SAMPLE. Answers. 1ax < 1 b x > 13 c x 3 d x 12 e x 6 f x > 3 g x > 2. h x 8 i x a x < 2

Transcription

1 Chaptr Eris A a 9 8 g h 7 i 7 j k l aa + a a a a a7 7 g 8 h i j k 7 l a a 8 g h 8 i j k 7 a a a a a a + g h + a a a 7a Eris a + =, =, + =, =, + ) =, 9 + =, 87 A = $8, = $, C = $ an 8 8kg.77 m 9,, 7 7, 9,, 8 L 9 km 9 an ozn 7. km/h. km, Eris C a =, = =, = =, = a = 8, = =, = = 7, = a =, = =., = m =, n = =, = s =, t = =, = g =, = 7 i =, = Eris D h p =, q =,.,. a$7 $ $ a$8 $ $ 7 an 8 an 7 pizzas, hamurgrs 8 Start with an ; inish with ah 9 $7 shirts an tis Outaks an ush Walkrs Mn = 8; Slourn = kg at $, kg at $ an kg at $. Eris E a < > > g > 7 h 8 i a < < < Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

2 7 g h i < > < > a > < > <, <,pags 87 Eris F a g h a S = a + + P = C = p T = p + q T = a + a. 7 av = p a = F m P = I r = w H rt C t = S lp V ) r = Pr V at = 8 = 8 h =.8 = aa + w) m h + ) m wh m ah + 8a + w)m 7aiT = p + q) + h ii 88 + p = A h q 8 a D = = n = r = a D = k ) k = D k = = a P = A = = A + a = a a = a r = q p v = u ) Multipl-hoi qustions D D C A C C A Short-answr qustions thnolog-r) a g 8 at = a a a a a < 8 < = z + t), 7 h a + a a = + = = = a + + a = a + 7 = a a + a Etn-rspons qustions a = 9 F = 8 = =. = k = a r = uv u + v m = v u at = w + l i T = 8w ii l =, w = i = L 8 =, = ii = aistan that Tom travll = ut km an istan Juli travll = vt km i t = h ii istan rom A = u u + v u + v km t =. h, istan rom town A = 7. km aavrag sp = uv u + v i ut vt + ut ii v v a a + i = a ii a + 7a 8, 8 + ) + 8 = 9, = 9 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

3 7 Essntial Mathmatial Mthos &CAS Chaptr Eris A a g h i j k An lin paralll to th on shown, ) a 8 g 7 h i j k l a a 7a = = Eris a a a g 8 8 Pairs whih ar paralll: a, an ; Non-paralll: h = = onl a Eris C a = + = + = a = = + 9 a = + a = + a = + = + 8 a = + = = = = = 7 Som possil answrs: a = = = = + = = Chk with our tahr or othr answrs. 8 a = + 9 = = = 9 a = + = + Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

4 77 = = = + = a = + = = + = + 8 a = + = = + = + = +. = +. Ys A: = + C: = + 9 AC: = 8 Eris D a, ),, ), ), ), ),, ), 8) 8, ) a = + = = = + a a a + = 7 + = + = + = a = 9, m = = +, m = =, m = =, m = 7a 8 a =, =, =, = Eris E 9 a = t = t + av = t V = + t w = n +, possil valus or n = N {} av =.t omain: t, rang: v v t C =.n +. ac =. + 8 $ 7 = t 8a w g) m) w =. + =. m 9aC =.n $9 a C = n + 7 Ys $7 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

5 78 Essntial Mathmatial Mthos &CAS Eris F a C a A t t ac = +. C = t = A. pm C 8 Fi harg mtho is hapr whn > 7. a A C t hours) C wins th ra C, laving hours atr, ovrtaks hours atr ha start an thn ovrtaks A hours atr A ha start. C wins th ra with a total haniap tim o hours hours or journ + hours haniap) with A an ahating or n, ah with a total haniap tim o hours. oth rat will pass ovr th point, ) ac T =.8, C = + > stunts $C 7 a A = t, M = 7 t 7 km) 7 9 t min). am Maurn km, Ann 7 km 8 a =.8 an =., m/s Eris G a.7 a. to.p.).7 to.p.) a 9 a7 m C =, m A = m C m A = = AC is a right-angl triangl m S =, m ST = S ST m UT =, m ST = UT ST Also n to show S = UT.) STU is a rtangl. 7 = + 8a = + = 8 9 l =, m = 8 Eris H a DN Eris I a, 8), ).,.7).7,.8) ) ) M A, ). M C 8,. MAC, Coorinats o C ar, 8.8) apm =. No, it passs through, a, ),.), ), ) + a, + ) ; a = 9, = Eris J a 9 9 Multipl-hoi qustions ) A E C D E 7 D 8 C 9 E E Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

6 79 Short-answr qustions thnolog-r) a 9 unin a a a = = + = + = aa = + = 7 + = a =, =, = 7a = = + = 8amipoint =, ), lngth = mipoint =, 9 ), lngth = 7 mipoint =, ), lngth = 9 = + = 7 Etn-rspons qustions a S 8 79 l Sin th graph is a lin o st it answrs ma var aoring to th mtho us;.g. i th two n points ar us thn th rul is S = 7 9 l. or l = 9 7 S + 8 ) 7 I a last squars mtho is us th rul is l = 8.S +.7. C 7 l Again this is a lin o st it. I th two n points ar us thn C = 8 l C or l = ) 8 A last squars mtho givs l =.C +.. ac = + 8n as Lss than as acost o th plug Cost pr mtr o th al.8 9 m ath maimum proit whn = ) sats Th proit rus $ or vr sat mpt. a ic =.9n ii C =. +.8n iii C =. +.n C $),.8),.),.) n kwh) i ForkWh, C =.7 ii For9kWh, C =.87 iii For kwh, C = kwh a = 7 + km south 7as = 7 s %). %) 7 % 7 % 7 Proal not a ralisti mol at this valu o s 7 8aA, = + ; CD, = Intrstion is at 8, ), i.. on th nar ank. 9 a 8 = No, sin graint o A is 9.), whras th graint o VC is.7 a No km to th ast o H 7 a = 8, 8) = + 78, ) a L = n + 7 L 8 n a C = + $ = 8 $ = 8 C = + 7 g P = Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

7 7 Essntial Mathmatial Mthos &CAS a Mtho : Cost = $.7; Mtho : Cost = $7; Mtho hapr Mtho Mtho 8 Cost th sam or appro. units ost $).7 units C =.8 + ) C =.7 + ) = a 7, ) = + a PD: = + ; DC: = + ; C: = + A: = + ; AP: = + At an C sin prout o graints is.g. m DC =, m C = ; = 7 a = +, ) = 8, ) Ara = squar units Ara = squar units Chaptr Eris A a a Onl th sats or top-lt to ottom-right iagonal ar oupi. [ 8 ] a = i = 7 7 = i = = = i =, = a =, = =, = =, = =, = Eris X + Y =, X =, Y + X =, X Y =, A =, A + = a A =, A =, A = a Ys Ys 9 a 8 7 a X =, Y = [ ] X + Y =, rprsnting th total proution at two atoris in two sussiv wks. Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

8 7 Eris C AX =, X =, AY =, 8 IX =, AC =, CA =, AC)X =, 9 CX) =, AI =, I =, A =, 8 A =, A =, 8 =, ACA) =, A C = 7 a AY, CI ar in, YA, XY, X, XI ar not in. A = No LX = [7], XL = A an A ar not in unlss m = n. 7 On possil answr[ is ] A =, =.. 8 On possil answr is A =, =,C =, A + C) =, A + AC =, 7 + C)A = 9 9 rprsnts John spning 9 minuts 8. onsuming [ oo whih ] ost him $8.. 9 John s rins spnt $8. an $. an took an minuts rsptivl to onsum thir oo rprsnts how muh ah stunt. spns in a wk on magazins.. s a SC = + s + s s + s + s SC rprsnts th inom rom ar sals or ah showroom. [ SC = s +s +s s u +s u +s u s +s +s s u +s u +s u ] rprsnts th inom or ah showroom or nw ar sals an us ar sals. CV givs th proit on ah nw ar an ah us ar or th thr mols. Eris D a a 7 7 os sin sin os k A =, =, A =, A) =, [ ] A =, A =, A) = A 7 a a Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

