Mathematics 1307 Sample Placement Examination

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1 Mathematcs 1307 Sample Placemet Examato 1. The two les descrbed the followg equatos tersect at a pot. What s the value of x+y at ths pot of tersecto? 5x y = 9 x 2y = 4 A) 1/6 B) 1/3 C) 0 D) 1/3 E) 1/6 2. Cosder the followg lear programmg problem. Whch of the pots lsted s NOT a corer of the feasble rego? Maxmze: P = 10x 3y Subject to: x + 2y 8 (L1) 2x + y 10 x, y 0 (L2) A) (0, 10) B) (0, 4) C) (4, 2) D) (8, 0) E) All pots lsted are corer pots The lear programmg problems problems 3 ad 4 have the followg commo corer table ad feasble rego. Corer Table Label x y P C A 0 16 B 4 8 C 10 2 D Cosder the followg lear programmg problem. Maxmze: P = 4x y Subject to: 2x + y 16 x + y 12 x + 2y 14 x, y 0 (L1) (L2) (L3) What s the label assocated wth the corer whch s the soluto of ths lear programmg problem? If the lear programmg problem has o soluto, the report the aswer to be E. A) A B) B C) C D) D E) E 4. Cosder the followg lear programmg problem. Mmze: C = + 4x y Subject to: 2x + y 16 x + y 12 x + 2y 14 x, y 0 (L1) (L2) (L3)

2 What s the label assocated wth the corer whch s the soluto of ths lear programmg problem? If the lear programmg problem has o soluto, the report the aswer to be E. A) A B) B C) C D) D E) E 5. What s the total amout due o a loa of $1500 at 12% smple terest at the ed of 4 moths? A) $1500 B) $1515 C) $1530 D) $1545 E) $ How may moths wll t take $10,000 to grow to $15,000 f t s vested at 9% compouded mothly? Be sure to roud your aswer up to the ext larger teger. A) 46 B) 49 C) 52 D) 55 E) Assume that you buy a televso set for $800 ad agree to pay for t 18 equal mothly paymets at 18% terest o the upad balace. Whch of the followg best estmates how much terest you wll pay? A) $119 B) $128 C) $138 D) $148 E) $ Whch of the followg best estmates the value of a auty at the ed of 5 years f $100 per moth s deposted to a accout earg 9% compouded mothly? A) $7,502 B) $7,522 C) $7,542 D) $7,562 E) $7, How may four-letter code words are possble usg the frst sx letters of the alphabet f o letter ca be repeated? A) 24 B) 360 C) 480 D) 720 E) There are eght teams a coferece. How may games must be scheduled f each team s to play every other team exactly oce? A) C 8,2 B) C 6,2 C) P 8,2 D) P 6,2 E) P 8,6 For the ext two problems cosder the followg scearo. A carto of twety calculator batteres cotas exactly two dead batteres. A radom sample of three batteres s selected from the carto ad tested. 11. How may samples ca be selected? A) 6 B) 1140 C) 2280 D) 6840 E) How may of these samples wll cota exactly oe dead battery? A) 2 B) 153 C) 306 D) 612 E) 1140 For the ext two problems cosder the followg expermet. Oe ur has four red ad two whte balls; a secod ur has oe red ad fve whte balls. A sgle far de s rolled ad f 2 or 5 dots show, a ball s draw out of the frst ur; otherwse a ball s draw out of the secod ur. 13. What s the probablty of drawg a red ball? A) 4/36 B) 8/36 C) 12/36 D) 20/36 E) 24/36

