Mathematics 11Final Exam2nd Sem AY 2015-2016May 21, 2016Directions:Show all necessary solutions. No solution, no credit. Use blue or black pen only. All answers must bewritten in simplest form. Box your final answers.I. Do as indicated.(2 points each)1. GivenU=R, find [1,2)Cand [1,2)C∩[0,3].2. Simplifyr15+√20-4√25.3. Ifzvaries jointly asxandy, andz= 3 whenx= 2 andy= 1, findzwhenx= 3.4. Give the sum of the first 100 terms of the arithmetic sequence with 40 as its first term, and-2 as its commondifference.5. LetCbe the center of the circle with equationx2-4x+y2= 4. IfOis the origin, find the length of the linesegmentCO.II. Factorx2y-y+ 2x2-2 completely.(3 points)III. Simplify the following expressions. (Assume all denominators are nonzero.)(3 points each)1.27x-5x131/32.x2x+ 3+ 12-22x+ 33.x3-84x-4÷x2+ 2x+ 4x2+x-24.2x+ 2+102x2+ 3x-2IV. Giveng(x) =x-22x+ 3. Find the following:1.g-1(x)(2 points)2. range ofg(1 point)3. (g◦g)(2)(1 point)V. Solve forx.(4 points each)1.x+√7-2x= 22.x3-6x2+ 7x+ 2 = 03.4x+ 12x≥14.