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اسم الطالبة الصف المادةرياضيات٣ التاريخكامل ومرتبعليه مﻼحظاتالواجبات ١٠ المهام ١٠ التوقيع أ.فاطمة بن صديق مهام وواجبات رياضيات ثالث ثانوي الفصل الدراسي اﻷول١٤٤٨هـ بداية طريق النجاح خطوة فنبدأها اﻵن
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23VEW(B6 !:qZC 1 ABCD 2 ABCD 3 ABCD 4 ABCD 5 ABCD 6 ABCD 7 ABCD 8 ABCD : !%&(%& !P&tM Ih3.f (x) = 1 x + 4 4x2 − 8x − 4 : +h !%&(%& e(.f (x) = | x − 2 | + 3 : {63@B auJ \]3^ &_&f (x) = 4x2 − 8f (x − 1) : !%&(:% R3-. =S,E I:E 3,. {Cf (x) = 2x − 6 : !%&(%& R3-.f (x) = 3x + 4 5 − x : !%&(%& 3F"J (E&1?B I?%& ;D?<%& 3.f (x) : +h !%&(:% I]3"V%& ="S,?%&f (x) = x + 1 : !%&' =S,E {i%& I]3"V%& }ZD%& '(P 4x2 − 2x − 94x2 − 8x − 124x2 − 9 W3@":% 2&(P6 4 (0,∞)[3,∞)(2,∞)(1,∞) [6,∞)[3,∞)[0,∞)(−∞, ∞) RR − {2}R − {5}R − {−5} (3,∞)(−∞, − 2)(1,3)(1,∞) /",":% 2&(P6 4L:)H:% a3B(P6=<ZH:% a3B(P6 190 : !$"$8%& !Q3ox& D?9&
9 ABCD 10 ABCD 11 ABCD 12 ABCD 13 ABCD 14 ABCD 15 ABCD 16 ABCD : 3F<ED>B ;'3)M (>Q (K) b:8?. !%&(%& =>-B I?%& !,"X 3.bf (x) = x2 − bx + 4 x − 4 x = 4 [−9,9] : +h !%&(%& e(.f (x) = x − 5 !%&(%& R3-. '(Pf (x) = 9 − x2 : 3F%3-. a3^ &_& !%&(%& e(.3.f (x) = x2 + 1−2 < x < 3 : !%&(%& R3-.f (x) = 3 − x x2 − 5x : 6 `%& /"Q !%&(%& D<5 (o6C25 : I03F] | R38B& l() =S,B I?%& !%&(%& : W63-,%& I]3"V%& ="S,?%& 3F:S,E b"B|& R&6(%& {C (−9,9)[−3,3](−3,3) 8 ℝ+ℝ− ℝ+ ∪ {0}ℝ− ∪ {0} 1 < f (x) < 95 < f (x) < 95 < f (x) < 101 < f (x) < 10 {x | x ∈ R}{x | x ≠ 0,x ∈ R}{x | x ≠ 5,x ∈ R}{x | x ≠ 0,x ≠ 5,x ∈ R} 64−43 652 f (x) = | x − 4 | − 3f (x) = | x − 4 | f (x) = | x + 4 | − 3f (x) = | x + 4 | + 3 191 : !$"$8%& !Q3ox& D?9&
17 ABCD 18 ABCD 19 ABCD 20 ABCD 21 ABCD 22 ABCD 23 ABCD 24 ABCD : !"Bç& R&6(%& /. !"o61%& !%&(%& 3. 5 : !E'DJ !%&' IBç& /. {& : ;D?<%& IJ !%&(:% D"v?%& R(>. [Z+?. (o6Cf (x) = x + 2[2,7] : !%&(%& e(.f (x) = 2 x2 + 3 : !%&(%&f (x) = x3 + 5x2 − x : !.+ZD,%& !%&(%& 3F"J 7X3K?B I?%& ;D?<%& '(P : +h b"%3?