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S4 Revision Package

The document appears to be a mathematics examination paper with various questions covering topics such as algebra, geometry, and trigonometry. Each question provides multiple-choice answers, and the paper includes diagrams that may not be drawn to scale. It also emphasizes the importance of respecting copyright as it is a licensed material from the Hong Kong Examinations and Assessment Authority.

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22 views48 pages

S4 Revision Package

The document appears to be a mathematics examination paper with various questions covering topics such as algebra, geometry, and trigonometry. Each question provides multiple-choice answers, and the paper includes diagrams that may not be drawn to scale. It also emphasizes the importance of respecting copyright as it is a licensed material from the Hong Kong Examinations and Assessment Authority.

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Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Ms ivis ‘The diagrams in this paper are not necessarily drawn to scale . Choose the best answer for each questi Lays A. 10m. B10™ Ca, oe D. 39" 2 then 2 = ey A 2 4 3y-b a b=3y cy 3y-@ > a-3y 3. 16-@x~3y)? = A 4n2x~3y 4428-439). B. (4-2x~3y'4+2x-3p). ©. 42x 43y (442x439), D. (4~2x+3y)(4+2e~3y). 4, 00875402 = 0.087 (correct to 2 significant figures) B. 0.0875 (correct to 3 decimal places), ©. 0.08754 (correct to 4 significant figures), D. 0.087540 (correct to $ decimal places) > 5. Let f(x) =x° + 3x? + ax— 5, where a isa constant. When f(x) is divided by x + 1, the remainder is 4 Find the remainder when f(x) is divided by x +2. A 27 eae] cB D7 6. Let (x) be a polynomial. If fx) is divisible by x +3, which of the following must be a factor of J3x=1P Ax Bo x3 Cc wwe Dara JK The solutions of 2x(s~ 2) 5(3 ~x) are A. xg-3orx2? 2 [Goon the next 2016-S4-Final Exan-Maths2-P.2 2 XK How many integral solutions does the compound inequality x+3s3x-Land 3y~1<2y-+ Shave? A3 Ba cs D6 YE The soltons of 5-2 ors 3~ 2e are A xsi. B x<2, ©. -2srs1, D. xs-2orr2 1. 6 The figure shows he sraph ofthe quadratic Function y=f2) salvef/)* <0 A Isx<2 B l3 D. x 12, Ifa and f are the roots of the equation 2x? ~ 6x + a+ 2and +2? AL 2 14r+21=0 B. 27+ 14r—21=0 C. t+ lay +21 = D. 2x7-14x-21=0 ) which of the following equations has the roots 13, Which of the following quadratic equations has a double real root? A ¥-9=0 BP =8r- ©. SP exa1 D. =the +15 M4. Which of the flowing Fires can represent the gap of ae ax 432 dA fe 2016-84-Final Exam-Maths2-P.3 15, The figure shows the graph of y=—x" + 3x—m + 1, Pind the range of values of m. A met Bo m>i cmb . 1 D. pot tdeomt! 16, The figure shows the graph of the quadratic function y= fix). Find fix). A ate ayes yeh Bayes Cle aK t D. Fe+3}-4) 17. Ifthe graph of the quadratic function y =x" + by +e passes through (3 ,-8) and (-5 ,-8), then the equation of the axis of symmetry of the graph is =3 a 1 pomp 18. Which of the following can represent that y is @ function of x? L , 4, i | \ > * m, y WV. A. Wonly Bland Ilonly ©. Land IV only D.