Senior Assessment ExamFall 2003 Senior Assessment Exam As part of MATH 490, you will take the Senior Assessment Exam (during the final exam period), which will count for at least 25% of your course grade. The exam will consist of 25 questions (22 multiple choice or fill in the gaps/short answer) and 2-3 free response questions (for example to draw the graph of a function with given properties). The questions will cover core ideas from the following courses: MATH 102/103(3-4)PrecalculusMATH 206-209(8)Calculus MATH 248(2)Discrete MathematicsMATH 255(2)Linear Algebra MATH 325(2)Proof and Notation MATH 455(2-3)Abstract Algebra MATH 465(2-3)Advanced Calculus The number in parenthesis indicates the number of multiple choice/short answer questions from each of the courses or course sequences. The three free response questions may come from any of the courses. This handout contains a description of the topics that you should be familiar with and provides sample problems for each area. Note that NO CALCULATORS or NOTES will be allowed in the exam. Assessment Exam Syllabus for College Algebra Operations with and simplification of polynomial, rational, and radical functions and solving simple equations involving them. Properties of exponential and logarithmic expressions Graphs of simple polynomial, rational, radical, exponential, and logarithmic functions. Composition of functions, inverse of functions. Applications of the above. e s e q t J oe u o N' eI' ps' cv / s. qb / I' B: s lI= x Z +yJ os u o q n l o ss r e q u n uI B e re q l J oI I B J Ol u n s e g . [' v' u / r l o pp e ^ o u e qI I I A Iq d u r 8 a q t J oI r v' e' r e A r o lu e A eo qi l 1 , t l01 er u r u m u p rl u e J ? d d ee q l. p' w n u r r u r ul u a r u d d uw e q r e 8 u o l o u d e u l0 1 3r u n m i l m r rl u e r e d d ea q J ,. c' 1 q 8 1 - ro W o l p s l o r u e qi l p \t xl vt u n u D r u r up e - r e d d ee q g. q' ; a q 8 r qu e A ee qi l y v \t ' xwt u n r u D c e r ul u e r e d d u e q g. e6 0> ,p I I s' I(b) for some < | | L xnN n >(c)there is an> Nwith|whenever 0 + < L xn| N n >(d)none of the above 3)Every convergent sequence on the real line is (a)Cauchy (b)monotone (c)bounded (d)(a) and (c) 4)Which of the following sets are open(a) =+ 1)12 ,11 (nn n (b){ } 1 : ) , (222122 1 + x x R x x(c) = +2]12 ,11 [nn n (d)(a) and (c) 5)The closure of a subsetis nR A (a)the union of with all its interior pointsA(b)the intersection of all the closed sets containingA(c)any closed set containingA(d)the intersection of with its complementA 6)Let( fbe a sequence of continuous functions defined on [0,1]. State what it means for the sequence to converge uniformly to a function f(x)on [0,1]. ) xn) (x fn