%& 23"K$K,%& IJ =5*& !f#] R+P =p3,?,%& LK$K,%& : Ñ+d>. 3F% Ä"% I?%& !%&(%& −5− 1 5 1 5 f (x) = cosx f (x) = x7f (x) = | x5 |f (x) = x + 3f (x) = x2 + 3 [3,∞)(2,∞)(−3,∞)[−3,2] c 3>. !"o6t6 !E'DJ 3%6 bE'DJ \@"% !"o6t !"o6t!E'DJ (−∞, − 1)(1,∞)(−1,1)(−∞,0) f (x) = sin xf (x) = tan xf (x) = cscx 192 : !$"$8%& !Q3ox& D?9&
25 ABCD 26 ABCD 27 A!#:f. eDv5B!":$. eDv5C!#:f. L,s)D!":$. L,s) 28 ABCD 29 ABCD 30 AI03F] |B{1<XC!%&tz% =Q3XDI%38<]& 31 ABCD : W63-,%& =dk%& IJ !%&(%& y+]3. !"o6t3%6 !"o6t \@"% !E'DJ !E'DJ!"o6t6 !E'DJ : W63-,%& =dk%& IJ !%&(%& e(. 3. (0,4)(0,4][0,4](−4,4) − {0} : !,"X ;D?<%& IJ a+dB W63-,%& =dk%& IJf (c)(a, b) : W63-,%& =dk%& IJ !$G+,%& !%&(:% l*& !@"0D%& !%&(% 3. y = | x | + 3y = | x |y = | x − 3 |y = | x | − 3 : W63-,%& I]3"V%& ="S,?%& IJ R38B|& l() y+] 3. [−4,4](−4,4)(−4,4](−1,3) l*& !"@"0D%& !%&(%& Ih \]3^ &_& W63-,%& =dk%& IJ : Ih !%'3>. auJ !%&(:% f (x) = x2 g(x)g(x) : W63-,%& I]3"V%& ="S,?%& IJ !%(%& R3-. 3.f (x) (x + 5)2 −(x + 5)(x − 5)2−(x − 5)2 193 : !$"$8%& !Q3ox& D?9&
32 ABCD 33 ABCD 34 ABCD 35 A!E'DJB!"o6tC|6 !"o6t \@"% !E'DJ Dn>. !"o6t6 !E'DJ 36 AI03F] |B{1<XC!%&tz% =Q3XD'($. D"U 37 ABCD 38 ABCD 39 ABCD : !%(%& R3-.f (x) = x + 2 x2 + 6x + 9 {x | x ≠ − 3,x ∈ R} L,s) !,"X 3F% IB|& I]3"V%& }ZD%& IJ !:S,,%& !%&(%& : : {63@B 3.(K) !#:f.x −2−113 : +h !%&(%& R3-. W63-,%& =dk%& IJ : !%&' !%&(%& a&f (x) = 1 x3 + 1 x + x : {63@B auJ \]3^ &_&f (x) = 4x,0 ≤ x ≤ 15 60,15 < x < 24 −6x + 15,24 ≤ x ≤ 40 f (5) : W63-,%& =dk%& IJ !%&(%& R3-. '(P : (K) !%&(%& IJ R38B|& y+] '(Pf (x) = 1 x − 8 x = 8 (−∞, − 3) ∪ [−3, − 2]R+ {x | x ≠ 5,x ∈ R}{x | x ≠ 3,x ∈ R}{x | x ≠ 2,x ∈ R} (−3, − 2) ∪ (−2,∞)(−∞, − 3) ∪ (−3,∞)(−3, − 1) ∪ (−1,∞)(−∞, − 2) ∪ (−2,∞) 602015−20 : !:8?. D"U !"%3?%& !%&(%& =>-E 2&W3"T%& {Cf (x) = x2 x − 49 x = 0x = 7x = 49x = − 49 R(−∞,0) 194 : !$"$8%& !Q3ox& D?9&