{, land LV only 19, The coordinates ofthe vertex ofthe graph of quadratic function are ¢ through (1,14) The quadratic function is 5) and the graph passes AL y= 9x 36e431 BL y=-9x" + 36x—31 ©. yas tay—t D. ye? 4x-9, 2016-S4-Final Exam-Maths2-P4 4 20, If and y are non-zero numbers such that (3y —4x) : @v +») =$ :6, then.x: y= A 7:8 B 8:29 c. 9:32 D. 13:34 21 2 2B, 24, 25. 2%, Itis given thats varies inversely as. If decreases by 20% then + A decreases by 25%. B. decreases by 56.25% C. increases by 25%. D. increases by 56.25% If varies directly as x and inversely as y*, which of the following must be constant? Ie is given that ais parly constant and partly varies directly as 62. When a=3,6= 1 and when a 82, Find the vae(s) of when a= -37, ae “20r3 ~3or2 “a0r3 pop It is given that varies jointly as Jp #1 and g When p =8 and q = 15, r= 5. Find the value of r when p= 3 and AL 9 B. 6 135 o 6 D. 12 In the figure, O is the centre of the citcle ABCD, The straight line BOD cuts AC at E and BOD is perpendicular to AC. IFAC = 6 and BD = 10, find the length of DE. a AL B 3 Cc 4 Dos ° z ° 4 D> In the figure, Q isthe centre of the circle ACDEB, AOB is a straight line. If ‘ZBOE ~ 60°, then ZAOC= A 30% BL 40" cso" DB. Go", 2016-S4-Final Exam-Maths2-P.s 3 27, In the figure, ACBD is a circle. AB and CD intersect at E. If ZCBE = 40° and ZBED = 15°, find BAD. A Aes Bans" Cc. 40 D. 75° 28. Inthe figure, two circles meet at P and Q. BPC and AQD are straight lines, If ZPCD = 104°, find ZPBA. A lod B76 Cc 37 ts ey 80° 50° 40° 44 30. In the figure, ABCis a circle. DE is the tangent to the circle at B and AB L DE. \f AC ~ 5 cm and ZCBD = 60°, find the diameter ofthe circle. 4 A. 10cm cay BN8 em CG. Sem BD. 2Sem . 31. Simplify J=23V=TE vv i pop> A Bo -15/2 Cc. isis D. -1sv2i 32, If'm isa real number, then A ol ets Co 1+ 2m D. -s—2mi 33, The LCM. of 9a°b, 12a‘b? and 15a is A 3a! B. 3o’b. C180 D. 1800"! 2016-$4-Final Exam-Maths2-P.6 6 6x9 ar Tex -9 35, Find the equation ofthe straight ine wth slope 1 and y-intrcept 5 A. x-2y-10=0 B. x+2y+10=0 ©. x-2y+10=0 D. x42y-10=0 36. Which of the following figures may represent the straight line L: ax + by +1 =0, where a+ b= and a>B? A c = x * B o. 37. Which of the following numbers is the smallest? ‘A 600" B. 400" Cc. 300% D. 200%" A. b+ 10-20 8 b+1-2a C. btina’. o. Mt, Fa 2016-S4-Final Exam-Maths2-P.7 7 39. log x then y= 40, ve of the following figures may represent the graph of y= 1.6"? Te Kit END OF PAPER “Title of the publication; [2016 HIRDSE Mathematics Compulsory Part Paper It Copyright owner Hong Kong Examinations and Assessment ‘Authority Date of making Wis copy: | 19” May 2016 "This material Ras been copied under a licence isued by the HKEAA, You are not permitted to make any further copy of this work, oF to make it available to other.__Itis important to understand and respect copyright 2016-S4-Final Exam-Maths2-P8 8 ‘The diagrams in this paper are not necessarily drawn to scale. ‘Choose the best answer for each question. Sei A 1 Se? Tay 2y" x= y AG yXSx+2y41) B.