9 7 Essntial Mathmatial Mthos &CAS a a 8, ;, ; k k k k,, k a a, a Eris E a 7 a 7 7 a = 7, = =, =. 7 = 7, = 7 =., =.9,[ ) ][ ooks ] $, CDs $8 a = is a singular matri, not a rgular matri. Thr is no uniqu solution or this sstm, ut a solution an oun. Th solution st ontains an ininit numr o pairs. Multipl-hoi qustions E C E C A 7 E 8 A 9 E D Short-answr qustions thnolog-r) a 9 a [ ] a a, a a A os not ist, AC, CD, E ist. DA = [ ], A = 7 A =, C = 7 A =, A = a i 8 iii 7 =, = 8 ii 8 9 Etn-rspons qustions a i ii 7 iii iv 7 7 i ii 8 9 iii iv a A CC a i [ ][ g C ] = Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

10 7 ii, iii iv 7, ) is th point o intrstion 7 o th two lins i = ][ 8 ii ; A is a singular matri lins rprsnt th quations ar paralll Chaptr Eris A a a + + a a 9 + a ) + + a a g + + h + i + z j a a + 8ai + + ii + ) i ) + ) + ii Eris a + ) a ) ) ) + ) 8 ) a ) 8a + ) a ) + 7) + ) ) g + ) h 7 + 7) i ) j ) k 7 ) l + ) a + ) + ) ) + ) ) + ) a + ) + ) a + )a ) a) + a) ) a ) + ) 9) + 9) 7) + 7) a ) ) ) + ) 7 + ) ) g ) + ) h + ) a 9) + ) ) ) ) ) + ) + ) a )a ) a + 9) g + ) + ) h + ) ) i 7) ) j ) ) k + ) + ) l a + ) + ) m ) ) n ) o + ) Eris C aor or or or or or g or h or a. or..8 or.8.8 or.8 a,,,, 7,, g, 8 h, i, j, k, l, m, n o, p, q, r, an 9, m,m $9, $ Eris D a i, ) ii = iii, ),, ) i, ) ii = iii non, ), ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

11 7 Essntial Mathmatial Mthos &CAS i, ) ii = iii, ),, ), ) i, ) ii = ) ) iii,,, i, ) ii = iii, ) i, ) ii = iii, ) g i, ) ii = iii, ) h i, ) ii = iii, ) i i, ) ii = iii, ), ) j i, ) ii = iii non, ) 9 8, ), ) k i, ) ii = iii, ), ) l i, ) ii = iii, ), ) m i, ) ii = iii, ),, ) n i, 8) ii = iii, ),, ) o i, ) ii = iii, ),, ) p i, ) ii = iii non, ), ) 8, ), 8), ), ) q i, ) ii = iii, ),, ), ) 9 r i, 8) ii = iii, ) +, ), 8) + 8 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

12 7 Eris E a g + h + 9 a ) ) ) ) ) ) g ) h + ) a ± ± ± 7 ± 7 ±, g ± k h ± k k i k ± 9k a = ) + = + ) t. pt, ) t. pt, ), ) = ) t. pt, ), = ) 9 t. pt, 9 ), 9 g = ) + t. pt, ), ), ) = ) t. pt, ), ) = + ) t. pt, ), ) h = + ) + t. pt, ), ) i = ) + 9 t. pt, 9), 9) Eris F a7 7 a 8 a g a, 8, 8 h, 9),, ), ),, ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

13 7 Essntial Mathmatial Mthos &CAS g ), 8, Eris G ) h, ) ) 8, ai ii i 8 ii 7 i7 ii i 9 ii i89 ii a a ± 7 ±, ± ± ± g ± h, i ± j ± k ± k k l k ± k k k) r =. m a.9.9., 7.).,.)....,.) ,.).., ), Eris H a Eris I a acrosss th -ais Dos not ross Just touhs th -ais Crosss th -ais Dos not ross Dos not ross aral roots No ral roots ral roots ral roots ral roots No ral roots a =, on rational root =, two rational roots = 7, two irrational roots =, on rational root = 7, two irrational roots =, two rational roots Th isriminant = m + ) or all m, thror rational solutions). Eris J a{ : } { : } { : < < { 8} { : } { : > } : < } { : < < } { : } { g : > } { : < } { h : } i { : } { j p : ) p + } ) k { : < } { : > } l { : } { : } ai < m < ii m =± iii m > orm < i < m < ii m = iii m > or m < i < m < ii m = orm = iii m < or m > i < m < ii m = or iii m > orm < p > p = < p < 8 Eris K a, ),, 7), ),, 9), ),, ), ),, ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

14 77 +, ),, + ) +, + ),, ) atouh at, ) Touh at, 9) Touh at, ) Touh at, 8) a = 8, = an =, = 7 =, = 7 an =, = =, = an =, = 8 =, = an = l, = 9 =, = an =, = 7 =., =.9 an =.8, =.9 a i.. ii m = ± = ± a = > a = ora = 7 = 8 = + ) an = ) + Eris L a =, = 8 a = 7, = 7 a =, =, = a = + = = + 7 = + = + = + = + ) + 7 = 8) 8 = + ) + 9 = a C D A = = = + 8 a = a ), a > = a + ) ), a < = 8 ) + = a 8), a < a = + + = + r = 8 t + t 8 7 a D Eris M a A = A Maimum ara = m a E. an.. an.77 a A = A m a C$) h Th omain pns on th hight o th alpin ara. For ampl in Vitoria th highst mountain is appro. km high an th minimum alpin hight woul appro. km, thus or Vitoria, Domain = [, ]. Thortiall no, ut o ours thr is a pratial maimum $ Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

15 78 Essntial Mathmatial Mthos &CAS a T ) t Œ.8,.8) t 887 units a... i. m ii 7mor+ 7mrom th at iii maov th groun. 7a = + = = + 8 a =, = 8, = 9 a a = 7, =, = S hunrs o thousans ollars.7 t as) is = $ ii S = $9 9 Multipl-hoi qustions A C C E C 7 E 8 E 9 D A Short-answr qustions thnolog-r) a + 9 ) + 9) ) + ) ) + ) a + a + a 9a g a h i a a j k u + v uv l + a ) + 8) 8a ) ) + ) au + v + w) a a) + a) g a) + a) h + ) ) i + ) ) j ) + ) k + ) + ) l + ) ) m ) + ) n a )a + ) o ) ) a, ),,, ), ) 9, +,, ) g a, ), ), 9), ) +, ) h, ), ), ), 9), 9) 7, ), 9) + 7, ), 9) +, ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

16 79 aii = 7, ) ii = 7, 8, 7 ii =,, ) 8 gii =, ) ii = 9,, ) ii =, ) 8, 9) ii =, hii =, ) 7a.,.., 7.7.,.8.,.8.79,.78.7,.7 8 = ) 9 = ) + = ) + a, 9),, ).8,.),.8,.)., ),., ), ),, 8) a m =± 8 =± m orm a = > Etn-rspons qustions a =.7 ).7 m an 9. m ) m an + m.8 m.7 m orrt to imal plas) a With o rtangl = m, lngth o rtangl = m A = Lngth or squar = 9 m an lngth or 7 rtangl = 8 m.. m) 7 a V =.7. hours a V = 8 + V =. + l =.8 m a l = A = A, ) Maimum ara = m whn = m = + 7 a + i ii a i = t + t.) = t t + ii km) t h) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