40 ABCD 41 ABCD 42 ABCD 43 ABCD 44 ABCD 45 AI03F]|B!%&tz% =Q3XC{1<XDé%_ D"U 46 ABCD : W+$. R+P b:p3,?. !"Bç& 23XY>%& {Cx −x2 − yx = 2 105−10−15 : +h !%&(%& R3-. W63-,%& =dk%& IJ : W+$,%& !%&(%& gf#B !f#] {C (K>J \]3^ &_&f (x) = 2x2 + 5x + 3y !:8?. D"U !%&' =S,E W63-,%& I]3"V%& ="S,?%& : R38B|& l() y+]3. W63-,%& LK$K,%3Q !:S,,%& !%&(%& Ih \]3^ &_& : +h !%&(%& LK$K. auJ f (x) g(x) = | f (x) | : ;D?<%& 1.W l&(T?Z3Q !"B|& !)+,-,%& w?dB−5 ≤ x < − 2 x3y = 8y = | x |−y2 = − 4x [−3,∞)[−4,∞)[−3, − 2) ∪ (−2,∞)(−4,∞) : {63@B auJ \]3^ &_&f (x) = 4x,0 ≤ x ≤ 15 60,15 < x < 24 −x + 15,24 ≤ x ≤ 40 f (25) (0,3)(3,0)(0,2)(0, − 3) [−5, − 2)(−5, − 2](−5, − 2)[−5, − 2] 195 : !$"$8%& !Q3ox& D?9&
47 A!E'DJBCD 48 ABCD 49 ABCD 50 ABCD 51 ABCD 52 ABCD 53 ABCD 54 ABCD L,s) !,"X6 (K) ;("P6 !":$. eDv5 !,"X 3F% a3^6 L:) !:8?. !%&' \]3^ &_& : É"$5 I%3?%& {HJ N (K) ;("P6 !":$. f (x)Rx = 3 x = − 2 : ;D?<%& IJ !%&(:% D"v?%& R(>. [Z+?. (o6Cx2 − 4x + 6[0,6] : !%&' !%&(%&f (x) = x5 + 3x3 − x IJ !8X3K?.6 IJ ;(E&1?.6 ;D?<%& IJ !:8?. !%&(%& \]3^ &_& : (K) !":$. L,s) !,"X 3F% auJ f (x)[−2,10](−2,3) ∪ (7,10) (3,7)f (x)x = . . . . . : (K) !:8?. !%&(%& =>-B I?%& \Q3S%& !,"X 3,J \]3^ &_&f (x) = { 2x2 + a, x ≥ 2 x + 5,x < 2 ax = 2 \]3^6 `% l*& !%&(%& Ih !%&(%& \]3^ &_& : {63@B auJ f (x)g(x) f (x) = x2 g(x) /. !fZ+?,%& !)D@%& auJ !%&(%3Q Lf>AB g<BD. a3d. /. [X3Z }@o 3F>f#E I?%& !J3@,%& : !"]3p L%M ;D?<%& d(t) = 16t2 02 3%6 !E'DJ \@"% !"o6t !"o6t!"o6t6 !E'DJ limx→∞ f (x) = − ∞ 624210 !%&(:% D<5 (o+E ;D?<%& IJ[−2,3] L,s>%& !,"#%& eDv8%& !,"#%& >!"o6t !%&(%& 37 −11 x2 + 2x2 − 2 64 : !%&(:% l*& !"@"0D%& !%&(%&f (x) = 1 x − 1 + 2 f (x) = x2 f (x) = x3 10−2 −2−1 x2 + 4x + 2x2 − 4x + 2 320−32 f (x) = xf (x) = 1 x 196 : !$"$8%& !Q3ox& D?9&
55 ABCD 56 ABCD 57 ABCD 58 ABCD 59 ABCD 60 ABCD 61 ABCD 62 ABCD : =Q3#,%& =dk%& IJ !:S,,%& !%&(%& W3<5C : Ih !%&(%& W3<5Cf (x) = − 2 3 x − 12 : {63@B =Q3#,%& =dk%& L:) è'3,?)&h(4) : =Q3#,%& =dk%& IJ !:S,,%& !%&(:% gf#,%&y R+P Ñ3d>]& }p W3@":% /"B(P6 Ç3$@]3Q !%&(%& LK$K. /. ã?KE LK$K. a3^ &_& : !