3 14. If a red ball s draw, what s the probablty that t came from the frst ur? A) 2/12 B) 4/12 C) 6/12 D) 8/12 E) 10/12 For the ext two problems cosder the followg scearo. A surace compay foud a partcular commuty that 30% of the drvers volved a accdet oe year were also volved a accdet the followg year, whle oly 10% of the drvers ot volved a accdet oe year were volved a accdet the followg year. 15. Suppose that 20% of the drvers ths commuty were volved a accdet What percetage of the drvers would you expect to be volved a accdet 2003? A) 6% B) 8% C) 10% D) 12% E) 14% 16. At steady state, let P deote the probablty that a drver wll have a accdet ad Q deote the probablty that a drver wll ot have a accdet. Whch set of equatos, whe solved, would lead to the correct determato of the values of P ad Q? A) 0.3P + 0.7Q = P B) 0.7P + 0.3Q = P C) 0.3P + 0.1Q = P D) 0.1P + 0.3Q = P 0.1P + 0.9Q = Q 0.9P + 0.1Q = Q 0.7P + 0.9Q = Q 0.9P + 0.7Q = Q P + Q = 1 P + Q = 1 P + Q = 1 P + Q = 1 E) 0.3P + 0.9Q = P 0.7P + 0.1Q = Q P + Q = Cosder the followg data (the values of x are to be assumed to be exact). x Frequecy What s the best estmate of the mea of these data? A) 3.25 B) 6 C) 6.08 D) 6.5 E) Suppose a far de s rolled fve tmes. Whch of the followg umbers best estmates the probablty that the face wth three dots wll be rolled at most oce? A) B) C) D) E) For the ext two problems cosder the followg scearo. Suppose that the weghts of Texas watermelos are ormally dstrbuted wth mea 100 lbs ad stadard devato 10 lbs. A watermelo s pcked at radom. 19.What s the probablty that ths watermelo weghs betwee 97 ad 103 lbs? A).118 B).226 C).236 D).3 E).6 20.What s the probablty that ths watermelo weghs at least 106 lbs? A).118 B).226 C).274 D).774 E).882

4 Facal Formulas r - aual terest rate t - tme years = r/m m - perods per year - perodc terest rate = mt Smple terest: I = Prt, A = P(1+rt) Effectve rate: r e = (1 + r/m) m -1 Compoud terest: A = P(1 + ) Growg tme: A l P = l(1 + ) Preset Value Formulas: PV = PMT = PV 1 (1 + ) PMT Future Value Formulas: 1 (1 + ) FV ( 1+ ) 1 = PMT PMT = PV ( 1+ ) 1 Permutatos ad Combatos: P, r! = ( r)! C, r! = r!( r)! Probablty: A * deotes the complemet of the evet A; P(A * ) = 1 - P(A) Evets A ad B are mutually exclusve f A B = φ Evets A ad B are depedet f P(A B) = P(A) P(B) The odds for a evet A are P(A) * P(A ) If the odds for A are a a, the P(A) = b a+b P(A B) deotes the probablty of the evet A gve B * P(A ) The odds agast a evet A are P(A) P(A B) = P(A) + P(B) - P(A B) P(A B) = P(A B) P(B) P(A B) = P(A) P(B A) = P(B) P(A B) Bayes' Formula: Let U 1, U 2,..., U be mutually exclusve evets whose uo s the sample space S. Let E be a arbtrary evet S such that P(E) 0. The P(U 1 E) = P(U 1 I E) + P(U P(U1 I E) I E) P(U I E)

5 Statstcs: Ugrouped data: x x (x x) = s = 1 2 Grouped data: = f x xf (x x) = s = 1 2 f Bomal Dstrbuto: P(x) - probablty of x successes trals p - probablty of success q - probablty of falure P(x) = C,x p x q -x Mea: µ = p Stadard devato: σ = pq Normal dstrbuto: The Bomal Dstrbuto ca be approxmated by the Normal Dstrbuto whe the terval from µ 3 σ to µ + 3σ les etrely wth the terval from 0 to. I the followg table, A(z) represets the area uder the ormal curve from 0 to z. x - µ z = x = µ + σ z σ Areas uder the Stadard Normal Curve Table etres represet the area uder the stadard ormal curve from 0 to z for z>0. A(z) 0 z z

6 Aswer Key 1.D 2.B 3.A 4.E 5.E 6.D 7.A 8.C 9.B 10.A 11.B 12.C 13.C 14.D 15.E 16.C 17.C 18.D 19.C 20.C Number correct Estmated Grade A B C Passg grade 14 correct aswers

GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME MATHEMATICS GRADE 12 SESSION 3 (LEARNER NOTES)

GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME MATHEMATICS GRADE 12 SESSION 3 (LEARNER NOTES) MATHEMATICS GRADE SESSION 3 (LEARNER NOTES) TOPIC 1: FINANCIAL MATHEMATICS (A) Learer Note: Ths sesso o Facal Mathematcs wll deal wth future ad preset value autes. A future value auty s a savgs pla for