17 7 Essntial Mathmatial Mthos &CAS iii t = ;. pm t = 9 ;.7 pm 8 iv.;.8 pm; istan. km i, ii ± = 8 + a = i = ±, = ii = = a = ± 7)a, = 7)a a =, =, h = i, + ) ii, ) iii, ), ), ), ), ) iv = i = + ii, ).,.) iii min valu o =. ours whn =. a i = ) 9 ii, ) 8 A, ), ) D, ) = O C, ) ith istan masur paralll to th -ais) twn path an pon. ii minimum valu = 7 whn = Chaptr Eris A a, ), ) g i k, h j l a =, = =, = =, = =, = =, = =, = g =, = h =, = i =, = j =, = k =, = l =, = Eris a 9, ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

18 7 g, ) an i g h a =, = =, = =, = =, = =, = =, = g =, = h =, = Eris C a an, ) an, ) 7 an, ) an, ) + an g, ) an, ) an Eris D h, ) an a + = 9 + = ) + ) = ) + + ) = 9 + ) + ) = + ) + + ) =.) ac, ), r = C, ), r = C, ), r = C, ), r = C, ), r = C, ), r = g C, ), r = h C, ), r = 9 a h Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

19 7 Essntial Mathmatial Mthos &CAS i k 8 ) + + ) = 9 ) + ) = ) + ) = 7 Cntr, ), raius = 8 -ais), -ais) 9a j l Multipl-hoi qustions, ) E E A A D 7 D 8 C 9 E Short-answr qustions thnolog-r) a, ), ) g i k, ), ), ) = =, ) = + h j =, ) =, ), ) = =, ), ), ) a ) + + ) = ) + + ) = ) + + ) = ) + ) = ) + ) = 8 ) + + ) = + = + = or = a ) + ) + ) + = =, ) ) + ) =, ), ) ) + + ) =, Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

20 7 a, ), ) Etn-rspons qustions a ) + = m =± P, ± ) a + = ii m =± ; = 8, = + 8 a + = ai ii + = 8or + = 8 a = + a, = a + = a ii, ) = i < k < ii k = ork < iii k > 7 a < k < k = or k Chaptr Eris A a{7, } {7, } {,,,, 7,,,,, } {,,,, } {} {, 7, } a, ] [, ] [, ), ) a a [, ], ], ) ],, ), ] g, ) h [, ) i, ] a {, 7} {7}, i.. {7,,,, }, ) a 7 7 Eris a Domain = [, ], ang = [, ] Domain = [, ], ang = [, ] Domain =, ang = [, ) Domain =, ang =, ] a, ) ang = [, ), 7) ang = [ 7, ), ) ang =, ], ) ang =, ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

21 7 Essntial Mathmatial Mthos &CAS, ) ang =, ] g, ), ) ang = [, ] a ang = [, ), ) ang = [, ] ang =, ], ) [ ) 9 g ang = 8, a 9, 8 Domain ang, ), 9) ang = [ 9, ] h, 9), ) ang =, 9) ang = [, ), ), ) ang = [, ), ) ang = [, ], ), ), ) [ ) h ang =,, ), Domain ang 7, Domain ang Domain ang Eris C a a untion Domain = [, ] ang = [, ] 8 a untion Domain = [, ) ang =, ] a untion Domain = \{} ang = + Domain ang 7 Domain 7 ang not a untion Domain = [, ] ang = [, ] 9 a untion Domain = { : } ang = { : } g, ) a untion Domain = [, ] ang = [, ], ) h a untion Domain = + ang = + not a untion Domain = [, ) ang = Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

22 7 a Not a untion, Domain = {,,, }; ang = {,,, } A untion, Domain = {,,,, }; ang = {,,,, } Not a untion, Domain = {,,, }; ang = {,,, } A untion, Domain = {,,,, }; ang = {} A untion, Domain = ; ang = { } Not a untion, Domain = {}; ang = Z g A untion, Domain = ; ang = h A untion, Domain = ; ang = [, ) i Not a untion, Domain = [, ]; ang = [, ] a i ii iii iv 9 i ii iii iv i ii iii iv a ) a i ii + a iii a iv a a a ±,,, a g ) =, g) = 8, g ) = h ) =, h) = 8, h ) = i g ) = 9 ii g ) = 8 + iii h ) = + iv g + ) = v h ) = + a ) = ; ) = 9 ang = [, ) 7 a ) = 7 = = 8 a ± l =± 9 a = > = 7 a :, ) = + :, ) = + :[, ), ) = + :[, ], ) = + :[, ], ) = + :[, ], ) = 7 a, ), ) ang = [, ], [ ) ang =, Eris D, ), 8) ang = [, 8], ) ang = [, ) On-to-on untions ar,, an g Funtions ar a,,, an g. On-to-on untions ar an g. a Domain =, ang = Domain = + {}. ang = + {} Domain =, ang = [, ) Domain = [, ], ang = [, ] Domain = +, ang = + Domain =, ang =, ] g Domain = [, ), ang = + {} [ ) h Domain =,, ang = [, ) i Domain =, ], ang = [, ) j Domain = \ { }, ang = \ {} k Domain = \ { }, ang =, ) l Domain = \ { }, ang = \ {} a Domain =, ang = Domain =, ang = [, ) Domain = [, ], ang = [, ] Domain = \ { }, ang = \ {} =, Domain =, ], ang = + {} =, Domain =, ], ang =, ] a :[, ), ) =, :, ], ) = Eris E a ang = [, ) ang =, ], ) ang = [, ) ang = [, ) ang = [, ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

23 7 Essntial Mathmatial Mthos &CAS a a ang =, ], ) ang = [, ) a, ) a 9 ang = ang =, ] +, 7 ) = +, <, Eris F a a =, = ) = 7 a i ) = 9 ii ) = a p) = p + p + h) = p + h + h i. ii. iii. iv 7 ) = 7 ) ) 8 ) = ) + 7, ang = [7, ) 9 a, ] [ 78 ) 8, ], ] a, 8), ) ang = [, 8] a, 9), ) ang = [, ] 8, ) a Domain Domain ang ang Domain Domain 9 ang ang Domain ang a {,,, 8} {,,, } {,,, } {,,, } ) = ) ); a =, = 9, = ) = ) + ) g) = ) + ) a k < 7 Eris G k = a {, l), ), ), 7)}; omain = {,,, }; rang = {,,, 7}. ) = ; omain =, rang = ) = omain = [, ], rang = [, ] ) = omain = [, ), rang = + ) = omain =, 8], rang =, ] ) = ; omain = + {}, rang = + {} g ) = + ; omain = [, ), rang = [, ) h ) = ; omain = [, ), rang =, ] i ) = ; omain = [, ], rang = [, ] j ) = ; omain = [, ], rang = [, ] k ) = ; omain = [, 8], rang = [, 7] l ) = + ; omain = [, ), rang = [, ) a, ) a, ) = ) = ), ), ) = ), ) an, ) a =, = a ) = a a = ora = Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

24 77 Eris H a a g i k a = = = = = = = = = = h j l = = = = = = = = = a a 9, ), ) + +, ) ang =, ) =, ) +, ), ) ang =, ) ang =, ) ang =, ) Eris I a i = ii = iii = iv = v = vi = = Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

