Name: ____________________________________________________________________ Pre-Calculus - Test 2 MATH 1500 Summer 2020 Instructions There are two parts to completing the test: 1) Entering your answers into the Quiz in D2L/Brightspace 2) Submitting your supporting work for those answers in an Assignment in D2L/Brightspace. You have 90 minutes from the time you start the Quiz to complete part 1. You have a few days to complete part 2 (which can also be done by physically submitting your work). Use additional pages if there is not enough room on the printed test. You are graded on how you solve the problem, not just your final answer. Be sure to submit supporting work for all questions unless otherwise noted. Please be organized and work neatly. Illegible or disorganized solutions may adversely affect your score. Feel free to re-write your supporting work after submitting the Quiz to make it easier to read. If you find you submit an incorrect answer in the Quiz, you may submit an updated answer with your supporting work. This will earn additional but not full credit. Please make sure this is clearly noted. You may use the book, PowerPoint slides, notes, etc., but you may NOT consult other individuals or other resources like external websites while working the text questions. You may NOT share the questions on the test nor discuss the test with other students until after the time and date for submitting the supporting work. Graphing calculators may be used except those with symbolic computation capabilities (eg TI-89, TI-NSpire CAS, TI-92, etc.). Each problem is worth 10 points. Points per problem: Total Points MATH1500 PreCalculus Test 2 !"# Page 1 of 6 1) Find the following for the functions !(#) = !$# and &(#) = # 5 if defined. If the composition is not defined write \"The value is not in the domain\". a) (! &)(14) = ___________ b) (& !)(2) = ___________ c) (& &)(30) = ___________ d) (" $)(&) = ________________________ (no need to simplify) 2) The given function is one-to-one. Find the inverse. !(#) = ! $# (#) = ________________________ 3 #2 MATH1500 PreCalculus Page 2 of 6 Test 2 3) Determine whether the functions in the given tables are linear, exponential, or neither. If linear or exponential, find a formula for the function. Circle the correct answer and give the formula. If the function is Neither, write NONE for the formula. Show supporting work x -1 0 1 2 3 f(x) 3 6 12 24 48 x -1 0 1 2 3 g(x) 4 8 14 22 32 x -1 0 1 2 3 h(x) 1 5 9 13 17 a) f(x) -is Linear Exponential Neither f(x) = _________________ b) g(x) -is Linear Exponential Neither g(x) = _________________ c) h(x) -is Linear Exponential Neither h(x) = _________________ MATH1500 PreCalculus Test 2 Page 3 of 6 4) Use the definition of the logarithmic function and the properties of logarithms for the following problems. No supporting work required. a) Change the exponential statement into an equivalent logarithmic statement 9% = 126 log = b) Find the exact value without using a calculator: log & 1 = __________________________ 64 c) Rewrite using only natural logarithms (ln): log ' 291 = ____________________ 5) Solve the equation. For full credit give an exact answer. logx343 = -3 x = _________________ MATH1500 PreCalculus Test 2 Page 4 of 6 6) Express as a sum and/or difference of logarithms. Express powers as factors. Supporting work required for full credit. log 7 &5 # 3 (&2 + 9)( 9 = ____________________________________________________________________________ 7) Ethan is 10 years old. His grandmother has promised to give him $10,000 on his 18th birthday. If his grandmother has $7000 today, at what interest rate must she invest the money to have $10,000 in 8 years? Assume monthly compounding. Interest Rate: ____________________ MATH1500 PreCalculus Test 2 Page 5 of 6 8) A particular isotope of Vanadium has a half-life of 330 days. How long does it take 800 mg of this isotope of vanadium to decay to 4 mg?. Days until 4 mg of vanadium remains: ______________ 9) The radius of the wheel on a motorcycle is 12.5 inches. If the wheel of the motorcycle turns at 1075 revolutions per minute, find the following. The following conversions may be useful: 5280 feet = 1 mile 12 inches = 1 foot 60 minutes = 1 hour a) The angular velocity of the wheel in radians per minute: b) The linear velocity of the motorcycle in inches per minute: c) The linear velocity of the motorcycle in miles per hour: = _____________ radians/min v = _____________ inches/min v = _____________ miles/hr MATH1500 PreCalculus Page 6 of 6 Test 2 10) Fill in the exact values for Sine, Cosine, and Tangent for the given angles (in radians) in the first quadrant. No supporting work required. !=0 != $ 6 != $ 4 != $ 3 != $ 2 sin ! cos ! tan ! 11) The terminal side of an angle, , in standard position passes through the point (5, -12). Find the exact value of each of the trigonometric functions. sin !\t= ______ csc ! = ________ cos ! = ______ sec ! = ______ tan ! = ______ cot ! = ______