(x—y)(Sx+2y—D). Core yx 2y+0), D.Ge+yXSx+2y=) 2 (ga) A sil B, 2x5!" 2 7 2 ic) D. 3. 0.000 3021 = ‘A. 0.000 30 (correct to 2 significant figures). B. 0.000 302 (correct to 3 decimal places), €.0,000 3 (correct to 4 significant figures). 1D, 0,000 302 (correct to 5 decimal places). 4p 8542 then armas ae 7 3 2 ¢ ® 19 pe 4 stand 32-0) al munter, hen A.-1.25, B.-I ci D. 125. 6. The straight line J passes through the point (-2 , 1) and is perpendicular to the straight line 3x + 4y~7=0. The equation of L is A. dx + 3y +50, B.dx—3y+1 C.3x + dy +2=0. D.3x-4y+ 10=0, 7. Straight line Ly is parallel to straight line 1, and the y-intercept of L2 is twice the y-intercept of Ly Ifthe equation of Ly is 3x - 2y + 6 =0, find the equation of Ls A.2x + 3y-18=0 B.2x+3y-9=0 C.3x=2y+ 12-0 D.3x-2y+3=0 2017-8 4-MATHL-Final-Exam 2-2 2 8. Inthe figure, straight lines Ly and La intersect at a point on the negative x-axis, Which of the following is/are true? lL axe k I, bod ML be ad catty +b=0 A.Tonly B.Ilonly 7 C. Land I only 7 D, 1and Ill only perereeo 9. Leta be constant. Solve the equation 4x? = (x ~ a)? A orx=-f B.x=aory= 3a C.x=-aor D.x=-aorx=3a 10. Let k be.a constant. Ifthe quadratic equation 2x” + 4x + 5k=2 has real root(s), find the range of values of &. Ak< Boks Dks 2 3 4 a 3 11, Inthe figure, ABCD is a rectangle, where AB = 10 em and BC = 12 om. Eis a point on AD, where AE=x om, P and Q are points on AB and CD respectively such that AP = AE and DQ= ED. If the sum of the areas of AAEP and ADEQ is 40 em’, then A. 2+ (12-2=40, xem £ B. x +(12~x)'= 80, ° © ¥+(10-3'=40. D. x #(10—x)°=80. tok 12, Let fix) =12- 4x +3. Ifa) = 8, then a " A.-Lors. rar B.-1 or 3. C. Lor. D.lor3 13, Let kbe a constant, If f(x) = x° ~2x+3k then 3) =A) A.-12 0 C6 6k 14, If m and 1 are constants such that 4x°-+m(x—1) -28 = mx(e¥3)+n(ue4), then A8 B.-7 4 D6 2017-S.4-MATH-Final-Exam 2-3 15, The figure shows the graph of y = hx? ~~, where h and kare constants. Which of the following is true? A.h> Oand k> 0 fF pektask B.h>Oand k<0 C.h0 D.h cosy I, cos.x> cos y lsinx > sin y A.tand Ionly B. 1 and Ill only C. and IL only B.A Mand HL 2017-8 4-MATH-Final-Fxam 2-5 7 28, Which of the following quadratic equations can be formed from the roots k and —1? Axt4(1-By-k=0 B.xr+(k-Dx-k=0 CP + (1+ Rr +k=0 D.xt+(1+Kr—k= 0 29. Let kbe a constant. and flare the roots of the quadratic equation x? ~ 2x + k= 0. Ifa~ B= 4, find the value of k. Ad B.2 C2 D3 30, Which ofthe following statements about the graph of y = -x7 + dx — 5 istare true? I. The equation of the axis of symmetry of the graph is x = ~2, IL The coordinates of the vertex of the graph are (2 ,~1). L-The graph cuts the x-axis at two points A.lonly B.Ionly C.Land I only D.tand Il only 31, sandy ae posivenumbers then FE ae a °F 32. The figure shows the graphs of y= 0", y=a' and y = b on the same rectangular coordinate plane, where «and 6 are positive constants. The graphs of y=", y= a' and y"~ B* cut the yeaxis at the same point P. Which of the following isare true? I. The coordinates of P are (0 , a). MN, ab<1 TIL, The