MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D Student s Printed Name: _Key_& Grading Guidelines CUID: Instructor: Section # : You are not permitted to use a calculator on any portion of this test. You are not allowed to use any textbook, notes, cell phone, laptop, PDA, Apple watch, or any technology on either portion of this test. All devices must be turned off while you are in the testing room. During this test, any communication with any person (other than the instructor or a designated proctor) in any form, including written, signed, verbal, or digital, is understood to be a violation of academic integrity. No part of this test may be removed from the testing room. Read each question very carefully. In order to receive full credit for the free response portion of the test, you must:. Show legible and logical (relevant) justification which supports your final answer.. Use complete and correct mathematical notation.. Include proper units, if necessary.. Give exact numerical values whenever possible. You have 90 minutes to complete the entire test. On my honor, I have neither given nor received inappropriate or unauthorized information at any time before or during this test. Student s Signature: Do not write below this line. Free Response Problem Possible Earned Free Response Problem Possible 7 0 5 5 5 5 6 6 5 7 5 Free Response 66 8 Multiple Choice Earned 9 5 Test Total 00 Page of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D Multiple Choice. There are multiple choice questions. Each question is worth points and has one correct answer. The multiple choice problems will count as % of the total grade. Use a number pencil and bubble in the letter of your response on the scantron sheet for problems. For your own record, also circle your choice on your test since the scantron will not be returned to you. Only the responses recorded on your scantron sheet will be graded. You are NOT permitted to use a calculator on any portion of this test.. If we know f (g(x)) = x + x +, and f (x) = x, which of the following is g(x)? ( pts.) a) g(x) = x + b) g(x) = x c) g(x) = x + x + d) g(x) = x e) g(x) = x +. Which of the following are even functions? I. f( x) = π + xsin x ( pts.) II. h(x) = x III. jx () = x x a) II only b) I and II c) III only d) I and III e) I only. Expand x + ( pts.) ( ) ( ) x x + 9 a) x x + 9x + 7 b) x 9x + 7 c) x + 7 d) x 7 e) x 6x 8x + 7 Page of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D. ( pts.) If sin x = 5 5 a) - and x π,π, then find tan x. b) - c) d) e) 5. What are the real roots of x! + x +? ( pts.) a) x = 5 c) x = e) There are no real roots of this equation b). x = ± 5 d) x = ± 5 6. Which of the following is a root of f x = x! + 7x! x 8? ( pts.) a) x = b) x = c) x = 5 d) x = 6 e) x = Page of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D 7. Below are the graphs of four relations. How many of these relations are functions? ( pts.) a) b) 0 c) d) e) 8. ( pts.) What is the domain of g(x) = x 9 5 x 7? a), 7 7, b) 7, c), 7 7, d), 7 e) (, ) Page of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D 9. ( pts.) Evaluate and simplify π π π cos + cot sin 6. a) + b) + + c) d) e) 0. Which function gives the following graph? ( pts.) a) y = ( x + ) b) y = ( x + ) + c) y = ( x + ) d) y = ( x +) e) y = ( x ) + Page 5 of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D. ( pts.) Which is the graph of y = cos x π? a) b) c) d) e). Which one of the following is equivalent to 0? ( pts.) a) c) π radians b) π radians 5 π radians d) π 6 radians e) π radians Page 6 of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D. Solve the following equation for x. ( t+ ) x= t x+ 5 ( pts.) a) x = t + 5 t + b) x = t + t c) t 5 x = d) x = t t + t+ e) t + x = t + 5. Find the equation of the line containing an x -intercept of 8 and a y -intercept of 6. ( pts.) a) b) c) d) e) y 6 = ( x 0) y+ 6 = ( x 0) y 0 = ( x 0) y+ 6 = ( x 8) y+ 6 = ( x 0) The Free Response section follows. PLEASE TURN OVER YOUR SCANTRON while you work on the Free Response questions. You are welcome to return to the Multiple