2015 CSEC Mathematics P1 #2-1

"ib, rEsr coDE 01254010 FORM TP 201s036 MAY/JIJNE 2OI5 CARIBBEAN EXAMINATIONS COUNCIL CARIRBEANSECONDARY EDUCATION CERTIFICATEO EXAMINATION ADDITIONAL MATIIEMATICS Paper 0l - General Proficiency I how 30 minutes 08 JUNE 2015 (p.m.) READ THE FOLLOWING INSTRUCTIONSCAREFULLY. l. This test consists of 45 items. You will have I hour and 30 minutes to answer them, 2. In addition to this test booklet, you should have an answer sheet. Each itein in this test has four suggested answers lettered (A), (B), (C), (D). Read each item you are about to answer and decide which choice is best. 4. A list of formulae is provided on page 2 of this booklet. ). On your answer sheet, find the number which corresponds to your item and shade the space having the same letter as the answer you have chosen' Look at the sample item below. Samole ltem (4-'1'1+ll-l= \to_,/ (A) 4-2' Sampl.e Answer (B) 4r (c) 40 (D) 42 @@o@ 's (40"' so (C) has been shaded. The best Bnswer to this item 6. lfyou want to change your answer, erase it completely before you fill in your new choice. when you are told to begin, tuni the page and work as quickly and as carefully as you can. 7. If you cannot answer an iiem, go on to the next one. 3. You may use silent, non-programmable calculators to answer items' I DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO' 4 cos Btcosl sin B cos (l + B) = cosl cos BFsin I sin B tun{exn)=fiffi Differentiation $-{ox+tY--or(ax+ b\l Ssir.+2fx+zgt+c=O (x+fl7+(1t+g)2=f pt = {trl +l) wherev=xi+. l(x. Lft. ' _!- S r-2 i= I'. P(A B) Probability ^ Kinematics V=U+At f=*+2as s= ut+ *aF GO ON TO THE NEXT PAGE rnra: 't. i-l n > f.l)d s.tl < .= a + (n .t:"ot" = -oin f "or.= + (n. '--I .-t)' S2=J=-= /rJ i'i . P(A w B) = P(A\ + P(E) .(J )- Statistics '-.r.LISTOFFORMULAE Arithmetic Series 7.r)dl +lza T=aft ^ sr=--=T- a(t"-l) S : a . -l <r< I or lrl <l Geometric Series ' | -r' Circle *+).Yj Vectors lvl "orA=ffi Trigonometry sin (l + B) = sin. = -j:j- " i. 4. lff -6r + l3 = a (. The set of values of x for which 3x+2> x-2is (A) (a+3) (c-b) (B) (a+3\ (b-c) (A) {x:x>21 (c) (a-3) (b+c) (B) lx: x<-21 (D) (a -3) (b . The values of: for which (: + lsy = Ux te 9. The roots ofthe equation 3. ac is equal to 7.r + i)' + tthen Functions/and g are defined by (A) a=l h:3 k=4 (B) a:t h=4 k=4 f :x-+?:. 2x-5' 2 5.Ex-17x+.O. (C) a=t h =-4 k:3 zx '. 6x .a=-r . 3b .**5 .r3 .r-8'-20. x+0 (C) distinct and not real (D) real and not distinct (D) *f . x+0 t (A) equal A (B) real and distinct (C) gf :x-+:-5. -J- l. Given that/("r) =rf + 4x -21.-Sand g:r-)4+ l.5 (A' gI:x-+z."r.2 isafactorof The range of values for which f-7x+10<0is (A) 4f -2f -s6 (B) 4f+2*-16 (A) 2> x> 5 (C) 2t' +2f -4x-8 (B) 2<x<5 (D) 3i -l0x'-5l2+ 4 (C) x<2andx>5 (D) x<-5andx>-5 The expression ab + 3c . 5=0 K are (B) gf :x-+3+:.(c) f (x)>as (D) f (x) s-2 CO ON TO THE NEXT PACE n r a<rnt n/E ant < .=. the range of/ (A) 3and5 (r) is (B) 9and5 (c) 3 and 25 (A) f(x)> -21 (D) 9 and 25 (B) -7 <f(x)<3 .c) (C) {xrr>0} (D) lx: x> 1l 3. (D) h:4 k=3 The composite function gfis defined by .. The expression r . . then the value of x (A) \ is /\ (A) (B) 3l:-5 \z | J (B) 2 4 t./ I 16. -4- . CE"n" is equal to sequence 8. \ (c) 8 (c) rl. \ to lf f :x-+2l i+5 I.t' + 3x + 4 = 0. then m (4 is (A) -t I (A) 4-4a (B) 9 -2t (B) 0 (C) 8-4a (c) t I (D) 13 . what is the value of (a+ PF? Given that 3 x27b=9. 2a) 14.-s J\z . . 18. then /-'(x)isequal \J / 3(x-2) Given that lo1o f :6. is (A) {[r'" (A) :- 4 (B) 3'+'N lt +l (B) :)5 (c) 3' (D) 3" 4m (c) 1 :- 2 I (D) : GO ON TO THE NEXT PAGE . Given that cr and p are the roots of the equation. 12. If function rz: r -+ 5 + 2x.4a (D) I /. . The common ratio of the geometric 13. thd value of.+s \z ) I (D) 64 1t . \ (D) *l. The value of x for which 4*r = 2 is 10.r is 9 (A) 16 (A) -4I (B) l (B) -l (c) I (c) e 4 (D) I (D) 16 17. the nn term is given by The equation ofC is (A) 5n-17 (A) *+). 200.