25 78 Essntial Mathmatial Mthos &CAS i = ii = iii = iv = v = vi = i = ii = iii = iv = v = vi = i = ii = iii = iv = v = vi = a Eris J, ), ), ),, a = = + = = = + = a = = + = = = = + a ia ilation o ator rom th -ais ollow a translation o unit in th positiv irtion o th -ais an units in th positiv irtion o th -ais ii A rltion in th -ais ollow a translation o unit in th ngativ irtion o th -ais an units in th positiv irtion o th -ais iii A ilation o ator rom th -ais ollow a translation o unit in th ngativ irtion o th -ais an units in th ngativ irtion o th -ais i A ilation o ator rom th -ais ollow a translation o units in th ngativ irtion o th -ais ii A translation o units in th ngativ irtion o th -ais an units in th positiv irtion o th -ais iii A translation o units in th positiv irtion o th -ais an units in th ngativ irtion o th -ais i A translation o units in th ngativ irtion o th -ais an units in th positiv irtion o th -ais ii A ilation o ator rom th -ais ollow a ilation o ator rom th -ais iii A rltion in th -ais ollow a translation o units in th positiv irtion o th -ais Eris K a i A = 8 + ) ii P = + + i A = 9 + ii < < iii A m ), ), 9), 9) 8 m) iv m ac =. or < m =. or < m =. or < m C $) 8 M g) Domain =, ] ang = {.,.,.} ac =. or < =. or < =.7 or < 8 =. or 8 < =. or < 7 =.77 or 7 C $) km) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

26 79 a ic = +. ii C = 89 C $) 8 > km C C 8 km) Multipl-hoi qustions E D C E 7 D 8 E 9 C D Short-answr qustions thnolog-r) a a, 7), ), ) ang = [, 7] aang = ang = [, ] ang = [, ] ang =, 9] ang =, ) {,, } g ang = [, ) h \ {} i ang = [, ] j ang = [, ] a a =, = Domain = \ {} a [, ], ), ) a =, = 7 a =, =, = 8a \{} [, ) [, ] { } \ [, ], ] 9,,,,, g, an j ar on-to-on a, 9), ), 9), ) a ) = +, Domain = [, ] ) = ), Domain = [, ) ) =, Domain = [, ) ) = +, Domain = [, ) a = + = = = = Etn-rspons qustions a km) X Y 7 t hour) Coah starting rom X: = 8t or t = or < t = 8t or < t 7 ang = [, ] Coah starting rom Z: = t t ang = [, ] Th oahs pass 8 km rom X. a P = n P hours) at =.8 7. T $) 8.7 Z Domain = {n : n Z, n } n ang = : n Z, n 8 ang = [87.7, 8.7] $ ) $877.7 to narst nt) a icn) = + n, n > ii Cn) n, ) i Pn) = n + n) = n ii Pn) n, 9) V = 8.n) = 8 n a = ) + ) = + ) ) 7., 7 ) Pri or ma = $7. n Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

27 7 Essntial Mathmatial Mthos &CAS 7a A) = a )) < < a ) m 8a i ) = + + ) + 9 ii i a +, + 8) ii. iii. or. i minimum at = minimum o ) = 8 ii rang = [8, + ] + 9 a A, + ),, ) i ) = + + ii = + + = = + ) ) + i maimum valu o ) is8. ii [, 8.] i A.,.).,.) ii ) = + iii ang = [, ] iv maimum valu o ) is Chaptr 7 Eris 7A a 7, ), ), ) 9, ), ) a g a, ) 7., ), ) a, ), ) 8 +, ), ), ), ), ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

28 7, ) 8, ), ) Eris 7 a g a ) ) ) a ) Eris 7C a 9 7 g h i 8 aa = a = a = a = Eris 7D a 8 a ) + ) + ) + ) ) 7 + ) ) + ) ) + ) ) + ) ) g ) ) h + ) + ) ) a ) + + ) + ) + ) )9 + + ) ) + + ) ) + + ) + )9 + ) g m n)m + mn + 9n ) h + a)9 a + a ) a + ) + ) + ) ) ) ) + ) ) + ) + ) ) a =, =, P) = ) + ) + ) 7 in o ii n vn 8aa = l, = l i P) = + Eris 7E a,,,,,,,,,,, g,, h,, i,, j,, a,,,,,, ± a,,, ±,, 8, ± 7 a, ± + a, ± ±, a a 9) ) + ) + ) + ) ) + ) 9) ) ) + ) + ) Eris 7F a + + Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

29 7 Essntial Mathmatial Mthos &CAS g i k + a.,.)...,.).,.)..., 8).,.7), 8) + + h + j +..,.9)..,.9).7,.), ).9,.) + ) + ) ) =, Graph just touhs th -ais at = an uts it at =. Eris 7G a { : } { : } { : } { : } { : < } { : < < } { : > } g > h Eris 7H a = 8 + ) = ) = ) = + ) a = ) + = = a = + = + ) a = = = + = = + = + g = + Eris 7I a = or = = or = or = or = = or = = or = = or = or = = or = g = or = or = h = or = or = i = or = or = j = or = or = or = k = l = or = a., 9.) 8.7,.).8.89, 8.7), 7) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

30 7 g i k.,.).,.) 9 9.,.).,.).,.9).,.) Eris 7J h j l.8, 8.).7,.).,.).,.).,.7) 7.,.7) a n) = n + n) = n n + n) = n + n + n n) = n + n + n n) = n a n) = n n) = nn + ) n) = n + n + n n) = n n n) = n + n + 7 n n) = n + n + n n) = n n n) = n + n + n n) = n n + ) Eris 7K al =, w = V = ) ) V V = 8 m) m) =. or =. V ma = 9.8 m whn =.8 a = h V = h h ) V Domain = {h :< h < 8} m ) 7 8h m). h =.8 or h =.7 g V ma.7 m, h =. ah = V = ), Domain =, 8) V m ) 8 m) =.98 or = 7. V ma 7.7 m whn Multipl-hoi qustions D A D A C D Short-answr qustions thnolog-r) a, ), ), ), ) +, ) +, ) +,, ), ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

31 7 Essntial Mathmatial Mthos &CAS g a g, 9), ), ), ) h h, ), ), ), +, ) ) a P = an P ) =, + ) =,, =,, + ) i P = ii ) + ) ) a ) = ) + k) + k + ) a =, = a, ), ), ), ), ), ), ), )....., ),,, ), ), ), ) 7a 9 8 = + ) ) ) 9 = + ) 8 a a =, = 8 + ) ) ) a = ) + = = = ) = ) = = 7 a = ) + = = + ) + a Dilation o ator rom th -ais, translation o unit in th positiv irtion o th -ais, thn translation o units in th positiv irtion o th -ais ltion in th -ais, translation o unit in th ngativ irtion o th -ais, thn translation o units in th positiv irtion o th -ais Dilation o ator rom th -ais, translation o unit in th ngativ irtion o th -ais an translation o units in th ngativ irtion o th -ais Etn-rspons qustions a v = t 9) t s = t 9) s Domain = {t : < t < 9} m),.) 8 t s) No, it is not asil sin th maimum rang o th tai is lss than. km km). Maimum sp = 9 m/s Minimum sp =. m/s a = a ) a = = 7) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

32 7 a7 m V = l l) V m ) l m) i l =.9 or l = 9.79 ii l = 8. or l =. V ma 7 9 m, l. m a a = 9, =.9, =, =.8 i Closst to th groun.9,.8), ii urthst rom th groun,.8) a V = 9 )8 ) = 8 ) V i < < ii V ma = 8 m whn = 8. 8 m m 97 m Chaptr 8 Eris 8A Th lins ar paralll. =, = m = a m = m = a i m = ii m = = m + ), = m + m + m orm a =, =, z = =, =, z = =, =, z = 7 7 =, =, z = w w + ) 8 =, =, z = w + ; i w = solution is,, ) 9 a =, = an = =, = an = =, = an z = =, = an = Eris 8 8 a a a +, ), ),, ), ),, ), ) a, ),, ), ),, ), ),, ) a, ), 7), 7), 7) 7, ) a 7 a 8 a T =, ) a = an =. 9 X + = X X = ) X, = ), = Eris 8C a m ) = + m m ) m, m + = m m a ) =, ) = + ) a = an =, i, ) an, ) ii = iii a, ) = a an = a a + 8a + a +, ) a + 8a + a an a + 8a a, ) a + 8a a Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