graph of y~ a" is the image of the graph of y = a" when reflected in the y-axis. A. ILonly B. Land Il only .Land IL only D.1and Il only 2017-S.4-MATH-Final-Exam 2-6 6 33. Which of the following is the best estimate of 3 465°? A101 B10" c. 100 D1 34, Let a and b be positive constants. If logs a+ 1 = 2 logs b, then 35, The graph in the figure shows the linear relation between logy x and logy y. If of aand k. Aa=4and k= 1 36. C. ogsy. psy 3 31. The L.CM. of 6x’y, 103 Auy. and 15x'y'zis Bugs C3094 D.30x% "2, 1 1 38 Fras * Fans © a (#3)a-5) —— GDE-9, © eS act, find the values loniy 39. In the figure, 4B is a diameter ofthe circle. DE is the tangent to the circle at C and BDL DE. IF ZABC = 40°, then CB 30°. B40", C.45°, D. 50° 2017-8 -MATHFinal-Exam 2-7 40, In the figure, Os the centre of the circle ABD. CB is the tangent tothe cirele at B and AODC is a straight line. IFAD = 4, find the length of BC. A2d BW ca Dias END OF PAPER, ‘Title ofthe publication, [2017 HKDSE Mathematics Compulsory Part Paper IL ‘Copyright owner: Hong Kong Examinations and Assessment Authorit Date of making this eopy: | 19 May 2017 ‘This material has been copied under a licence issued by the HKEAA, You are not permitted to make any further copy of this work, or to ‘make it available to others. It is important to understand and respect, copyright. 2017-8 4-MATH-inal-Exam 2-8 Swor> ‘The diagrams in this paper are not necessarily drawn to scale, Choose the best answer for each question. I 27") _ oa” AL 4 B. 4" cn D. an 2. 0.087542 = A. 0.087 (correct to 2 significant figures). B. 0.0875 (correct to 3 decimal places) C, 0.08754 (correct to 4 significant figures), D. 0.087540 (correct to 5 decimal places). 3. ifm +2n+6=2m—n=7, then n= AW4 B.-1 C3 Di 5. Miss 4h-17 3-h 4h-7 34h 4n-17 a+h Chan sells two cars for $ 80080 cach, She gains 30% on one and loses 30% on the other one. After 2 transactions, Miss Chan A. loses $15 840 B. gains $5 544 C. gains $10 296 D. has no gain and no loss. 2021-S4-MATH-Final-Exam-Paper 2 PS Goonto thenent page > 6 16 Qx—3y2= A, (4— 2x — 3y)(4 + 2x + 3y) B. (4—2x—3y)(4 + 2x - 3y) C. (4=2x + 3y)(4 + 2x + 3y) D. (42x + 3y)(4+ 2x - 3y) 7. Ifmisa real number, then the real part of (3 + mi)(1 ~ 2) is A, 342m, B. 3—2m. Cc. m-6 D. m+6 8. Find the imaginary part of | + 2/—3? + 4? — si. A. -2 B. -1 c 6 D. 9 9. Find the area enclosed by the lines x + y= 7, x—2y= 10 and the y-axis. A. 48.5q. units B, 64 sq. units C. 72.sq. units D. 965g. units 10. Ifthe straight lines 3x + 2y— find k. A. 3 B- Cc 6 D. Oand 4x — ky + 1 = 0 are perpendicular to each other, 2021-S.4-MATI I-Exam-Paper 2 Pa u 13, 14. 