Oct 2000 Term #1 - €OLU €01 Department of Mathematics...

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Unformatted text preview: €OLU €01 Department of Mathematics University of Toronto WEDNESDAY, NOVEMBER 1, 2000, 6:10 - 8:00 PM MAT 133Y TERM TEST #1 Calculus and Linear Algebra for Commerce Duration: 1 hour 50 minutes Aids Allowed: A non-graphing calculator, with empty memory, to be supplied by student. Instructions: Fill in the information on this page, and make sure your test booklet contains 10 pages. In addition, you should have a multiple-choice answer sheet, on which you should fill in your name, number, tutorial time, tutorial room, and tutor’s name. This test consists of 10 multiple choice questions, and 4 written-answer questions. For the multiple choice questions you can do your rough work in the test booklet, but you must record your answer by circling the appropriate letter on the answer sheet with your pencil. Each correct answer is worth 4 marks; a question left blank, or an incorrect answer, or two answers for the same question is worth 0. For the written-answer questions , present your solutions in the space provided. The value of each written-answer question is indicated beside it. ENCLOSE YOUR FINAL ANSWER IN A BOX AND WRITE IT IN INK. TOTAL MARKS: 100 FAMILY NAME: GIVEN NAME: m STUDENT NO: ___________ SIGNATURE: TUTORIAL TIME: ___________ TUTORIAL ROOM: T.A.’S NAME: m M9A T0101A BF323 T0501C T0101B $31070 T0501D T0101C BF215 T0601A T0201A MP118 T0601B T0201B BF323 T0601C T0201C RW142 TO701A T0201D UCS28 TO701B T0301A RW142 T0701C T0301B LM157 T0801A T03OIC PGlOl TO801B P0301D w1523 T5101A T0401A LM155 T5101B T0401B W1524 T5101C To4o1c BF215 T5201A T0501A ss2127 T5201B T0501B UCl44 W3C W3D M9B MQC M3A M3B M3C M3D T3A T38 T30 T3D W9A W9B WQC W3A WSB FOR MARKER ONLY Multiple Choice B1 Page 1 of 10 PART A. Multiple Choice 1. [4 marks] How many months, to the nearest month, does it take for $1,000 to grow to $5,000 at a rate of 9% compounded monthly? “ fi .04 A. 210 2(000-: looo<l+fi B. 200 at 5’ 1 n gt 0* ‘z—‘fl: @ 215 I D 225 n ’ % f a: 2 If ‘I / ' E 230 , 04 ) % (l 4‘ '71 2. [4 marks] Which of the following interest rates corresponds to the greatest effective annual rate? A. 10.4% compounded annually . l0” 2 3 .a B. 10.3% compounded semi-annually ( l ‘l' Luz; ) / I ’ . l0 . ~ @ 10.2% compounded quarterly C l 4. , |02 9" i ' I . . . L, D. 10.1% compounded monthly :1, (1+ .1004 : I’M3I., E. 10.0% compounded daily l2. ( 36 3:2,? ' J0 Page 2 of 10 3. [4 marks] A person purchases a car by making a down payment of $1,500 followed by 60 monthly pay- ments of $300 each beginning at the end of the first month. If money costs 3% compounded monthly then the price of the car, to the nearest dollar, is: A. 20,894 B. 19,500 lfoo+3ooa 307% C. 9,803 03 '60 18,196 ‘-’ 1920* 3001:!“ U‘PLT; ] E. 14,987 fl 1 2. 2n§m<41 4. [4 marks] A debt of $2,000 due today and a debt of $2,000 due three years from today are to be paid off by four annual payments: $1,000 a year from now, $1,000 two years from now, $1,000 three years from now, and a final payment of $ X four years from now. Interest is 7% annually. The value of X to the nearest dollar is compounded A. $1,000 B. $1,547 0 a 7- 3 ‘f C. $1,426 I“ 2000 X é $1,322 Moo I000 IOOO E $1,101 ( X<m32Lef Page 3 of 10 5. [4 marks] A $150,000 mortgage is amortized over 20 years at 7% compounded semi-annually with payments at the end of each month. Just after the 60th payment, the principal outstanding (to the nearest $5) is l n ’1 B. $111,685 r ‘ . ‘ P‘O‘ ' Ra 1804 : [yo/aooalfljd C. $112,500 F D. $128,775 W1 fl 9'0 D P 0”) : |{o)000[l-— (LOBgfgoj [1,0,0'33' AM] Going/13?, 43 6. [4 marks] On September 11, 2000, a bond issued by the Government of