{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1 - B/MapleTA" MATH 135 1119 Algebra for Honours...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: B/MapleTA." MATH 135 1119 Algebra for Honours Mathematics : Grades — «v Maulesoft' System Homepage » Class Homepage » Gradebook » Student Grades » Assignment Details Welcome Bill Zimou Peng MyProfIle Gradebook Help Logout v\fiew Panel Refresh View Rows: 20 F Grade Data '_' User Data , Start date _‘ Starttime f1? Lastname f1? Given Name '— Class Name _ _ _ End date End time ‘ MI ‘ Login am)“ to CSV Style: Numeric ' ‘ #Attempts _‘ Duration _‘ Emai _‘ Student ID Showing Best grades, Completed assignments, All users Student Details VAssignmenH Score: Duration: 1 hrs 42 min Started: 9/13/11 12:40:07 PM 11,12'0 finished: 9/13/11 2:22:55 PM V Bill Zimou Peng Login: bzpeng Assignments Email: [email protected] Completed: 9 Active: 0 Student ID: 20430954 To Be Reviewed: 0 Passed: 7 Page:1of1Rows:1-12 of12 - 0 _‘ Question 1 Question Grade: Weighted Grade: F 2 Question Grade: Weighted Gade: 1.0 (1/1.0) 1.0 (1/1.0) Your response Consider the following statement P. I“ If X is a positive real number, then X2 > X Which ofthe following is true of P ? P is a false statement. (100%) Comment: P is a false statement. To see this, consider X = E. 2 l 1 1 Wh — :— —. eave(2] 4} 2 Thus,we have a real number X which does notsatisfy X2 > X, and so the statement P is false. Your response Consider the statement: I? Let flX} = “i 3 X . Then flX} = X forsomereal number X with U S X S l . correct Which choice corresponds to the conclusion ofthe above statement? There exists a real number X , U S X S 1 such that flX} = X . (100%) Comment: When working with mathematical statements it is important to be able to distinguish which parts form the hypothesis and which form the conclusion. In a statement“lf P,then Q“, P is the hypothesis and Q is the conclusion.Awayofthinking about which parts belong where is to ask 'What is being given to me“ (for the hypothesis) and “What is the statementtrying to show" (for the conclusion). \fiewed in this light itshould be clear thatthe statements claim was thatthere is some number X in the interval [0, 1] such that flX} = X. Hence the correct choice of conclusion is: "There exists a real number X, 0 S X g 1 such that flX} = X." 3 Question Grade: Weighted Grade: I 4 Question Grade: Weighted Grade: 1.0 (1/10) 0.0 (0/1 .0) Note,the hypothesis was simplythat flx} = ,f 3 X . Your response Consider the statement: J“ If AD bisects ASAC of aSACJhen — : AC AB SD Correct DC ' Which choice corresponds to the hypothesis of the above statement? SAC is a triangle and AD bisects A SAC. (100%) Comment: When working with mathematical statements it is important to be able to distinguish which parts form the hypothesis and which form the conclusion. In a statement "If, P then Q ", P is the hypothesis and Q is the conclusion.Awayofthinking aboutwhich parts belong where is to ask 'What is being given to me" (for the hypothesis) and "What is the statementtrying to show" (for the conclusion). Hence, in the statement If AD bisects LSAC of aBAC,then — 2 AC AS SD DC I We have that the hypothesis is “ AD bisects A SAC of A SAC,“. This is equivalent to the correct option: SAC is atriangle and AD bisects A SAC. Your response Considerthe statement: Let fand g be real-valued functions with fix} } QM} for all X E [R . fixolhtxo) > 5iixoihlxol f°’ anyreal-valued function h and any X0 E IR. Which choice corresponds to the hypothesis of the above statement? f and g are real-valued functions with flx}> 9pc} for all x E IR ._(0%) Correct response Consider the statement: ‘xl‘ Let fend g be real-valued Incorrect functions with flx} > fix} for all x E [R . flxolhlxo) > thoihlxo) ”my real-valued function h and any XOER. Which choice corresponds to the hypothesis ofthe above statement? f, 9 and h are real-valued functions with flx}> g{x} for all x E IR. XOEIR. Total grade:0.0><1l1 = 0% Comment: When working with mathematical statements it is important to be able to distinguish which parts form the hypothesis and which form the conclusion. In a statement"lf P,then Q", P is the hypothesis and Q is the conclusion.Awayoffl1inking about which parts belong where is to ask 'What is being given to me" (for the hypothesis) and "What is the statementtrying to show" (for the conclusion). \fiewed in this light it is clearthat the hypothesis was composed ofthese bits ofgiven information: 1. f, g and h are real-wlued functions flx}> g{x}foraii x 6 IR XOEIR Hence the correct choice offor the hypothesis is: " f, g and h are real-valued functions with flx}> QM} for all X E IR. x0 E IR " 5 Question Grade: Weighted Gade: 6 Question Grade: Weighted Grade: 7 Question Grade: Weighted Grade: 1.0 (1/1.0) 1.0 (1/1.0) 1.0 (1/1.0) The conclusion was simply " ftxo)h(x0) } g(x0)h(x0)" which happens to be false in this example. Your response Which choice mostcloselycorresponds to the following statement? Everyquadratic polynomial fix} = x2 + bx + C can be factored into a productof “ two linearfactors. If flx} = x2 + bx + C, then fix) = (x— r1) (x — r2) for some numbers r1 and r2 .(100%) Comment: This statementbegins with the hypothesis that fis a quadratic bystating flx} = x2 + bx + C, and then concludes that fis the product oftwo linear factors bywriting flx} = (x — Fl) (x — r2). Thus, the oorrectanswer is: "If flx} = x2 + bx + C,then fix) = (x — r1) (x — r2) forsome numbers F1 and r2 ." Your response In orderto prove the implication "If A , then B", we assume that A is true, and use that “ assumption to prove that B is true. In orderto use the implication "If A, then B" we mustfirst Correct establish that A is true. If A is true, we can conclude that B is true. An element C E IR is called a root ofthe real polynomial fix) 2 {2an + - - - + alx + :20 if flc} = 0. Considerthe following proposition: If C is a root ofthe polynomial flx}, then {x — C} is a factor of fix}. If fl—l} = 0,then which ofthefollowingisafactorof fix} = x3 — 12 x2 + 23 x + 36 ? [x + 1} (100%) Comment: We are given that fl—l} = 0 , and so —1 is a root ofthe polynomial. [Verifythis yourself. You can find a root by plugging values of x into fix}. Start close to zero and work your way outward (e.g., x = :l: l, :l: 2, ). Usingthisapproachwefind: fl—l} = [—1}3 — 12 (—1}2 + 23 (—1} + 36 = 0.] Thus, bythe proposiiton we have that { x — {-1)} = [x + 1} is afactorof fix}. Your response In orderto prove the implication "If A , then B", we assume that A is true, and use that assumption v to prove that B is true. In orderto use the implication “If A,then B“ we mustfirstestablish that A Correct is true. If A is true, then we can conclude that B is true. Consider the following statement about planar geometry: "If C is acircle and Iis a Iine,then C and I intersectin atmosttwo points." Using onlythis proposition, underwhat circumstances could you correctlyconclude that there are at mosttwo points ofintersection? All of the above (100%) Comment: ...
View Full Document

{[ snackBarMessage ]}