+G-4y+3=0 (B) 5n-12 (B) *+f-3=0 (c) -12 .6) (c) 630 (c) (-s. The equation ofl. -2) and radius 4. The first four terms of a convergent 24. E .+3x-2y-3=0 20.4) (D) t960 (D) (0.3. 80.7 and the line x + 3y = 7 and 50 is intersect at the point (A) 60 (A) (4.-7.-7) 19. The sum to infinity ofthis (A) have the same magnitude and GP is different directions (B) have the same magnitude and same (A) 200 direction (c) are parallel and in different 500 (B) directions J (D) have different magnitudes and are (c) 300 in the same direction 2500 (D) The vector a is given as 5i + l2j. -12. A line L passes through the point (6. 32. 5) and is perpendicular to the line whose equation (B) l95i + 468j is3x+ 4y-7 =O. is I (A) 3x-4y-3O=0 (c) ' (si + 12j) IJ (B) 3x+4y-ll=0 (C) 4x+3Y-7 =9 (D) 4x -3Y -9 = O (D) 3 (si + r 2j) l3 CO ON TO THENEXT PACE . t) (B) 600 (B) (8.J.. Two vectors ar€ equal ifthey geometric progression (GP) is given by 500. A unit vector parallel to a is (A) l5i + 36j 21. 5n (C) *+1P-6x+4y-3=O (D) 5n+ 17 (D) *+). The sum ofthe ODD integers between 10 The line y = 2s.. For the arithmetic progression A circle C has centre (3. -5- lE. 2): 0 is 28. measured in radians. 30. The EXACT value of -----:-.l) (cos d. (B) (D) The acute angle between P and q is 45'. is given as cosl )u- (A) I (c) I (B) E (c) (D) (D) Item 2E refers to the following triangle. J (D) ^ 25 GO ON TOTHENEXTPAGE . -6- 26. The position vector ofthe point P relative 29. The size ofangle X. sin 150' 27. Which of the following graphs represents to an origin O is given 65 p = Ji + 2j and Y = sin x'! the position'iector of Qrelativetoan origin O is given as q : -4i + l0i.' (A) 2tc (B) 5 J 1f 4E (B) (c) -. (A) Which ofthe following statements isTRUE? (A) p and q are parallel. E is (A) . l0 . The smallest positive angle within the range O < 0 <2n that satisfies the equation (2 cos 0 . (C) .' (c) 5tt (D) -. (B) The acute angle between P and q is 60'.p and q are PerPendicular. --+ = -J .r =l3 I (B) . -7 - 31.4 dx = (D) 1') (A) sin 2. If sin 0 = : and 0 is obtuse. 45') is equal to 35. then tan 0 = IJ (A) a point of inflexion (B) an optimum point (A) -12 (C) a minimum tuming point l3 (D) a maximum turning point (B) -.r I +cos: (D) 2 sin?-x (A) 2 sin r (B) 2 tan x (c) 2 sinx (D) tanz x GO ON TO THE NEXT PACE 0r2s40r0/F 20ls .z Sln zr 34.. 4) is 33..hx'+4 -:1 radians converted to desrees is 5- (A) 72 (B) tM At he point (7.xrs . Given that v = co s X. sin (ct . then . The trigonometrical expression sin x sin.rdentrcal to (c) -2sin2x I .o) (A) r. 4) on the curve y : l.r) (c) 180 dv U^and d2v (D) 288 ---:.*ov= (A) l4x lftrino-*.oro) TX (D) j{cosa -sina) (c) ffi 7 (D) At . dx= dx' The point (7. lz (c) :-t2 37. frJ-r.Jlx'+4 (c) j{rin o -.cos.lTx'+4 (B) -sina) lftcosa 7x (B) |------_ . f d' (x + 3)'z . then (-2. - If I. (D) 4 ^ (A) 6 (B) l0 (c) 36 (D) 72 43.axis. sin x *c (D) 3.(6+3r) &=72. The volume (A) ofthe solid generated can be found from: (r+ 3)' 3x(x +2) (B) (. sin .x +c (B) .h"n d i. 5) is It (zx-s)" . sin . I 39.t'. 5). lf y : jf + cos r then JI dx= (A) :i. -8- t' .r(r + 6) (c) I:f* (D) (x + 3)z (D) o[''od. rf v: -r+3 & 41. n (C) a minimum turning Point (B) (D) a maximum tuming Point 8 (zx-s)o (c) 8 .r + c GO ON TO THI NE)<T PACE . !{z* -\'a.15. then a = 2(2r-s) . - (rr. = f' (x) = f . (A) an intercept 4 -" (B) a vertex (zx-s)' . the x--axis and the linesr:0andx = I is -3x(x + 2) rotated 360oabout the x.t' .where a> 2. The region bounded bY the curve Y : .t'+ sin x + c (C) 6x. 3E.r + 3)'z (A) r!'x'ax (c) -x(r + 6) (B) I. The curve C with equation y = J(*) has a stationary point at (-2. the lines r: 0 and r:l . 45. The area ofR is (A) 2 (B) 4 (A) I (B)t (c) 42 . -9- u. CHECKYOURWORK ON THISTEST. The region R is enclosed by the x-axis. (c) 2 (D) $ (D) Z 3 END OFTEST IFYOU FINISH BEFORETIME IS CALLED.. 012540t0/F 2015 . the l'(t+r+")or= curve y = -* + 2. 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