33 7 Essntial Mathmatial Mthos &CAS Eris 8D = 9 = + 8 = = = + = + 7 = = a =, a =, 8a =, 7a = a 8 = 7 9 a =, =, =, = = a a =, =, =, = = + Multipl-hoi qustions E E D 7 C 8 C 9 D C Short-answr qustions thnolog-r) a, ), ), ), ), ) =, = an z = 7 a = +. i ii < a < a ) a, a + a a + ) + a a a a, a ) a [ a =± ] [ ] < a < + = ][, = an = [ ] + = ][, = + an = Etn-rspons qustions a h = ± a =± a = 8, = a =, 7 =, + = + 9 = a = 8 = or = i = or = + 8 ii = 8 ) a + a + a a, a = a = a = + a + z = an + z =. This iniats th solution is going to a straight lin. = = a = + z = 8, = +, z = 7 u = a, v = a Chaptr 9 9. Multipl-hoi qustions A D D C C 7 A 8 E 9 A E D D E 7 D 8 E 9 D D D A D D 7 8 C 9 A C A C D E E 7 C 8 C 9 C A A E A C 9. Etn-rspons qustions ac = +. I =. I an C I =. Proit C = +. P av = + m V litrs) P = m minuts) hours minuts Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

34 77 a L{ t t V = t + < t 9 V litrs)., ) t minuts) a A r = A s =..). A T =.. +. A T..,.8) 7,. m ara o rtangl = ) g rtangl: 9, squar:, = ) or rtangl: ; squar: 7 7 a m m. m a A = i m ii m m A V = = g =. 7a i A = + ) ii P = + + ) i A = + ii m iii iv A m 7, ), ), ) m) 8a A = i =. m ii =. m 9a.9 m t =. sons ht).,.9).8 sons.8 t a + V = + 7 S = V V = + 7 an S S = t. m m a + = i, ) ii D8, l) units. units a km/h tap A min; tap 7 min m a h = V = ) < < V m ) m) i = 8. or =.8 ii =.7 or = 9. V ma = 9.8 m whr =. g i S = ii Sma = m,whr = 7 7 h =.8 or =.99 a = 7. ).7 +. = 7. ) m a = = + 8 D8, ) units units a i = ii V = ) = ) V m ) m), ) =.78 or = 7.8 V ma = m,whr =. an = 8. Chaptr Eris A {H, T } {,,,,, } a lus, harts, spas, iamons lus an spas ar lak, iamons an harts ar r Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

35 78 Essntial Mathmatial Mthos &CAS a, king, qun, jak g h a{,,, } {H, H, H, H, H, H, T, T, T, T, T, T } {MMM, MMF, MFM, FMM, MFF, FMF, FFM, FFF} a{,,,,, } {,,,,,, } {,,, } a{,,,,...} {,,,,...,} {,,,...} 7a{,, } {FFF} Ø 8 H T H {HH, HT, T, T, T, T, T, T} T 9a{, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, )} {, ),, ),, )} a {, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, )} {l, ),, ),, )} a {, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ), ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ), ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, ),, )} {, ),, ),, ),, ),, ),, ),, ),, ),, )} a W W W W W W W W W W W W W W W W {), ), ), W), W), WW ), W), W), W), WW ), WW ), ), ), W), W), WW ), ), W), W), WW ), W), WW ), W), W), W), WW ), WW ), W), W), WW ), W), WW ), WW )} a S H S H C D S H C D S H C D S H C D S H C D {SHS), SHH ), SHCS ), SHCH ), SHCC ), SHCDS ), SHCDH ), SHCDC ), SHCDD ), SHDS ), SHDH ), SCDCS ), SHDCH ), SHDCC ), SHDCD ), SHDD )} Eris a 7 ano answrs will var answrs will var Ys As th numr o trials approahs ininit th rlativ rqun approahs th valu o th proailit. ano answrs will var answrs will var Ys As th numr o trials approahs ininit th rlativ rqun approahs th valu o th proailit. Pra rom irst i) 78 =. Pra rom son i) 7. hoos th irst i. a.7.7 Th aov stimats or th proailit shoul ralulat..7 Pr) = 7 Pr) = Pr) = Pr) = Pr) =, Pr) =, Pr) = 8 PrA) =. 9 PrA ) =.77 Eris C a 8 8 a a 9 a a 9 a 8 8 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

36 79 7 a 8 9a a G i 7 Y la G G G Y la la Y Y la G G G G G G G G G ii 9 la Y Y la la la Y Y Y la la Y 7 iii i. ii =. iii a a iv 9 n all st all, ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ), ) a i a m Eris D ii iii 9 a{,,,, } {, } {,, 7, 8, 9, } {l, } {,,,, 7, 8, 9, } {, 7, 8, 9, } a{,,,,, 7, 9,, } {,,, 7, 9, } {,,, 8,, } {,,, 7, 9, } {,,, 7, 9, } a{e, H, M, S} {C, H, I, M} {A, C, E, I, S, T} {H, M} {C, E, H, I, M, S} {H, M} a a l 8 a 7 a ; 8a 9 7 Eris E a....7 a a a....7 a a9% % 7a A = {J,Q,K,A,J, Q, K, A, J,Q,K,A,J, Q, K, A } C = {,,,,,7,8,9,,J,Q,K,A } i Pra pitur ar) = ii Pra hart) = iii Pra hart pitur ar) = iv Pra pitur ar or a hart) = v Pra pitur ar or a lu, iamon or spa) = 8 a 8 7 9a a Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

37 7 Essntial Mathmatial Mthos &CAS a a Multipl-hoi qustions C A C D E 7 E 8 D 9 A Short-answr qustions thnolog-r) a.7 a a. 87 a{,,,,, } 7 a 8 No 9a a Etn-rspons qustions a + + a..8 T 8 9 Pr a..7 p.. a. Chaptr Eris A 7 a a.. a. 7 a... a. 7 7a..7 8 a l.8 9 % a 9 a a g h 8 a.8....; 8% 7 a i. ii. iii. iv.78 v.9.7 i.78 ii. 8 a i. ii. iii. iv.8 v a 9 a A A = Ø A Eris ays Ys No. No a...88 a a ;No 9a..87 a 8 8 g h 8 ;No a i.7 ii. iii.9 No No i 8 ii 8 iii 7 8 i.9 ii.8 iii.9 iv. a 8 a a 7 a 8 Eris C.. a... a 7 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

38 7.. a PrWi+ ).. PrWi ) a = PrL i+ ).. PrL i ). PrLi+ ).. PrLi ) a = PrT i+ ).7.9 PrT i ).8 i PrAi+ ).7.. = a. PrE i+ ) a Eris D ai ii iii i ii iii a i ii iii i ii iii a i ii iii i ii iii a i ii iii i ii iii a..77.% at th inoor pool,.9% at th outoor pool.9.98 a 9.% a 7 popl a.7.89.% shool A,.% shool.% shool A, 9.% shool..7 a.. i. ii.... a.7. i. ii.. a.8% to Dr lak, 8.% to Dr Whit.7. a..8 garag A, 99 garag garag A, 98 garag Multipl-hoi qustions E C A C D 7 E 8 D 9 E C Short-answr qustions thnolog-r) a 9 7 a. No a.. a a Etn-rspons qustions a A : : 9 A : 8.. ais a sust o A A an ar mutuall lusiv A an ar inpnnt a i ii n : 9 [ ].9. Mlourn a Tullamarin Mlourn 7 Tullamarin.. a [.7.8 ]... i ii Chaptr Eris A a 7 9 a a Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

