2012 DSE Math Paper 2 PDF

There are 30 questions in Section A and 15 questions in Section B. The diagrams in this paper are not necessarily dra,vn to scale. Choose the best ans,ver for each question. Section A 1. 2x 5. 2 A. 3x 7 B....

There are 30 questions in Section A and 15 questions in Section B. The diagrams in this paper are not necessarily dra,vn to scale. Choose the best ans,ver for each question. Section A 1. 2x 5. 2 A. 3x 7 B. 3x. 7 C. 4x. D. 4x 59. 2. (4x+ y) 2 -(4x-y) 2 = A. 0. B. 2y 2. C. 8xy. D. 16xy. 3. lfp and q areconstantssuchthat x 2 +p=(x+2)(x+q)+IO, then p= A. -4. B. -2. C. 6. D. 10. 2012-DSE-MATH-CP 2-2 2  3 2 4. If k is a constant such that x + 4x + lex -12 is divisible by x + 3 , then k = A. -25. B. -1. C. 1. D. 17. 5. If ,n + 2n + 6 = 2111 - n = 7 , then n = A. -4. B. -1. C. 3. D. 11. 2 6. The figure shows the graph of J' = a(x+b) , where a and b are constants. Which of the following is true? A. a>O and b>O y B. a > 0 and b < 0 0 X C. a< 0 and b > 0 D. a< 0 and b < 0 J' = a(x +b) 2 7. The solution of 15 + 4x < 3 or 9 - 2x > 1 is A. x -3. C. x 4. 2012-DSE-MATH-CP 2-3 3 Go on to the next 8. In a company, 37.5% of the employees are fe male. If 60% of the male emp loyees and 80% of the fe male emplo yees are marr i ed, then the p ercent age o f marri ed emplo yees i n the company i s A. 32.5%. B. 45%. C. 55%. D. 67.5%. 9~ 6x+5 y If x and y are non-zero numbers such that = 7, then x : y = 3y -2x ABCD : 4 · 5 · 4 : 1 3 5l: 4..... 34 10. i s given that y p artly vari es direc tly as 豆 and part ly vari es i nversely as x. When x = 1, y = -4 and It when x=2, y =5. When x=-2, y= ABCD 11 5.. 一＿.... 5l l 11. Mary per fo rms a typin g task fo r 7 hours. Her avera ge typing speeds fo r the frr st 3 hours and the las t 4 hours are 63 words per m inute and 56 words per minu te respectivel y. Fin d her avera ge typing speed fo r the 7 hours. A. 17 words per minut e B. 3 5 words per m inut e C. 59 words per m i nute D. 60 words per m inute 4 2012-DSE-MATH-CP 2-4 12. In the fig me, the 1s t patt ern cons i sts o f 1 do t. For an y pos iti ve i nteger n, the (n + 1) th pattern i s fo rmed by add ing n do ts to the nth patt ern. Fi nd the number of do t s i n the 8th patt ern. 。 八／ \V \y 。.. :> 0 0 [ 0 0 。 0 0 0 [... 0000 ABcD 2967 2233... 13. 0.0322515 = A. 0.032 (conec t to 3 significan t fig ures). B. 0.0322 (conec t t o 4 deci mal places). C. 0.03225 (correc t to 5 signifi cant fig ures). D. 0.032252 (correc t t o 6 de cimal places). 14. The len gth of a piece of thin stt·ing i s measured as 25 m correc t t o the neares t m. If the string i s cut i nto n pieces such that the length of each piece i s measured as 5 cm correc t to the nearest cm, f md the greates t poss i ble value of n. 4665 ABCD 4556 567O.. 15. In the fig ure, the area of quadril at eral ABCD i s c A. 144 cm2. 6cm D B. 160 cm2. c 178cm2. 8cm D. 288 cm2. B A 5 2012-DSE-MATH-CP 2-5 Go on to th e next pa ge  ^ ^ 16. In the fig ure, OAB and OCD are sec tors with centre O. If AB= 12兀 cm, CD= 16,r cm and OA = 30 cm, then AC = 。 