6) an has on o its x-axis intrpts at 4, in th valus o a an. 4 A quarati rul or a partiular paraola is o th orm y a( x ). Th paraola has vrtx ( 1, 4) an passs through th point with oorinats (1, 4). Fin th valus o a, an. 5 A paraola has vrtx with oorinats ( 1, ) an passs through th point with oorinats (, 15). Fin th quation or th paraola. 6 A paraola has x-axis intrpts an an passs through th point (, 4). Fin th quation o th paraola. 7 A paraola has vrtx with oorinats (,) an y-axis intrpt 4. Fin th quation or th paraola. 8 A paraola has vrtx with oorinats (,5) an passs through th point with oorinats (1, 4). Fin th quation or th paraola. 9 A paraola has x-axis intrpts 5 an 1 an passs through th point (, 14). Fin th quation o th paraola. 10 A paraola has vrtx with oorinats (, 4) an y-axis intrpt 1. Fin th quation or th paraola. Evans, Lipson, Walla, Grnwoo 016 1

11 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht K 11 Dtrmin th quation o ah o th ollowing paraolas: a Evans, Lipson, Walla, Grnwoo 016

12 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht K Answrs y x y 4x 8 y x 8x y ( x 1) 4 y ( x 1) 6 y ( x )( x ) ( ) x y 4 y ( x ) 5 9 y ( x 5)( x 1) 10 5 ( ) x 4 y 9 11 a y x 4 1 ( ) x y 1 y ( x )( x 4) y x( x 4) y x y ( x )( x 4) Evans, Lipson, Walla, Grnwoo 016

13 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht L 1 A pi o wir o lngth 14 m is to orm into th shap o a rtangl. Th lngth o th rtangl is x m. a Fin th with o th rtangl in trms o x. Fin th ara o th rtangl, A, in trms o x. Skth th graph o A vrsus x Fin th maximum ara o th rtangl an th valu o x or whih th ara is a maximum. A armr uss 1000 mtrs o ning to onstrut a rtangular shap il. His lan is loat alongsi a rivr, so h only ns to n thr sis o th il. Thr is also a rtangular shap am o ara 5000 m within th il. Lt x th with o th two shortr sis o th il. a I y is th lngth o th il, xprss y in trms o x. Lt A m th ara o th armal lan insi th n. Show that A x x Skth th graph o A x 1000x Us your alulator to in th oorinats o th turning point o th graph. Fin th imnsions o th il whih givs th maximum armal ara, an stat th maximum ara? Eithr y omplting th squar or othrwis, xprss th rul or A in th orm A a( x h) k. Th numr o tals N sol y an outoor urnitur stor uring a partiular yar an approximat y th quation: yar, m [1,1]. N m m 14 71, whr m is th numr o months into th a Skth th graph o th sals or th stor ovr 1 months How many tals i th stor sll in Marh? In whih months i th stor sll 47 tals? What is th minimum numr o tals sol in a month an in whih month i this happn? Evans, Lipson, Walla, Grnwoo 016 1

14 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht L Th stor ns to sll at last 4 tals in a month in orr to mak a proit. For how many months o th yar i th stor mak a proit? 4 A all is thrown rom a alony that is 0 mtrs aov th groun. Th path o th all is sri y th quation: h a( x 5).5, whr h mtrs, is th hight o th all aov groun lvl, whn th all has travll x mtrs horizontally. a Show that a 0.1. Skth th graph o h 0.1( x 5).5. What is th maximum hight rah y th all an how ar has it travll horizontally whn it rahs its maximum hight? What is th hight o th all whn th horizontal istan rom th alony is 10.5 mtrs? Giv your answr orrt to th narst ntimtr. What is th horizontal istan o th sor all rom th alony whn it is 1 mtrs high? How ar os it travl horizontally or it hits th groun? Evans, Lipson, Walla, Grnwoo 016

15 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht L Answrs 1 a With = 7 x Ara x( x 7) Maximum ara is 1.5 m, whn x =.5m a y 1000 x (50, 1000) Fil is 5 m 500 m an th maximum armal ara is m A ( x 50) Evans, Lipson, Walla, Grnwoo 016

16 Camrig Snior Mathmatial Mthos AC/VCE Units 1 & Chaptr Quaratis: Skillsht L a 8 Fruary an Dmr in July 9 months 4 Skth th graph o h 0.1( x 5).5..5 m, 5 m m m 0 m Evans, Lipson, Walla, Grnwoo 016 4