39 7 Essntial Mathmatial Mthos &CAS Eris a a a a a 8 a 8 a a a 7 8 Eris C a a a9 9 a a a 79 a 7 8 a a Eris D a...7 a a a 8 a a 7 a a 7 Multipl-hoi qustions E D A D C 7 C 8 A 9 E E Short-answr qustions thnolog-r) a99 8 8n 7 7 8a 9 a Etn-rspons qustions a88 8 a7 8 a a 8 a a 7 Division :.8 7 Division :.7 Division :.7 Division :. Division :. 8a.9.9 Chaptr Eris A ano no s no no aprx = ) PrX > ) PrX ) PrX < ) PrX ) PrX > ) g PrX ) h PrX ) i PrX ) j PrX ) k Pr < X < ) a{} {,, } {,,, } {, } {,, } {,,, } g {,, } h {,, } i {, } a a.9.9 a a..7 8a{HHH, HTH, HHT, HTT, THH, TTH, THT, TTT} 8 p) a{,,,,, 7, 8, 9,,, } p) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

40 7 a {,,,,, } a.9.. a p) Eris Eris C a.8. a.9.9 a.7.. a a..9 ).8 7 a PrX = ) =.).9) =,,,,, or p) Most proal numr is a a...8% a i.7 ii. iii.78 will var aout or mor a 8 a a 9 a 9 a ).9 a... Eris D Eat answr.7 aaout : On st o simulations gav th answr.9 Eris E Eat answr 9.9 aon st o simulations gav th answr 8.. On st o simulations gav th answr.7. Eat answr is.9. aon st o simulations gav th answr.. Multipl-hoi qustion A C A E C 7 A 8 D 9 E Short-answr qustions thnolog-r) a.9..8 a p) p) 8 st hoi n hoi {,,,,, 7, 8, 9,,,,,,,, 7, 8 } 7 PrX = ) 8 9 PrX = ) 8 PrX = ) a a 9 7 7a a p ) p ) 9 a p ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

41 7 Essntial Mathmatial Mthos &CAS p ) p + ) p ) p ) + p a 7 m = Etn-rspons qustions a p)..... a i. ii. iii i. ii.8 a 7 i ii i ii 7 a a. n 8a q q + q < q < 9.9 at answr) a.7 at answr) Aout 7 simulation) a 8.7 PrA) =.7, Pr) =.7, PrC) =., PrD) =. at answr) Chaptr. Multipl-hoi qustions E C E E E 7 C 8 C 9 D D D E A E E 7 8 C 9 C A E E C D D D 7 A 8 E 9 C. Etn-rspons qustions a i ii 7 iii i ii 9 a a a a 9 9 ) a 7 i 8 ii 9 9 7a i ii 9 8 i ii 8 8a im =, q =, s = ii m + q = 7 9a.8..8 a 8. a a i m ii m iii m i. ii. iii. i. ii. a a i.8 ii. iii.7 i ii 8 a i. ii.8 iii.8 i 9 ii a i 8 9 ii 7 8. Chaptr Eris A =. =.9 =. =.8 All pass through, ) as >, inrasing as <, rasing horizontal asmptot, = = = = = For = a -ais intrpt, a) an ar rltions o a an in th -ais horizontal asmptot, = =.87 =.87, ) =.778 =.778, ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

42 7 a a =, ) =, ) Eris, ) a 8 7 a g h i j a 9 7 q 8 p 9 a 8 8 g m n p h a a 8a 8 9 a 8 z n p a a n + n + n a 7n n a n n + n n g n n h = 7 i a = 9 = = 7 Eris C a 7 9 h i j k 7 l = = = = g a a 7 a a a ) / ) / + ) / ) / ) + ) / Eris D a g h i a 8 g h i 8 j k l m 7 a a,,, a a > > < > g Eris E < 9 alog a) log log g log a h 9 a 7 g h i 9 j k l a 7 9 log a g h a 7 8 g 8 h i j a a 9a Eris F or 8 ) 9 a g. h.8 i. j.8 a > <. <..77. a = = Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

43 7 Essntial Mathmatial Mthos &CAS log.8 = = =.88, m =.9 Eris G a.. Domain = + ang = Domain = + ang = a = log = log Domain = + ang =..9 = log. log. = Domain = + ang = Domain = + ang = Domain = + ang = = = a = log ) = + ) = log = log + ) = = ) g = + h = log a = Domain =, ) = log Domain =, ) Domain =, ) Domain =, ) a = log ) = = log = log or, ] = log ) + log ) 9 a = ) Eris H an k = log Domain =, ) Domain =,) ) = log =..7 p =.. t a Total thiknss, Cuts, n Shts T mm) = log ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

44 77 T =.) n T. 8 n 78. m a p, q millions) = pt) = qt).7. t i t =....mi 9) ii t = 7....mi 987) Multipl-hoi qustions C A C C A 7 A 8 A 9 A A Short-answr qustions thnolog-r) aa m n a a a g a h n8 i m p q 8 j k a l a + a a alog 7 log 7 log ) 7 log + log + log g log h log a 7 g h ) a alog log log ) a ) a log log log a = = or = = = or = a =., ), ), ) =. = =. = = +, ) = 7 a = 9 = a k = q = 7 a a = = or = Etn-rspons qustions a n M 7 M = n M n 7 M 7 n Thr iss Tims mov, ) = Four iss Tims mov 8 n = ) n ) n a n = ) n ) n a 79 8 tims aath =.9) n ath =.9) n ars ax $.8 Y $. Z $. X $.7 Y $.7 Z $.7 Intrst at t =.78...an t =.9...thror Fruar 997 until Sptmr 998 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

45 78 Essntial Mathmatial Mthos &CAS Fruar 998 until Sptmr 998, approimatl 8 months. 7a.8 ars 7.8 ars 8atmpratur = t i87. ii 8. tmpratur = t i8.7 ii minuts 9aa =. an = iz = log ii a =. an k = log a =.8 =. ) = log Chaptr Eris A a 7 8 a g h a g 7. h.77 a g.9 h.7 a 7 8 g 9 h 9 a 7 Eris a,,,,, l, g, h, a g.8 h. a; ; ; ; ; ; g ; h ; Eris C a unin unin unin a g. a Eris D a g. h.778 i.7 aa =.7, =.8 =.7, =.8 i os =.7, sin =.8 ii os = os Eris E a g.7 h.7 a a 7 a a = = = = tan ) = tan ) = a a g. h. Eris F a sin =, os =, tan = sin =, os =, tan = sin =, os =, tan = sin =, os =, tan = sin =, os =, tan = sin =, os =, tan = g sin =, os =, tan = h sin =, os =, tan = i sin =, os =, tan = j sin =, os =, tan = a g h i a not in g h Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

46 79 Eris G Prio Amplitu a a g h i Amplitu =, Prio = Amplitu =, Prio = Amplitu =, Prio = Amplitu =, Prio = θ Amplitu =, Prio = g h i a Amplitu =, Prio = 7 Amplitu =, Prio = Amplitu =, Prio = 9 Amplitu =, Prio = 7 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

47 7 Essntial Mathmatial Mthos &CAS, ailation o ator rom th -ais amplitu =, prio = ilation o ator rom th -ais amplitu =, prio = ilation o ator rom th -ais amplitu =, prio = ilation o ator rom th -ais ilation o ator rom th -ais amplitu =, prio = ilation o ator rom th -ais rltion in th -ais amplitu =, prio = rltion in th -ais amplitu =, prio = g ilation o ator rom th -ais ilation o ator rom th -ais amplitu =, prio = h ilation o ator rom th -ais ilation o ator rom th -ais rltion in th -ais amplitu =, prio = i ilation o ator rom th -ais ilation o ator rom th -ais rltion in th -ais amplitu =, prio = a 7 = sin = os Eris H a Prio =, Amplitu =, =± Prio =, Amplitu =, =± Prio =, Amplitu =, =± Prio =, Amplitu =, =± Prio =, Amplitu =, =, θ θ θ θ θ, Prio =, Amplitu =, =, Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