2021-S.4-MATH-Final-Exam-Paper 2 PS In the figure, the equation of the straight line Lis ax + by + 15 = 0. Which of the following are true? L a>b Y I. a>-3 3 mM, b>-S A. Land only B. Land Ill only C. Mand Il only D. 1, Mand til If +4 is a root of the equation +x? + kx + 12 = 0, find the other root. A. -3 B. 3 cea) D. -4 If the quadratic equation x? — (4k — 15)x + 4 = 0 has two distinct real roots, find the maximum integral value of k. AO B, cr D. era The figure shows the graph of y = —2x? + ax +b, where a and b are the constants. The equation of axis of symmetry of the graph is A x=2, y BL x=3. C. x=5. D. x=8. a 15. Suppose @ and Bare roots of ¥” +5x-2=0. Find a 28. a A. -29 B. 29 a 2 D. 29 4 : a +6a+3=0 : 16. Ifa and 6 are distinet real numbers, and} «find the value of a? + 6. b +6643 A. 25 B. 30 Cc. 35 D. 40 17, The base of a rectangle is 2x cm and the height is (4 — 2x) cm. The maximum area of the rectangle is AL dem? B. 6em’, Cc. 8em’, D. 10cm? 18, LetF(a)=8~3x,60)= V2v=3 and My FSD Find the value of H(2), Ga) A. -10 eel 2 cil D. 2 19, x + kx — 25, where k is a constant, If (4) = —37. find the value of k. 7 B. -I cot Dee7, 2021-S.4-MATH-Final-Exam-Paper 2 P6 20. Iffx+4)= 1 5x, then flx) = A Sx. B. 55x. C. -19- 5x. D. 21-5x. 21. Ifx’ + ke + 15x—4 is divisible by x + 4, then k= pomp 22. Suppose f(x) is a polynomial. If fx) is divisible by 3x ~ 7, then which of the following must be a factor of fix + 2)? A. 3x-7 Bo x+2 Cc. 3x-1 D. 3x1 23, 8173. 27? = AL gto B. 3h Cc get D. 385 24. Which of the following is the least? AL L1nytoe B. 2.229550 c. 3333800 D. 4.44q2s00 25. Ifa=log 3 and b = log 7, then top = A. 6+10-2a B. b+1-2a C b+. vp, 24, 2a 2021-S.4-MATH-Final-Exam-Paper 2 PT Goon tothe next logx+logyx 26. Simplify ees logx Bie BL 2 co 3 4 vp 3 8 27, Itis given that logs y isa linear function of logs x. The intercepts on the vertical axis and on the horizontal axis of the graph of the linear function are 7 and 8 respectively. Which of the following must be true? A, xyl=3% B. cc) D. yt = 3% 28. The relation between the intensity / W/m? and the intensity level D dB of a sound can be represented by the following formula: D = 10 log Pod If the intensity of a sound is increased by 170% when compared with the original intensity, what is the increase in the corresponding intensity level? A. 1434B B. 2.30dB C. 4314B D. 174B 29. The L.C.M. of a+ 4a+4,a?—4 and a+ 8 is A. at2 B. (a—2)(a+2)*(a? -2a+4) C. (@-2)(a+2)*(a? + 2a +4) D. (@-2)(a+2)*(a? ~ 2a +4) 2021-S.4-MATH-Final-Exam-Paper 2 P8 . 6 +9x+20 20. Simply Syaeata F-16846 A (x+2)(x-3) (x+ 6)(x+4) p 42043) (e+ (r+ 4) (x+2,00+3) (e+ 6)(x—4) D. 3. if 242 #9 _. find the values of the constants @ and b. x-5 xt+9 x7 +4x-45 A. B. Cc. D. 32, In the figure, OA // CB. If ZOAC = 25°, then ZAPB= A. 65°. 70°. = AD 33. In the figure, O is the centre of the semi-circle ABCD. If AC = BD and. 2COD = 48° then “ABD = 3 — 33° . az 4g gop> 2021-S.4-MATH-Final-Exam-Papet 2 Po Goon tothe next page > 34, In the figure, 74, 7B and PQ are tangents to the circle. If TP = 12 em, 7Q = 10 em and PQ= 8m, then BO= pop> dom, Sem, 5.5 om. 6em. A, yi 12cm a 10cm Q B 35. Inthe figure, AB: CD =3:2. If ZAMB=65°, then ZACB= pap 26°. 30°. 35°. 39°. 36. Inthe figure, BQ is a tangent to the circle. AP // BO and AB= AC. ZTAB = 108°. Find ZCBQ. A. B, G D. 32° 36° 48° 72° 2021-S.4-MATH-Final-Exam-Paper 2 P10 31. 