%&(%& =S,E I:E 3,. {HJ =<Z*& L%M 2&(P6 áYp Ç3$@]& }p W+$. g(x)f (x) = x xg(x) : !%&' =S,E !:Q3#,%& !%&(%& IJ I]3"V%& ="S,?%& : W63-,%& =dk%3Q !:S,,%& !%&(:% !#:f,%& eDv8%& !,"#%& 14!JD>. D"U 0,1,5 −18−121218 0,2,60,8, − 8(o+E3% −20 g(x) = −x + 2 − 3g(x) = − x + 2 − 3 (K) !:8?.x = 3(K) !:8?. D"U {1<X R38B& l() x = 3 −7 : (K) !%&tz% =Q3X R38B& l() 3F% !"%3?%& R&6(%& /. {Cx = 2 f (x) = x2 − 4 x − 2 f (x) = x2 + 4 x − 2 −1 (K) !:8?. D"U !%&tu:% =Q3X R38B& l() x = 3(K) !:8?. D"U I03F] 3% R38B& l() x = 3 12 g(x) = − x − 2 + 3g(x) = x + 2 − 3 36~'+o+. D"U f (x) = x2 − 4 x + 2 f (x) = x − 2 197 : !$"$8%& !Q3ox& D?9&
63 ABCD 64 ABCD 65 ABCD 66 ABCD 67 ABCD : {63@E auJ \]3^ &_&f (x) = x2 + xg(x) = 9x( f + g)(x) : I]3"V%& ="S,?%& IJDm +:Z 48E I:E 3,. {C : R3-. auJ N \]3^ &_&g(x) = xf (x) = x2 + 4( f g )(x) x2 + 10x lim x→+∞ f (x) = ∞ lim x→−∞ f (x) = ∞ lim x→+∞ f (x) = − ∞ lim x→−∞ f (x) = ∞ lim x→+∞ f (x) = ∞ lim x→−∞ f (x) = − ∞ lim x→+∞ f (x) = − ∞ lim x→−∞ f (x) = − ∞ x2 + 8xx3 + 10xx2 + 9x : {63@E auJ \]3^ &_&f (x) = x2 + xg(x) = 9x( f . g)x 9x2 + 9x9x3 + 9x9x3 + 99x3 + 9x2 (−∞,0](−∞, ∞)[0,∞)(0,∞) : +h R3-. auJ N \]3^ &_&g(x) = xf (x) = x2 + 4( f − g)(x) (−∞,0](−∞, ∞)[0,∞)[0,∞) 198 : !$"$8%& !Q3ox& D?9&
23Q3ox& É"B3<. 12345678910 AABBCABBCC 11121314151617181920 CDDDCBDAAA 21222324252627282930 BCBBACDBCB 31323334353637383940 DAAAAABACD 41424344454647484950 CBAACAABCA 51525354555657585960 ACBDABADBD 61626364656667 AABADDC 199
200
23VEW(B6 !:qZC 1 ABCD 2 ABCD 3 ABCD 4 ABCD 5 ABCD 6 ABCD 7 ABCD 8 ABCD 9 ABCD 10 ABCD : =>-B I?%& !,"X (o6C \]3^ &_&f (x) = 2xn − 16nf (2) = 0 9 : !,"X 3,J \]3^ &_&9x+2 = 3x+7 x : {63@B auJ \]3^ &_&logx81 = 2x : !,"X 3,J \]3^ &_&logx(32) = 5x : ìJ3dB !"Z*& ;W+8%&53 = 125 : !KE3V?,%& =P 3.2x+2 > 1 64 : !"ZC L%M !"%3?%& !",?EW3U+:%& ;W+8%& R+Plogxy = k : !,"X3.log25 + log24 = . . . : !,"X3.log1255 : I:E 3,"J !,"X 3.x3x−1 = 27 81273 3425 2345 12532 log5125 = 33log5 = 125log53 = 125log2125 = 5 x > − 8x > 8x < − 8x > − 4 xk = yyx = kk x = yky = x log220log420log2 5 4 log4 5 4 1 3 1 232 5432 206 : !$"$8%& !Q3ox& D?9&
