Math 1010 - Practice Final ExamUniversity of UtahFall 2009Name:• There are 20 p roblems, and each is worth five points. So, there are100 points possible.• You are not allowed to get help from your textbook, class notes, otherstudents, or any other form of outside aid. You’re only allowed touse scratch paper if you need it. If you have questions, please askyour instructor. You may not talk with other students during theexam.Problem Scores:1 2 3 4 56 7 8 9 1011 12 13 14 1516 17 18 19 20Total Score:11 When Math had Numbers. - Simplify the fraction:34−11015.22 Absolutely Equal. Find the solution(s) to the e quation:|x + 8| = |2x + 1|.33 Working Together is Fun. A ma ster gravedigger can dig Ophelia’sgrave in five hours. An apprentice gravedigger can dig he r grave in8 hours. How long does it take the two of them to dig the grave ifthey work together, assuming they don’t talk.44 Going the Distance. Find the distance between the points (1, 3) and(4, −2).55 Find that Line. Find an equation for the line with slope 2 and x-intercept 5. Note that it says x-intercept, not y-intercept.66 Master of Your Domain. Find the d omain of the function:f(x) =√x2− 1 +x − 2x2− x − 2.77 Working the System. Solve the following system of linear equations:x − 2y = −1x − 5y = 288 Not the O’reilly Factor. Factor the following polynomial:15x2− 11x + 299 Keep It Simple. Simplify the following expression. Your answermust contain only positive exponents:(2x−2y4)3y(10x3y)2.1010 Add ’Em Up. Perform the indicated operations and simplify:xx2− 9+3x2− 5x + 61111 Grow, Grow, Grow!. A biologist starts a culture with 100 bacteria.The population P of the culture is approximated by the model below,where t is the time in hours. Find the time required for the popula-tion to increase to 800 bacteria.P =500(1 + 3t)5 + t.1212 Thesis, Antithesis, Synthesis. Find the quotient and remainder:x5− 13x4− 120x + 80x + 31313 Step One Is?. Solve the rational equation:15x+9x − 7x + 2= 9.1414 Rules for Radicals - Simplify the radical expression:−4s42y781x4.1515 Even More Radical - Combine the radical expression, if possible:3y4q2x5y3− x4q162xy7.1616 It’s Easy If You Try - Write the complex number in standard form:(Note : Standard form is a + bi).√−25 −√491717 The One Equation You Must Know! - Find the solution(s) to thequadratic equation:3x2+ 7x = 2.1818 Real Graphs Have Curves - Write the equation of the parabola withvertex (−2, 2) and y-intercept (0, −2). Graph the parabola. (Hint:x = −b/(2a)).1919 It’s Logarithm, Logarithm, It’s Big It’s Heavy It’s A Function1-Compute the following logarithms:• log4(256)• log2(0.25)• log16(8) (Hint: Use the change of base formula.)Narf! Zoit! Egad!1This is a very obscure and butchered reference to Ren and Stimpy.2020 Ben Franklin Would Be Proud - You invest money at an annual in-tere st rate of 7 percent. How long (in yea rs) will it take for your in-vestment to triple (increase to three times its original amount)? Giveyour answer as a logarithmic expression, don’t worry about a de ci-mal