38, 39, 40. In the figure, AB is a tangent to the circle. AO L OB, Od = 8 em and AB = 12 em. Find the radius of the circle. (Give the answer correct to 3 significant figures.) A. 4.47¢em A B. 5.96 em C. 6.71Lem N2cm D. 7.45 em i sin (180°—@) _ cos (270°) tan 225° sin330° A. -sin 0 B. 3sin0 C. sin 042008 0 D. sin 0-2cos 8 B cos10° + cos?20° + cos*30° + ... + cos*80° = iS 7) B. 4 Cc. 6 D. 8 Find the minimum value of (2 + cos @)(2—cos 0). A. B. Cc. D. End of Paper 2021-S.4-MATH-Final-Exam-Paper 2 PAL Goon tothe next page > yossay ee ¢—x nog sna BopMooY 2130 UM “T= ( ? “a * o>prea>? -¥ gona sr BoLMoTOS 30; Hmm pp 2a P94 re = ni gE et Zpor z- ideo soquna fast “a oot 22S ~cayoonsvny ajo uemop ag st Sumonoy AB ;O HSH *S = I Bassa A * = gton'9 = Y= (OY Svemsueg ase > pe gD 9 9+ r= CY £ sero fer a wap bax ermmter 9 © cere ber @ x10 nae pate fiery ‘om €+ x01~ 4 wonenbs apangos “¢ orretex a o=r-k-x 9 okex a ont-x ‘andy amy uy 7 aun wens jo uonenbe om pus -Z rmwpopSuumaaresi “a sequins Awuseus amd vstx “D aqui (Moone UE SI soda iwsts conn sr aymoys5 AA JOWPNM'D= PITH “T ‘yong ‘jams om fo sup am pay “uD Z= dO pu ub § BY HEY T dO POR Hod ew Mes ZY PEE JO "HIRO NHL ARTY MLL “st 2a oo ea 340-8 en 90 pan 99.7208 aossonxo psoesaip pu Worssan2 98 por >,q.am stossaxico 2053 30 WO'1H POE THOR “81 har 1 sud ov are at aon. tama e ee (+0-9) = ose) uni = pSoy‘m ms 81H “ST és0a o 44 @ v 2 pi go sydd ayqssod 39 saous Burmoros 9 30H ‘z= so qd om suosandor29 ro on pee 7 = jo ye om Sosa 1D aT a ° a y 0<¢fs00—0 om ocd un +0 ed ms0 509 gana og sa Suenos 9g} 30 Gong me Nesp uy sq pw IpINb UF aH 3 “ > 06 10} 900 = yo ei oon doen} M40 PHN FE rod > ‘a 9 Fp 10 9F ‘uo §1 ? ™ oma oct T ena am Founoqy 130 A, ‘onnoadsar 0 = 4-39 poe | = 40am ey pow 7 sou sens omy suoneno se NS up OL “CE 460K ‘30 ye Kove aoe soo und Ame OE, 191 ebo sb yo ye yeas a, “equimy yeare st ‘Gog sas Sumo OS so sory Ras anya Sab pm Essa sea ogame pes ¥eg @ 27 “ie ‘auon29g ‘Baworsg a J0 HUN ‘Lz ROH O YogEBsLUADOIE- AED ore » x Asoranis ang son 5p BHAT) 980 PH & sin) _2yeAinpesd saeeaioop euz0q fo qu a 2 . —— . ke @ v # 4 (8) - o> vom eH IC “a \ a * eee ees \-a097 Fe tst=0"7 ‘etstnasn gaan roe toons neo AE HE l= wor a 4 woyz A wet “@ 901° zt ¥ aL 8 ‘a 30 89] 2 pu WD Cf = 20 cos pu mo = 40 = gO ‘sou Breas om a9 paw gay ‘spa jo anus Amn 308 210] “OE ‘Do47 pra’.95 = 407 Wwe 0° = ¥407 ‘sennsadsas rpm ‘yw ara om or BEN om a SG PUR Ou ‘xg ADF amma O ‘ANB ANT] “Fe } a aks : 2 4 ”, aca a9 caKe oe x messtet ‘d¥ Jo 909 a9 PUL ZI = OY PUR 9=GO‘L=ad So ET sqydus “61 ‘pasmodsan pam 3 3s HHO: Poe OY GY MMOL aU “EL ea” oat Ce ep 5 in seg Ky w senbypma a 30 pete pm ae eet OF 15 PoE 1 atm 6 Asp poe Ay ur pumoo ya) yenbuwe a jo sopMENTS esx 2m SY + Y Bo] m sad two} a Kg Fousasdas 94 oo posnsroW ORE, ‘onus Jo my aprudam og pu axenbapae we Jo Jy apron am Uoouoq UOURATOA, era fe 9 ue 8 Tey apm => oo apm 5=0 3, apm 6-20 8 neg pur = oy f wp (GYJosmone am ¢ + pm Z— xj sumsUOD eg pur Dam OE —H9 — a4 = VT eD(or+e) “a wo (ne4) y se ova aus um 7 >> 0p mos aod eto aayn Kara Toy wa a9) an ram pon ance presence Pe ae ee ve 0 0 70t- °O >a 7 Vv ‘seu 251 qi’) = $¢— 4 + -ruonenbo aneipenb ayn 0 noes aM 2a HED BT “ee o>o0>9 a o<0>" o>d:0<¢ & o<20e8 V vou 0 9 + Ag +3517 oun Bens ajo worenbs aj SY