48 7 g h i Prio =, Amplitu =, =, Prio =, Amplitu =, =, Prio =, Amplitu =, =, a ) = ) =,, a ) =,, θ θ ) =, a ) = ) =,, a = sin, = sin = sin = sin ) = sin + ) Eris I a an 7 an 7 a.9 an.. an.98. an.9. an.7. an.9.77 an. a an an an an an an a.,.98,.9, 8.78, 7,,,, 7, 8 a,,,,,,,,,,, 7 a 7,, 9,,,,,,, 7, 7,,,,, 7, 7, 9 8, 7 8, 8, 8 8a.,.78,.7,.8.89,.8,.,.9.8,.,.7,.7.9,.78,.,.88,.98,.97 Eris J a 7 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

49 7 Essntial Mathmatial Mthos &CAS a, ), + ) 7, ), + ) 9 a, ) 7 +, ), ) ,.),.), ), ) 7 7, ), ), + ) + 7, + ), + ) +, + ) +, + ) 7 7 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

50 7 +, ), ) + Eris K a ) g. h. i. j. 7 a sin = an tan = os = an tan = sin = an tan = Eris L a a = = = = = = = = = = = = = = = = a 7 8, 8, 8, 8 7 8, 8, 8, 8, 7 8, 8,,, 8, 7 8, 8, 8, 8, 7 8 a, ), ), ), ) = = Eris M = =, ), ), ) a.7..8 or.8 or.88 = a sin + ) + a a =.99 =.998 =. =.99 a =. =. =. =. a =.97 =. =. =.97 Eris N n + ) n + ) a = or = n ± ) n + ) = = 8 a = or = = or = 8 8 = or = Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

51 7 Essntial Mathmatial Mthos &CAS n ) = n or = ; =,,,,, or 7 = n ; =,,, = n or = n + ; =, 7,,,,,, Eris O a D 7 8 t {t : Dt) 8.} ={t : t 7} {t : t 9} {t : t }.9 m a p =, q = D 7 t A ship an ntr hours atr low ti. a t =. s,.8 s,.7 s t = s,.7 s,.9 s Partil osillats aout th point = rom = to =. Multipl-hoi qustions C D E C E D 7 E 8 E 9 C Short-answr qustions thnolog-r) a 9 9 g h 7 i 9 a 9 g h 9 i a g h a Amplitu a Prio = sin = sin 9 passs through g 7 = os a,,,,, 7 h = os point, ) is th inal point = sin +, 7 Etn-rspons qustions a i.8 hours ii.79 hours April t =.8) August t = 7.8) ) t a9. C D = + os D 8 t {t :< t < } Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

52 7 a m).8. 8 t hours). am. pm. am 9. am 9. pm. am i. pm ii trips D m) 8 t hours) t = 8. pm) t = an t = 8. am an. pm) pth is m i. m ii.8 m 9 hours 7 minuts Chaptr 7 7. Multipl-hoi qustions E D A 7 D 8 C 9 A A D A D D D 7 A 8 E 9 D D E A E D 7. Etn-rspons qustions a h m) h = t hours) t =.9 an t = 8.7 Th oat an lav th harour or t [.9,.8] a atria i atria ii atria iii 8 7 atria N, ), ), ) t hours) minuts, = ) hours a sons h m) = Atr sons an th ar at this hight vr sons atr th irst attain this hight. At t =, t = an t = or t [, ] a V t s) t = 8 s t = k s, k =,, a iprio = sons ii amplitu = iii = h =.7 h mtrs) ht) = + sin t.7) t min) a i ii 9. iii h h t) =.) t 7 a htars), 9.), ) t hours) θ C) t. t min) minut 7.7 8aP A = 7 + t P = 7 + t P C = 7. t P 7 i P C P ii P A i ars ii 7 ars 9a i illion ii.9 illion iii 7. illion a V ) = V ) = V litrs), 8.8) t t s) [, ] t 8.8 litrs t = an t =. Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

53 7 Essntial Mathmatial Mthos &CAS a h m) 8 8 = h t), ), 8) 8 t hours) t =. Approimatl.9 am orrt to narst minut) i 9. am 8 + t mtrs Chaptr 8 Eris 8A Not: For qustions thr ma not a singl orrt answr. C an D ar th most likl. Sals shoul om into our isussion. hight m) sp km/h) Ag ars). istan rom A km) C or ar th most likl. aistan mtrs) sp m/s) a volum tim sons) tim sons) volum 7 V volum hight h volum hight 8 D 9 C a [ 7, ), ] [ 7, ), ] a [, ), ] [, ), ] Eris 8 km/min = 8 km/h km) US $ m a km/h t min) 7 8 A $ m/s m/min = km/h = m/s.9 km/h. m/s a8litrs/minut litrs/minut litrs/min 7 litrs/min t.. A L) 7 A 7.. 7, ) t min) $ pr hour = $.8 pr hour 7 8 m/s 8 V m ), ) hight hight t s) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

54 77 Eris 8C a 7 a am/s m/s a$.9. m/min C 7 istan km) Car Eris 8D $. pr ar Car 7 8 tim s) a kg/month answrs will var) kg/month answrs will var) kg/month answrs will var) a. m /s answrs will var). m /s answrs will var). m /s answrs will var) a =. litrs/kg m 8 a.7 litrs/kg m a 8ars 7 m/ar a Cat hours C/h. C/h.9 7a.. 8a 9a m /min m /min a 8 million/min 8. million/min a m /min lowing out m /min lowing out 8 m /min lowing out 7.9 a a a i.7 ii.9 iii.99 iv a i 9 ii. iii.89 iv.9. Eris 8E am/s. m/s m/s, ) an, ), ) a i km/h ii km/h iii km/h s V km/h) 8 t h) 7 t, ), ) 7, ) ac A a+v slowing own +v sping up v slowing own v sping up agrauall inrasing sp onstant sp hols sp attain at a) inal sping up to inishing lin 7at = m/s 7. m/s m/s m/s m/s 8at =. t <. m sons m/s 9a m/s m s.8 s m/s a t =, t =, t = 8 < t <. an t > t =. an t = Multipl-hoi qustions C D E D 7 C 8 E 9 A A Short-answr qustions thnolog-r) a pth pth tim tim pth pth tim tim Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

55 78 Essntial Mathmatial Mthos &CAS a pth km) tim 8 t min) pth onstant sp = km/h = 8 km/min istan m) istan = 9 km/min tim s), )., )., ) tim tim m /m a a m/s. m/s m/s Etn-rspons qustions ays, th rlation is linar.. ohm/ C a i9.8 m/s ii 9. m/s i.98h h ) ii.98 h) iii 9. m/s a i m/s ii. m/s a alration m/s ) w m) 8 tim s) 78 n as) graint = ;Avrag rat o growth o th watrmlon is m/a. m/a Full Hal ull Quartr ull 8 8 tim h) a + a a ). 7 a, ;graint =.,.98; graint =... graint is 8 9a kg/ar. kg/ar {t :< t < } {t :< t < } {t :< t < 7} {t :< t < 7 } a i. l 8 ii 8.7 illion/ar i. illion/ar ii. illion/ar ars atr a i 9. ii. iii 97.7 iv 7..8 a a + a + 7. a A m s.98 m/s,.7 m/s,. m/s a i m ii m iii m rsults ar th sam Chaptr 9 Eris 9A m/s 7 pr a a + + a + + a + h. a.8 + h 7a + h. Eris 9 a + 8 g + a a g + h 8 + a g + a i ii a a = ) or all an graint o graph or all = or all 8 + Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