11 ABCD 12 ABCD 13 ABCD 14 ABCD 15 ABCD 16 ABCD 17 ABCD 18 ABCD 19 ABCD 20 ABCD : I:E 3,"J !,"X (o6Cx26x−3 = 8−3 x ≥ 32 : I:E 3,"J !,"X (o6Cx6(4x−2) = 36 : !KE3V?,:% !"Z*& ;W+8%&log2x ≥ 3 : !%'3>,%& Å#$B I?%& !,"X (o6&x1 + 2log2(x + 1) = 5 : W&(#,%& !,"X 3.log2781 = . . . . : !,"X3.log2 1 32 : W&(#,%& !,"X 3.log464 : W&(#,%& !,"X 3.log 1 6 1 216 : W&(#,%& !,"X3.log313 − log35 : !,"X 3,J a3^ &_&log392−x = 0x x ≤ 32 x ≥ 23x ≤ 23 −14121 5461 3−312 1 8 4 3 5 36 1 3 5−51 5 − 1 5 41639 1236 log513log3 13 5 log135 13 5 12−1−2 207 : !$"$8%& !Q3ox& D?9&
21 ABCD 22 ABCD 23 ABCD 24 ABCD 25 ABCD 26 ABCD 27 ABCD 28 ABCD 29 ABCD 30 ABCD : !%&(%& R3-. /")f (x) = log x2 − 4 log5 5 2x − 5 : !,"X3.log100010 : {63@E W&(#,%&2log5x − log5(2x − 5) : !f#K%& IJ W+$,%& gf#E !"Z*& !%&(%& LK$K.f (x) = ( 1 2 )x y : !",?EW3U+:%& !%&(:% gf#,% 3.yf (x) = log2(x + 1) + 3 : !%&(%& e(.f (x) = log3x : ;W3V>%& !,"Xlog2(log2x24) − log2(log2x3) : !KE3V?,%& Å#$B I?%& !,"X 3.x(9)x−2 > ( 1 27 )x : auJ O"$Q \]3^ &_&f (x) = logx1 ≤ x ≤ 10 : !%'3>,%& Å#$B I?%& !,"X3.x 2 −41−x = − 2 log5 2x − 5 x2 log5 x2 2x − 5 log5 x 2x + 5 {x | x ∈ R − [−2,2]} 3 1 3 − 1 3 −3 (0,0)(0,1)(1,0)(1,1) 3210 R[3,∞)R+W 2348 x < − 2x > 3x > 4 5 1 ≤ f (x) ≤ 10 21−1−2 {x | x ∈ R − (−2,2)}{x | x ∈ R − [−2,2)}{x | x ∈ R − (−2,2]} x < 4 5 0 ≤ f (x) ≤ 10 ≤ f (x) ≤ 1010 ≤ f (x) ≤ 100 208 : !$"$8%& !Q3ox& D?9&
31 ABCD 32 ABCD 33 ABCD 34 ABCD 35 ABCD : !KE3V?,%& Å#$B I?%& !,"X 3.x( 1 2 )x − 1 8 < 0 2 :: !",?EW3U+:%& ;W3V>:% !qJ3d,%& !"Z*& ;W+8%& 3.log100 = 2 : !%'3>,%& Å#$B I?%& !,"X 3.x7x−1 + 7 = 8 : !",?EW3U+:%& ;W3V>%& !,"X3log3(9) − log5 1 25 : !%'3>,:% c YP =S,E I:E 3,. {Clog4x − log4(x − 1) = 1 2 145 x < − 8 100 = 102100 = 210 10 = 1002 2 = 10100 121084 − 1 2 1 2 −22 x < − 3x > 1 2 x > 3 209 : !$"$8%& !Q3ox& D?9&