A. 5cm. B. 10cm. c 20cm. c D D. 40cm. I 7. In the fig ure, ABCD i s a parallelo gram. E and F are points lying on AB and CD respec ti vel y. AD produced and EF produced mee t at G. It i s given that DF: FC = 3: 4 and AD: DG =I: 1. If the area of ~DFG i s 3 cm 2, then the area o f the parallelo gram ABCD i s G A. 12 cm2. B. 14 cm2. C. 18 cm2. c F D. 21cm2. A E B 18. In the figure, D i s a point lying on AC such that BD i s perpend i cular t o AC. If BC=£, then AB= £s in a B A. , cos /3 es in/J fJ B.. cosa €cos a C.. sin/3 Z、 a z I ecos /J C D A D... sma 6 2012-DSE-MATH-CP 2-6  cos60° cos 240° 19. 十 I -cos(90° - 0) I - cos(270° - 0) 1 A.. cos2 。 cos0 B.. tan0 t an 0 C. cos0 1 D.. cos 0 t an0 20. In the fig ure, 0 i s t he centr e of the circle ABCD. If乙 BA0=28°, 乙BCD= 114° and 乙 CD0=42°, then 乙 ABC= B A. 90°. B c 96°. C. 100°. D. 138°. 21. In the fig ure, AB i s a di ame ter of the circle ABCD. If AB = 12 cm and CD = 6 cm, then the area of the shaded re gion i s A. (12 tr -9)cm2. B. (1 2兀 +9)cm2. C. (12冗－ 9✓3)cm2. D. (1 21r+9✓3)cm2. A 7 2012-DSE-MATH-CP 2-7 Go on to th e next pa ge 22. Wh i ch of the fo llow i ng statements about a re gular 12-si ded pol yg on are trne? I. Each ext er i or an gle is 30°. II. Each i nteri or an gle i s 150°. III. The number of axes of re fl ec ti onal syinme tly i s 6. A. I and II only B. I and III only C. II and III only D. I, II and III 23. The rec tan gular coord inates of the point P are (- 3, －這）．If P i s ro tated anti clockw i se about the origin 血ough 90°, t hen t he polar coordinates of its image are ',`,,\(( ABCD 3l3 5 3 6 0OOO 3l6 5 33 、丿丶丿、、J、,' 0. ','.,... 00o 24. If P i s a moving poi nt in the rec tan gular coordi na te plane such tha t the di stance be tween P and the poi nt (20, 12) i s equal to 5, then the locus of P i s a A. ci rcle..B. square. C. parabola. D. tri an gle. 8 2012-DSE-MATH-CP 2-8  25. In the fig ure, the equa ti ons of t he st ra ight lines L」 and L2 are ax+ y =b and ex+ y = d respec ti vel y. Whi ch of the fo llowi ng are trne? I. a< 0 II. a< c III. b > d IV. ad> be A. I, II and III only B. I, II and IV only C. I, III and IV onl y 。 x D. II, III and IV only L1 L2 26. In t he fig ure, the radi us of t he ci rcle and the coordi nates of the cenn·e are r and (h, k) respec tivel y. Whi ch of the fo llow ing are tru e? I. h+k>O II. r -h > 0 III. r -k > 0 A. I and II only B. I and III only C. II and III only D. I, II and III 。 x 27. 9* 令is a 3-d igit number, where 責 and 令 are i ntegers fr om O to 9 it1clusi ve. Fmd the probab ility t ha t the 3-d igit number i s di vi si ble by 5. I A. 5 B 7 33 c 20 99 19 D. 100 9 2012-DSE-MATH-CP 2-9 Go on to th e next 2旦ge 28. The st em-and-leaf di agram below shows the di stri buti on of the ages of a group of members i n a recrea ti onal centre. Stem (tens) Lea f (units) 5 。 5 6 6 8 6 1 4 5 5 7 8 8 9 7 3 4 4 6 7 9 8 9 1 A member i s randomly selected fr om the group. Fi nd the probab ility that the selected member i s no t under t he age of 74. A. 0.2 B. 0.3 C. 0.7 D. 0.8 29. The bar chart below shows the di stri buti on of the numbers of ri ngs owned by the girls i n a grou p. Find the st andard devi ati on of the di stJ:·ibu ti on correct to 2 de cimal places. A. 1. 04 8.....,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ll BCDl699 lO 2................................................................................................. SI.I!~ 642O..................................v,,..;v,1.................................................................................. J 0 J O F ,~ J ,,,,,................................................ ，，，，，，，，，，，，，，，，＇疊.,...,,................................., """""""" l 3 4 。 2 Number of rings 30. Cons i der the fo llowi ng dat a: 19 10 12 12 13 l3 14 15 n 16 "1 If both the mean and the medi an of the above data are 14, which of the fo llowing are true? I. m 2l4 II. n :s; 16 III. m + n = 30 A. I and II only B. I and III only C. II and III only D. I, II and III 2012-DSE-MATH-CP 2-10 10 Se cti on B 3 1. The H.C.F. and the L. C.M. oftlu·ee express i ons are ab2 and 4a 恬攣 respectively. If the fi rst express i on and the second express i on are 2a 2b 4 c and 4a 恬攣 respectively, then the thi rd express i on i s A. ab. B. ab5. C. 2ab~c. D. 2ab c. J 32. The graph in the fig ure shows the linear relati on be tw een x and lo g 3 y. If y = m n'「,then n = l lo g3 y A. 1. 8l5 4 B. C. 9. D. 81. 。 X 33. AD000000201216 = A. (10)1611 +(1 3)1610 +8210. B. (1 0)1612 +(1 3)1611 +131360. C. (1 1)1611 +(1 4)1610 +8210. D. (11)1612 +(14)1611 +131360. 34. Le t f (x) be a quadra tic fu nc ti on. If the coord inates of the vertex of the graph of y = f (x) are (3, -4), whi ch of the fo llowing mus t be true? A. The roo ts of the equation f (x) = 0 are integers. B. The roo t s of the equati on f (x)-3 = 0 are rati onal numbers. C. The root s of the equati on f (x) + 4 = 0 are real numbers. D. The root s of the equa ti on f (x) + 5 = 0 are nonreal numbers. 2012-DSE-MATH-CP 2-11 11 Go on to th e next pa ge 35. i 3( /Ji -3)= A. f3 +3 i. B. /3一 3 i. C. -/3 +3 i. D. -/3一 3 i. 36. The fig ure shows a shaded re gion (includ i ng the bounda1-y). If (h, k) i s a poi nt lying in the shaded re gion, wh i ch of the fo llowing are true? I. k ~ 3 II. h-k ~ -3 y =x+3 III. 2h+k s 6 A. I and II onl y B. I and III only y =3 C. II and III onl y 。 D. I, II and III x y= 6-2x 37. Le t a11 be the nth te1m of an arithme tic se quence. If a18 = 26 and a23 = 61, whi ch of the fo llow ing are true? I. a14 < 0 II. a1 -a2 < 0 III. a1 + a2 + a3+ …+ a27>0 A. I and II onl y B. I and III onl y C. II and III only D. I, II and III 2012-DSE-MATH-CP 2-12 12  38. Whi ch of the fo llowi ng may represent the graph of y = f (x) and the graph of y = f (x-2) + 1 on the same rec tan gular coordi nate system? A. B. y = f (x) y = f (x) y=f (x-2)+1 y=f (x-2)+1 。 。 c D. y =f (x-2)+1 y = f (x) y = f (x) y = f (x-2)+1 。 。 39, The fig ure shows Xo A. the graph of y = I+ 3 cos —. 2 7 ,............................................................................................. 7 B. the graph of y = l + 3 cos 2x0, XO C. the graph of y = 4 + 3 cos —. 2 D. the graph of y = 4 + 3 cos 2x0. l............................................, ! 。 90 180 2012-DSE-MATH-CP 2-13 13 Go on to th e next E 40. The fig ure shows a re gular tetrahedron ABCD. Fi nd the an gle be tw een the plane ABC and the plane BCD correct to the neares t de gree. ABC 456 83O 0 A. 0.. 0 D. 71° B - - －一－－－ - - - - - - D c 41. In the fig ure, P Q i s the tangent to the circle ABC at O, where O i s the centre of the sem i circle P BQ. It i s given that BCP i s a straight line. If乙BPQ = 12°, then 乙BAC= A. 18°. A 464 235 BCD 。。。..... P Q 。 42. Fi nd the range of values of k such that the ci rcle x2 +y 2 +2x-4 y -13=0 and the str aight line x - y + k = 0 intersect at two di stinc t points. A. -9 < k