AR BT TE ratwr=s ¢ ber 3 a o-* ¥ ip equine Area amndw 51 1(¢~—) + (p~ 251 OqUMU OEE aq=I2T “IE quonoes sesnqucog eonuop! z put sift essreymbo (eantOD! gz JOESHCD MOIRA AIT oy ann st Suymonoy 0930 oH Popes ase sasngmo Om ay 42009 0= +080) HSS (F~ 06) HZ vopenbs axa soap moor ump Kms NOY .09E 50560204 “FC side jo pug 1 2 wa ae 2 wt oe ov 30 srupes mn py '9 = 79 DUR 02 ~ OD 11 BF HL “pal ho siaoRue 3i9 am 3 pu Daya SmBU AM YL Ty ‘Da 30 wogenba x9 pus 04 406 nom UT a NOgE ssucqpop PRION MN fg fot NH amp UH pa‘ayar eT Y"(G-* ¢) ale Y JO STEMS DU], “sy oy sofa nam ya pur SERB lo 8 r é sc =o 00 90 = 451 ao + “oy pan xwoong woumas 2 ag sno ily an UB “OF £ cee a 4 z € ou a z ¢ Tames a SEEM SARTORI SE EI+9 BOL 08 9 soe JO SEA Pi CEE OPN jo ones une a PE NERC PE “th aerial oat ae 2021-2022/F/R.4/Mths./2/22 * ‘The real part of 2i7* + 3173 + 5i7* + 7475 is A -3 a i Cee D. 10. 2 , which of the following are Let 2 = 22% , where @ is a real number. If w, = +5 and we = true? 1 wy isaxeal number. TI, The real part of wz is equal to 0 TH. The imaginary part of z is equal to the imaginary part of +. A. Tand only B. Land Ill only C. Wand It only D, 1, Mand II In the figure, the equation of the straight line L is ax+by+¢=0 . Which of the following are true? a y L se L mw ¢<0 ml. £<0 O = A. [and only B. TandIifonly C. Iand II only D. I, Wand WL If the two straight lines ax—y+1=0 and 2x+3y+b=0 have infinitely many points of intersection, find the values of a and_b. A. Zand b B, and b= c and b= 2021-2022/F/R Maths 2/23 In the figure, A, B and C are points on a rectangular coordinate plane. AC and BC are parallel to the y-axis and x-axis respectively. If the coordinates of C are (1,—2) and the equation of the straight line AB is x+2y—3=0 , find the distance between A and B. ew > a o a ‘The equation of the straight line Ly is x-+2y —6=0. The straight line Lz is perpendicular to Ly and intersects L, at a point lying on the x-axis. Find the area of the triangular region bounded by Ly, Iq andthe y-axis, A. 12 B15 Cc. 45 D. 90 aand f are the roots of the equation 2x* ~ x + 2 = 0. The quadratic equation with two roots —* and A. 2x?@-x4+2=0 BL 2x*+x—-2=0. C. 2xt+x4+2=0. D, 2x*-x-2=0. The driving speed of Mr Chan is (x +$) km/h, He can drive 100 km in (x — 10) h. Find the value of x. A 10 B. 15 (csa20) D. 25 10. i. 12, 2021-2022/8/F.4/Matbs./2/P.4 If the quadratic equation kx? + 8x + (8 — k) = 0 has one double real root, find the value of k. A. B. ic ene D. If g(x) = x3 + 2x? +2 , then g(—2) + g(2) A. -12. B. 0. clea D. 20. Tf f(e—1) =x? + 2x-4 , then f(x) = was. x?42x-4. oe > xt +2x-3 xt 4x1 S The figure shows the graph of y= —2x*+ax-+b, where a and b are constants. The equation of the axis of symmetry of the graph is ” Bs? hax AS ca peBttarth 5 ——s, B. x=3 olf CG xat, 2 Do x57. 1B. 2021-2022/F/R A/Maths /2/PS Ifthe minimum value of y = 4x? + 16x +d is —15, find the value of d. At B. 10 G12 D. 15 14. If 0 q > 0.If log(p + q) =x and log(p — q) = y, then log yp? — q xy ae x B. 2 C. fery D. Jxy. Which of the following is the greatest? A. 23538 B. 3525% cc. 523258 D. 53275 If 10% = 2 and 10” =7, then log2, = A. b-a-2 B. b+a-2 > Qs > dD = 9 9 BP 1 4 25. 