23Q3ox& É"B3<. 12345678910 AABBAAAAAB 11121314151617181920 CADABBCCBB 21222324252627282930 CABBAABCBB 3132333435 BDACD 210
211
: 1sin 𝜃 = − 1 2 180° ≤ 𝜃 ≤ 270°........sec 𝜃 A1 3 B√3 3 C − √3 2 D − 2√3 3 2𝑐𝑜𝑠 𝜃 = 1 3 270° < 𝜃 < 360°𝑠𝑖𝑛 𝜃 = A2√2 3 B − 2√2 3 C√2 3 D8 9 3𝑠𝑒𝑐 𝜃 = 13 12 0° < 𝜃 < 90°....................𝑠𝑖𝑛 𝜃 = A5 13 B13 5 C5 12 D12 5 4𝑐𝑜𝑡 𝜃 = 30° < 𝜃 < 90°..............𝑡𝑎𝑛 𝜃 = A 3 B1 3 C√10 3 D3√10 10 5sec 𝑥 𝑐𝑠𝑐𝑥 = ⋯ A𝑡𝑎𝑛 𝑥B𝑐𝑜𝑡 𝑥C𝑠𝑒𝑐 𝑥D1 6𝑠𝑖𝑛 𝜃 𝑡𝑎𝑛 𝜃 .............. ABCD 7𝑐𝑜𝑠𝜃 𝑐𝑠𝑐𝜃 𝑡𝑎𝑛𝜃 A𝑠𝑖𝑛𝜃B𝑡𝑎𝑛2𝜃C𝑠𝑒𝑐2𝜃D𝑐𝑜𝑡2𝜃 8sec2𝜃 − 𝑡𝑎𝑛2𝜃 = ⋯ A−1B0C0.5D1 9𝑠𝑒𝑐𝜃 𝑠𝑖𝑛𝜃 (1 − 𝑐𝑜𝑠2𝜃)............. A𝑐𝑠𝑐𝜃B𝑐𝑜𝑡𝜃C𝑡𝑎𝑛𝜃D𝑠𝑒𝑐𝜃 10𝑐𝑜𝑠𝜃 1−𝑠𝑖𝑛2𝜃 A𝑐𝑠𝑐𝜃B𝑐𝑜𝑠𝜃C𝑡𝑎𝑛𝜃D𝑠𝑒𝑐𝜃 215
11(1 − 𝑠𝑖𝑛𝜃)(1 + 𝑠𝑖𝑛𝜃)...... A𝑐𝑜𝑠2𝜃B𝑠𝑖𝑛2𝜃C𝑡𝑎𝑛2𝜃D𝑠𝑒𝑐2𝜃 12......𝑐𝑠𝑐2 𝜃 − 𝑐𝑜𝑡2𝜃 = A−1B1C𝑡𝑎𝑛 𝜃D𝑐𝑜𝑡 𝜃 13𝑡𝑎𝑛2𝜃 ( 𝑐𝑜𝑡2𝜃 − 𝑐𝑜𝑠2𝜃) A𝑠𝑖𝑛2𝜃B𝑐𝑜𝑠2𝜃C𝑡𝑎𝑛2𝜃D𝑐𝑜𝑡2𝜃 14𝑐𝑜𝑠𝜃0 < θ < π 2 A 𝑐𝑜𝑡𝜃 𝑠𝑖𝑛𝜃 B 𝑡𝑎𝑛𝜃 𝑐𝑠𝑐𝜃 C1 − 𝑠𝑖𝑛2𝜃 𝑐𝑜𝑠𝜃 D𝑐𝑜𝑠𝜃 𝑐𝑜𝑠2𝜃 + 𝑠𝑖𝑛2𝜃 15𝑡𝑎𝑛2𝜃+1 𝑡𝑎𝑛2𝜃 A𝑡𝑎𝑛2 𝜃B𝑐𝑜𝑠2 𝜃C𝑠𝑖𝑛2 𝜃D𝑐𝑠𝑐2 𝜃 16𝑠𝑒𝑐𝜃 𝑡𝑎𝑛2𝜃 + 𝑠𝑒𝑐𝜃 = ⋯ A𝑠𝑒𝑐3𝜃B𝑐𝑠𝑐3𝜃C𝑡𝑎𝑛 𝜃D𝑐𝑜𝑡 𝜃 17𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃 𝑡𝑎𝑛𝜃 + 𝑐𝑜𝑠2 𝜃 = ⋯ A−1B1C𝑐𝑜𝑠𝜃D𝑡𝑎𝑛2𝜃 18𝑠𝑖𝑛15° ABC√6 − √2 4 D√6 − √2 2 19𝑠𝑖𝑛 15° 𝑐𝑜𝑠45° + 𝑐𝑜𝑠15° 𝑠𝑖𝑛45°............................. A√3 2 B1 2 C − √3 2 D − 1 2 20𝑐𝑜𝑠 45° 𝑐𝑜𝑠15° + 𝑠𝑖𝑛45° 𝑠𝑖𝑛15° A√3 2 B√2 2 C1 2 D1 21𝑠𝑖𝑛(60 ° + 𝜃) 𝑐𝑜𝑠𝜃 − 𝑐𝑜𝑠 (60 ° + 𝜃)𝑠𝑖𝑛𝜃 A1 2 √3C2 √3 D√3 2 √6 + √2 4 √6 + √2 2 216
22𝜃0 < θ < π 2 𝑠𝑖𝑛−1(𝑐𝑜𝑠𝜃) = 𝜋 6 Aπ 3 Bπ 6 Cπ 4 D5π 12 23𝑆𝑖𝑛−1(𝑐𝑜𝑠72°) A72°B18°C38°D108° 24𝑠𝑖𝑛𝑥 = cos 50°𝑥 = ⋯ A10°B40°C50°D90° 25cos 𝜃 = 3 5 270° < 𝜃 < 360° cos 2𝜃 A − 24 7 B − 7 25 C7 25 D − 24 25 26𝑠𝑖𝑛𝜃 = 3 5 𝜋 2 < 𝜃 < 𝜋𝑠𝑖𝑛2𝜃 =. . . . . .. A − 24 7 B − 7 25 C7 25 D − 24 25 27𝑡𝑎𝑛𝜃 = −2270° < 𝜃 < 360°𝑐𝑜𝑠2𝜃 = ⋯ …. A − 4 3 B3 5 C√3 2 D − 3 5 28cos 𝜃 = 3 5 270° < 𝜃 < 360° cos 𝜃 2 A√5 5 B − √5 5 C 2 √5 5 D −2 √5 5 29cos 𝜃 = 1 2 0° < 𝜃 < 90° sin 𝜃 2 A√3 2 B√2 2 C1 2 D1 4 30𝑡𝑎𝑛𝜃 = 2𝜋 < 𝜃 < 3𝜋 2 𝑡𝑎𝑛2𝜃 = ⋯. A1BC√2 2 D − 4 3 31cos4𝜃 − 𝑠𝑖𝑛4𝜃......................... A𝑠𝑖𝑛2𝜃B𝑐𝑜𝑠2𝜃C𝑐𝑜𝑠𝜃D𝑐𝑜𝑡𝜃 3 4 217