Ontario, maturing on March 11, 2003, with semi-annual coupons at an annual coupon rate of 8%, had an annual yield to maturity of 6%. The price the bond traded at was (to the nearest $0.10): B. $108.40 P, mo (Lfiyfik 0] a C. $105.40 D. $103.70 96 E. $106.10 ’ 6,03 Page 4 of 10 7. [4 marks] Find all pairs (2:, y) so that the matrix is in row-echelon form. A" (227]) = (01 0) and (may) = (120) B' (37y) = (1’ 1) only E- (03,21) = (0,1) only 8. [4 marks] 3 l 4 7 T If A = _5 6 , B = __2 6 , and B denotes the transpose of B , then I T_ _ 3 I ‘l '2’ _ ‘1 2) AB 33— (4 LXI; a) (.4, 18 —2 6 A' [—26 —17 7 ,zu) —35 —57 2 B' [52 16] (7-7 73 a 7 —21 28 28 7 6 D‘ [1 28] 10 —30 E- [_2 25] Page 5 of 10 9. [4 marks] The solution to the matrix equation AX = C Where —1 2 2 a: A-1= 1—3—2 ,X=y, 1 ——1 —1 z isgivenby A. x=1,y=——3,z=—2 B. $=—1,y=——3,z:3 X’ C. $=3,y=—3,z=0 -. ’l 2- D. :z:=0,y=—3,z=—1 I «3 @m=1,y=—3,z=0 : —l a I '3 0 10. [4marks] Consider the linear system Ax = b Whose augmented matrix is Then the system has infinitely many solutions with one parameter B. C. D. no solutions infinitely many solutions with two parameters a unique solution E. infinitely many solutions with three parameters Page 6 of 10 HHOH [\Dl—ll—IH N HOD-JO l—‘NOH l 1 | 1 | 1 | 2 i l o | | O 0 l I I 0 l l O 0 0 / PART B. Written-Answer Questions 1. (a) [8 marks] Sixteen monthly deposits of $50 each, followed by eight monthly deposits of $75 each, are made into an account. What is the accumulated value in the account right after the last deposit of $75, if the account earned 12% compounded monthly during the first year, but only 9% compounded monthly during the second year? (All monthly deposits are at the end of the month.) 0! ~17. I3..-|b 17---.” l; {o {0 5'0 50 7‘ 7f 3 :7. . q { +fl) 50$ l+-.2_)+4 5 {OSmfl'U ‘2 + [z baa % (b) [’7 marks] A person wishes to borrow $5,000 now and another $5,000 at the end of 5 years. He wishes to pay both loans off by 10 equal semi-annual payments, the first one due at the end of 3 years. If the interest rate is 8% compounded semi-annually, then find the “hr—payment to the nearest cent. few ’anfl ml 0 3’ b 4 7 qu u (L (3 m :( W {000 ' 5000 ' 'Rri'RRR Ran R K” Ra fl 0“, C|qu)'(c {000 4“ {OOOCLWr'O Page 7 of 10 2. A loan of $100,000 is paid off with monthly payments (at the end of each month) over 20 years. Interest is 6% compounded monthly. Find [5] (a) the monthly payment; [7] (b) the interest and principal paid in the 77th payment; [3] (c) the total interest paid. a) \oo,ooo : R a $37.06 ‘2. R = I00,000x.00{ A, N I \-— (Loos/Two Page 8 of 10 3. Ramus has a debt of $10,000 which is accruing interest at 8% compounded annually. He wishes to pay off the debt in equal annual payments of $1,000 each, starting one year from now, but he realizes that the very last payment will be less than $1,000. [5] (a) How many annual payments are there? [10/ (b) How much is the very last payment? a) 10,000 = IOOO a?” Page 9 of 10 4. Consider the system of linear equations $1 - 2232 + $3 — $4 = -1 —-2m1 + 42:2 — 933 + $4 = 3 ' ‘ — $1 + 2232 — (123 + [621134 2 k [6'] (a) Solve the system by using row reduction in case k = 1 . [.9] (b) Is there any value of k such that the system has no solution? Justify your answer. \ — 2 l ’1 " -2. ‘l «I I 3 .4 2 rl km k 'L , of Clo/l 19 l“ W" \ w xfia bwo ram M Ill \chl) 19L; [6196’ MW (c 0 , My 0/6. wo §a\n§. Awwals 1 , Page 10 of 10 ...
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This note was uploaded on 03/02/2010 for the course MAT Mat133 taught by Professor Igfeild during the Spring '10 term at University of Toronto.

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Oct 2000 Term #1 - €OLU €01 Department of Mathematics...

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