2021-2022/8/R.A/Maths 2/P.8 The figure shows the graph of y =logax and the graph of y = logy. on the same rectangular coordinate system, where a and b are positive constants. If a vertical line Z cuts the graph of y =loggx , the x-axis and the graph of y = logy x at the points A, M and B respectively, which Of the following are true? Looa>i y IL ab>1 rasta m. f= logab A. Land Il only 0 B, and IM only C. Mand If only D. 1, Mand Il 27. The H.CF. and L.C.M. of three expressions are 2x*y? and 36x5y® respectively. If the first expression and the second expression are 2x*y? and 12x°y? respectively, then the third expression can be AL 18x7y5 . B. 18x5y, C. 86x5y7. D. 36x7y® 2021-2022/R/R4/Maths./2/P.9 28. In the figure, OPSTQ is a quadrant. QS and PT intersect at R If P3:5P: FO +3, find ZPRQ P ‘A. 108° es, B. 120° Cc, 135° D. 144° @ lO 29, Inthe figure, AB =8 cm, BC = 17 cm, ZABC = 90° and DCE correct to 1 decimal place. B A. 39 cn B. 4.9 om A Cc 75 cm D. 94am ic D 30. In the figure, ABCD is a circle. AC and BD intersect at £. It is given that AED = 82° If AB =BC and BA // CD, then 2CBD = A. 33° B. 41° Cc. 49°, D. 57° 31. In the figure, AD is a diameter of the circle ABCD. It is given that PBCQ is a straight line. If AD = 60 cm and BC = 48 cm, then AP +DQ 24 om 36 cm 48 cm. 60 cm. eow> S 32. 33. 34, 35. 2021-2022/R/F.4/Maths/2/P.10 ° Inthe figure, ABE and DCE are straight lines. AB isa diameter of the circle and AD = CD . If ZAED = 24°, find ZACD . D A. 33° B, 36° G, Cc. 38° 5 — A D. 57° In the figure, AD is the altitude of AABC . E and F are the points on AB and AC respectively such that AB 1 DE and AC 1. DF . Which of the following are true? 4 1, AEDF is acyclic quadrilateral. I. B,C, F and E areconoyclic. Mil, If M isthe mid-point of AD , then M is the cireumcentre of AEF. F 2 Dp c Tand II only Land III only Mand If only 1, Hand It Soup In the figure, O is the centre of the inscribed circle of AABC If 2AOB = 114°, find 2ACB A. 33° a a In the figure, AD and CD are tangents to the circle at A and C respectively. AB is a inser of the circle. AB produced and DC produced meet at F . If AD =15 cm and CE = 10 cm, then A. Sem B. 7.5 om. Cc. 10m D. 15 om as S 36. 37. 38, 39. 2021-2022/R/R 4/Meaths./2/P.11 In the figure, two circles touch each other externally at one point, where A and B are the points of contact. AB is the common tangent to the two circles. If the radius of the larger circle is 9 om and AB = 12 cm, find the radius of the smaller circle. A. 3om B. 40m C. 6 om D. 7.5 cm If sin@cos@ <0 , then @ may lie in quadrants A. LorlV B. Worlll. Cc. Morlv. D. Iorlv. For 180° < 6 < 360°, the greatest value of 1 +3 sin(180° + @) — 4cos(270°— 6) is pomp ao If A+B = 180°, which of the following must be true? L sind=sinB Il, cosA =sinB UI. cosA = cosB A. Tonly B. only C. Tend Ill only D. Mand Il only For 0° < @ < 360°, how many roots does the equation 2 sin@ = tan 0 have? ae he C4 D. 5 END OF PAPER

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