32(𝑠𝑖𝑛𝜃 + 𝑐𝑜𝑠𝜃)2 = ⋯ ⋯ A1 + 𝑠𝑖𝑛2𝜃B1 + 𝑐𝑜𝑠2𝜃C𝑐𝑜𝑠2𝜃 + 𝑠𝑖𝑛2𝜃D𝑐𝑜𝑠2𝜃 − 𝑠𝑖𝑛2𝜃 33𝑠𝑖𝑛15° 𝑐𝑜𝑠15°.................. A2 − √3 4 B2 + √3 4 C√3 − 2 4 D1 4 34sinθ + cosθ = 7 5 0° < θ < 90°sin2θ.................. A3 4 B8 25 C24 25 D5 7 351 − 2sin2 𝜋 6 = ⋯ A1 2 B√3 2 C√2 2 D0 36𝑠𝑖𝑛𝜃 − 𝑐𝑜𝑠𝜃 = 1 A0°B90°C180°D450° 37𝑐𝑜𝑠𝜃 = 20° ≤ θ ≤ 360°................ A0°B90°C180°D 38𝑠𝑖𝑛𝜃 = 1 2 0° ≤ θ ≤ 360°................ A30°, 150°B30°, 120°C30°, 45°D60°, 120° 39𝑡𝑎𝑛𝜃 = −10 ≤ θ ≤ 2π A7𝜋 4 B3𝜋 2 C5𝜋 4 D𝜋 4 40𝑠𝑒𝑐𝜃 + 2 = 0 𝜋 2 < 𝜃 < 𝜋𝜃 = ⋯ A60°B90°C120°D240° 413 cos2 𝜃 − 4 𝑐𝑜𝑠𝜃 = 00° < θ ≤ 180° A30°B90°C30° , 330°D 42𝑠𝑖𝑛2𝜃 = 𝑐𝑜𝑠𝜃0° < θ < 180°.......................... A30°B30° , 120°C30° , 90°D30° , 90° , 150° 218
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220
12 ( 4) 8( 3)x y− = + A( 4 , −3)B( −4 , 3)C( 4 , −1)D( 6 , − 3) 22 ( 4) 8( 3)x y− = + A( 4 , −3)B( −4 , 3)C( 4 , −1)D( 6 , − 3) 32 ( 4) 8( 3)x y− = + A𝑥 = 4B𝑥 = 6C𝑦 = −3D𝑦 = −5 42 ( 4) 8( 3)x y− = + A𝑥 = 4B𝑥 = 6C𝑦 = −4D𝑦 = −5 5(𝑦 − 5)2 = 8( 𝑥 − 3 )........... A6B5C8D10 6𝑦 2 = 40 𝑥 A𝑥 = −10B𝑥 = 10C𝑦 = −10D𝑦 = 10 73,5𝑦 = 1.................. ABCD 8𝑥 2 = 144 𝑦 A144B72C36D12 9(−2 4)(−2 7) A(𝑥 + 2)2 = −12( 𝑦 − 4 )C(𝑦 − 4)2 = 12( 𝑥 + 2 ) B(𝑥 + 2)2 = 12( 𝑦 − 4 )D(𝑦 − 4)2 = −12( 𝑥 + 2 ) 104,0𝑥 = −2 A𝑦2 = −12(𝑥 − 1)C𝑦2 = −12(𝑥 + 1) B𝑦2 = 12(𝑥 − 1)D(𝑦 − 1)2 = 12𝑥 11 ( 4, −1)𝑥 = 6 A(𝑦 + 1)2 = −8(𝑥 − 4)C(𝑦 + 1)2 = 8(𝑥 − 4) B(𝑥 − 1)2 = −8(𝑦 − 4)D(𝑦 − 1)2 = −8(𝑥 − 4) 225
12 A𝑥 = 5B𝑥 = − 5C𝑦 = 5D𝑦 = − 5 13 A(𝑥 − 6)2 = −4(𝑦 − 15)C(𝑥 − 6)2 = 4(𝑦 − 15) B(𝑥 + 6)2 = −4(𝑦 + 15)D(𝑦 − 6)2 = −4(𝑥 − 15) 14 ABCD 151,3 A(𝑥 + 3)2 9 + (𝑦 + 1)2 6 = 1 C(𝑥 + 1)2 9 + (𝑦 + 3)2 6 = 1 B(𝑥 − 1)2 9 + (𝑦 − 3)2 6 = 1 D(𝑥 − 3)2 9 + (𝑦 − 1)2 6 = 1 16(𝑥−2)2 9 + (𝑦−1)2 5 = 1 A(−4 , 1) , (0 , 1)B(0 , 1) , (4 , 1)C(1 , 4) , (1 , 0)D(0 , −1) , (4 , −1) 17(𝑥+1)2 9 + (𝑦+3)2 36 = 1 A3B5C6D12 18(𝑥−3)2 9 + (𝑦−1)2 16 = 1 A3B4C6D8 226