56 79 7a, graint =, graint =, graint =, graint = 8, graint = 9, graint = ) 8a i,,, ii +, 7,, ) iii +,,, ) iv, 7,, ) oorinats o th point whr graint = 9at + z z 8 9.t a, ), 8) an, 8), ), ), ), ),, ) 7 Eris 9C an a, an a = = > l < l = ) a, ),, ), ) {, } a C D A F E a,.), )., ) { l, l.} 7a = ) = ) = ) = ) 8a, ), ) 9 a, ), ) a a.)t. m/s,. m/s, m/s a hight = m; sp = m/s t = s a a =, =, ) 8 Eris 9D a g h i j k l 9 a, 7 aas ) =, lim ) = ut + lim ) = as ) =, lim ) = ut + lim ) = as ) =, lim ) = ut + lim ) = = Eris 9E a = ) = ) = ') { + i ) = i < = ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

57 7 Essntial Mathmatial Mthos &CAS, ), ) { + i ) = i <, ), ) { i ) = i < Multipl-hoi qustions D E C C 7 A 8 E 9 A D Short-answr qustions thnolog-r) a l) + l a + 7 a; ; ; 8; a, ), ), ),, ), 8), ) 7, ), ), ), ) a = = > < { } = 8 aa =, =, ) 8 7 = ) 8a, ), ), ) {, } Etn-rspons qustions = a i7 ii 89 km a.,. =, =.. Th hight o th pass is. km. at =,.9 m/s.97 m/s aat =, graint = ; at =, graint = Angls o inlination to positiv irtions o -ais ar supplmntar. Chaptr Eris A a = ; + = 8 = ; + = = + ; = = + ; + = 9 = = ; = 8 ; oth hav graint = ; istan apart = = + ; = + atangnts oth hav graint ;, ), ), ) 7a =, ) 8a =, ), 8) Eris a ; = 8 h 8 at t 8 ollars/month At t = an t = a m/s s a 9.8t m/s 9.8 m/s a p ; For P < 7. rvnu is inrasing as P inrass. a i popl/ar ii popl/ar iii rasing popl/ar 7aimL ii 8 ml V t) = 8 t t ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

58 7 V t) ml/s,.) t s) 8ai m/s ii m/s iii m/s 9as,s,s m/s, m/s, m/s; m/s,m/s,m/s m/s a m/s m/s a m to th right o O mtoth right o O moving to th lt at 7 m/s whn t =. san th partil is. m to th lt o O m/s.9 m/s a atr. s m/s. m whn t =. san th partil is. m to th lt o O a mtoth lt o O moving to th right at m/s v = t t + atr sans m to th right o O an 9 m to th 7 lt o O s a = t g whn t = s an th partil is 7 m lt o O moving to th lt at m/s a whn t = s an a = m/s, an whn t = an a = m/s whn t = s an th partil is moving to th lt at m/s whn t = s,v = m/s, a = m/s, whn t =, v = m/s, a = 8m/s, whn t = 8s,v = m/s, a = m/s a t = san t = t = s Eris C a, ), ), ), 8), );, 8), );, ) a =, = 8, = a =, =, = aa =, =, ) 8 a = 8 a = 7 7a.,.) 8, ) 9, 7), ), 8), ), ), ).,.) 8aa =, = 9 a = 9, =, =, = 7 Eris D amin, ); ma, 8) min, 7); ma, ) Stationar point o inlion, ); min, 7) 9, 8), ), 7), ).9, ).8, ), 7) 8 a, ) ma;, ) min 7, ) min;, ) ma, ) min ), min;, ) inlion 79, 7) min;, ) ma 7, ) min;, ) ma 7 a, ), ), ), ) ma at, ) min at, ) intrpts, ) an, ), ), ), ) +, ), ), ), ), ), 8) min at, 8) ma at, ) intrpts, ) an, ) min at, ) ma at, ) intrpts, ), ±, ) an, ) Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

59 7 Essntial Mathmatial Mthos &CAS a, ) ma, ) stationar point o inlion a, ), ), ) ma;, ) min, ), ), ), ) 7 { : < < } 8a{ : < < } { : < } 9 a = ; =, ), 7, ) ma at, ) 7 min at, ) intrpts, ), ), ), ), ), ), ), 8), ), ), 7) Tangnts ar paralll to -ais at, 8) an, 7). a i, ) ii, ), ) iii {, }, 9), 8) point o inlion 7, ) 7, ), 9), 7), ), ), 9), ) min at, 9);, 9) ma at, 7) intrpts ± 7, ) ±, ), 7) Eris E a ) + )) ) + ) ), ), 7 = ) ) a i a, ii, a = + = a a ], a a ia ) ii m = a ) a, a ) ) = a ) a + a + ah = a = a =, = a, ) a, ) ) a + a ) aa, ), 7 loal minimum at a, ) ) a + a ) loal maimum at, 7 i = a ) ) ii = a ) iii = a) 7a ) ) ) ) + ), ), ), = 8 a a = 9, =, = an = 8 = a ) + ) + whr a,, an tak th valus o a. Eris F a. km.7 km /h at =, a = 8 m/s ; t =, a = m/s ; t =, a = m/s 8 m/s ai.97 m ii. m iii.8 m =, = 8 7 i =.97, =.9 ii =.8 V = 7 m 8 m asolut minimum = 9 asolut maimum = asolut minimum = 8 asolut maimum = 7 asolut maimum = asolut minimum = 8 Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

60 7 8 asolut maimum = asolut minimum = 9 V = whn = a 8 minimum = maimum = 7 a 7 7 A = ) =. m 8 Multipl-hoi qustions D E E A C D 7 D 8 A 9 A C Short-answr qustions thnolog-r) a = = + a 8 =, ) a ; =± & minimum whn =, = maimum whn =, = 8 a = stationar point o inlion = maimum minimum whn =, maimum whn = minimum whn =, maimum whn = maimum whn =, minimum whn = maimum whn =, minimum whn = g maimum whn =, minimum whn = h maimum whn =, minimum whn = a, ) minimum, 9, ) maimum 9, ) maimum,, 7) minimum, ) maimum,, 9) minimum 7 a, ), ), ), ), ) 8, ) Etn-rspons qustions a m/s 8 m/s a V litrs) 7 t minuts),,,, i7. minuts ii.9 minuts V = t) t minuts 8. minuts a 7 W tonns) 7 = Vt) = V t), 8), 78.7) as) t, 8) atr.7 as until.9 as =, W W = ; =, = ; =, W = t/a =, W = 78.7 a C C/min, C/min, C/min, C/min, C/min C), ) t min) a78 units/a, 9, 8, t = Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar

61 7 Essntial Mathmatial Mthos &CAS a swtnss units), ) tim as) = s t = st) t minuts).9 am;. pm km, km km/min = km/h km/min = km/h 7a t i 7 L/h ii 9 L/h 8a8.8 m 7. 7, 9.) m), 8.8) km) Path gts too stp atr 7 km. i.8 ii. iii. 9 a = = + For <, minimum vrtial istan ours whn =. Min istan = unit 8mmor maimum an mm or minimum a = P = ) maimum valu =., whn =. an =. a = A = ) 7 ; =, = a = 8 s = + 8 ) ; 8 m m = m 7 = 8 9 maimum P = km km= maimum o km p =, q = 8 a = S = ) < < S,) m) =, = 7 C < < V m ), ) m) m, m, m =.8 or =. Maimum whn =, = 8 a m shoul us to orm irl, m to orm squar All th wir shoul us to orm th irl. 7 With. mtrs, lngth 7. mtrs 8 a A = A = 8 ) < < A m ) m 9 a = 97, h = 88 a = A = ) A m ) 8, ) 8 m), m) maimum at = a smiirl a h = V = V = = 7.8 V m ) m) 7.89 m g =. an h = 7. or =. an h =. a r =. m, h = 8. m r =. m, h = 8. m Camrig Univrsit Prss Unorrt Sampl Pags 8 Evans, Lipson, Walla TI-Nspir & Casio ClassPa matrial prpar in ollaoration with Jan Honnns & Davi Hiar