19(𝑥−3)2 9 + (𝑦−1)2 16 = 1................ A5B6C√7D11 20(5 , 8) , (−2 , 8 )................ A3B4C5D7 21................ AB3C4D6 2210 , 8𝑥 ................ A𝑥2 100 + 𝑦2 64 = 1 B𝑦2 25 + 𝑥2 16 = 1 C𝑦2 100 + 𝑥2 64 = 1 D𝑥2 25 + 𝑦2 16 = 1 23(−7 , −3) , ( 13 , −3)(−5 , −3) , ( 11 , −3) A(𝑥 − 3)2 10 + (𝑦 + 3)2 6 = 1 C(𝑥 − 3)2 36 + (𝑦 − 3)2 100 = 1 B(𝑥 − 3)2 100 + (𝑦 + 3)2 36 = 1 D(𝑥 − 1)2 100 + (𝑦 − 1)2 36 = 1 24(𝑥−3)2 25 + 𝑦2 16 = 1................ A𝑦 = 0B𝑦 = 5C𝑥 = 3D𝑥 = 4 25 𝑘 𝑥2 16 + 𝑦2 𝑘 = 1( 0 , 3 )................ A1B7C13D25 26𝑥2 25 + 𝑦2 16 = 1................ A(±3,0)B(±9,0)C(0, ±3)D(0, ±9) 227
27 A0B1 4 C1D9 5 28(𝑥−1)2 25 + (𝑦+5)2 16 = 1................ A4 5 B3 5 C5 4 D5 3 29 ABCD 300.5𝑥 A10√3B20√3C3√10D3√20 31𝑥2 16 − 𝑦2 9 = 1................ A3B4C7D8 32(𝑥−2)2 9 − (𝑦+1)2 16 = 1............. A(2 , 1)B(2 , −1)C(−2 , −1)D( −2 , 1 ) 3310 A𝑦2 9 − (𝑥 − 1)2 25 = 1 C𝑦2 25 − (𝑥 − 1)2 9 = 1 B𝑦2 9 − (𝑥 − 1)2 10 = 1 D𝑦2 10 − (𝑥 − 1)2 5 = 1 34(𝑥+2)2 4 − (𝑦−3)2 16 = 1............. AB4C8D16 228
35(𝑥+1 )2 9 − (𝑦−2 )2 16 = 1 A𝑥 = 1B𝑥 = −1C𝑦 = 2D𝑦 = −2 36(𝑦−1)2 9 − (𝑥+2)2 16 = 1............. A 𝑦 − 1 = ± 3 4 (𝑥 + 2) C 𝑦 − 1 = ± 16 9 (𝑥 + 2) B 𝑦 − 1 = ± 9 16 (𝑥 + 2) D 𝑦 − 1 = ± 4 3 (𝑥 + 2) 37( 2 , − 4)(7 , − 4)8 A(𝑥 − 2)2 9 − (𝑦 + 4)2 16 = 1 C(𝑥 − 2)2 16 − (𝑦 + 4)2 9 = 1 B(𝑥 − 2)2 9 + (𝑦 + 4)2 16 = 1 D(𝑥 − 2)2 16 + (𝑦 + 4)2 9 = 1 38( −1 , 2)2,1𝑦 − 2 = ±2𝑥 A 𝑥2 − (𝑦 − 2)2 4 = 1 C 𝑥2 − (𝑦 + 2)2 4 = 1 B𝑥2 4 − (𝑦 − 2)2 = 1 D 𝑥2 + (𝑦 − 2)2 4 = 1 39(2 , 0), (−2 , 0)12 A𝑥2 4 − 𝑦2 36 = 1 B𝑥2 2 − 𝑦2 6 = 1 C𝑦2 4 − 𝑥2 36 = 1 D𝑥2 2 − 𝑦2 6 = 1 40(𝑥+3)2 9 − (𝑦−1)2 7 = 1................ A4 3 B1 2 C2 5 D1 10 414𝑥2 + 𝑦2 − 3𝑥𝑦 + 4𝑥 − 5𝑦 − 8 = 0 ABCD 229
24𝑥2 − 3𝑦2 − 4𝑥 − 6𝑦 + 4 = 0 ABCD 43𝑐4𝑥2 + 𝑐𝑦2 + 2𝑥 − 2𝑦 − 18 = 0 A−8B−4C4D8 444𝑥2 + 𝑦2 − 4𝑥𝑦 + 4𝑥 − 5𝑦 − 8 = 0 ABCD 454𝑥2 + 𝑦2 − 5𝑥𝑦 + 4𝑥 − 5𝑦 − 8 = 0 ABCD 230
12345678910111213 ACDACACCBBAAA 14151617181920212223242526 DDBCDCDCDBADA 27282930313233343536373839 BBCBDBAACACAA 404142434445 ABCCAC 231