Choice section at any time. Page 7 of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D Free Response. The Free Response questions will count as 66% of the total grade. Read each question carefully. In order to receive full credit you must show legible and logical (relevant) justification which supports your final answer. Give answers as exact answers. You are NOT permitted to use a calculator on any portion of this test.. (7 pts.) Graph the following piecewise function: x x < f (x) = x < x x > Awarded Proper line.5 Proper domain for line 0.5 Open circle on line right side 0.5 Flat line 0.5 Proper domain for flat line 0.5 Closed left, open right flat line Absolute value.5 Proper domain for absolute value 0.5 Open left side absolute value 0.5 - not a function -5 all functions drawn completely - nothing erased (severe case of not a function ). ( pts.) Given f (x) = x, g(x) =, and h(x) = x +, find ( f! g! h)(x) = f (g(h(x))). x f (g(h(x))) = x + Awarded Insight into g(h(x)) Can be implied Correct answer work does not have to be shown for full credit Page 8 of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D. (5 pts.) Find an equation of the line that passes through (,) and is perpendicular to x 5y+ = 0. Present your answer in slope-intercept form. given line: x 5y + = 0 5y = x y = 5 x + 5 so m tan = 5 desired line: y = 5( x + ) change form: y = 5x 0 y = 5x 7. ( pts.) Find the x -intercept(s) of the function f (x) = x x +. State your answer(s) as point(s). cannot be factored so with quadratic formula: x = ± 6 8 = ± 8 = ± as points: +,0,,0 = ± Awarded Identify slope of given line (can be implied) Identify slope of perpendicular line pt negative pt reciprocal Perpendicular slope properly used in line OR find correct y-intercept Slope-intercept form -0.5 for sign errors aside from slope of perpendicular - missing parentheses leading to an error -0.5 missing parentheses poor notation additional error not involved - another errors going to slope/intercept incorrectly work was followed after error Awarded Constants into quadratic formula properly Simplified Answers presented as points -/ for g(x)=roots -0.5 for error each error in quadratic formula -0.5 switching x and y in points 5. ( pts.) Sketch a graph of f (x) = + x. Awarded proper vertical asymptote proper horizontal asymptote (, 0) 0.5 (,-) 0.5 Proper shape Page 9 of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D 6. a. ( pts.) Place the following quadratic equation into the form y = a(x h) + k. ( ) + ( ) + 7 y = 7 x x + y = 7 x x + y = 7( x ) 5 y = 7x x + b. ( pt.) What is the vertex of the quadratic equation y = 7x x +?, 5 right or wrong based on part a ( ) Awarded Factor leading coefficient out of 0.5 first two terms Add and subtract proper constant.5 Answer in proper form - a not factored out but tried to complete the square anyway - moving numbers in or out of the parenthesis incorrectly 7. (5 pts.) Sketch the curves y = x + and y = (x ). Shade the region enclosed by the two functions. Clearly mark the point(s) of intersection. Awarded Line proper y intercept 0.5 Line proper slope Parabola faces up 0.5 Parabola proper vertex Parabola proper shape 0.5 Intersect in right place - do not have to show coordinates Proper shading 0.5 Page 0 of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D 8. ( pts.) Write the equation of a circle with center (5, -), that passes through the point (,). d = ( 5 ) + ( ) = 6 + 9 = 5 = 5 equation of circle: ( x 5) + ( y + ) = 5 9. (5 pts.) Find all real solutions of the equation x + x 5 = 0. Awarded calculate radius Equation of circle -0.5 for several missing equal signs -0.5 or - minor calculation error, dependent on severity - incorrect point as center - points for equations other than circles (lines, parabolas, etc.) **Work was followed through with incorrect r- value **It was not necessary to use the distance formula, and there was no penalty if r was found by substituting point into the circle equation x + 5 x = 0 x + 5 = 0 x = 0 x = 5 x = x = 5 x = 7 Awarded Solve the quadratic by factoring, or quadratic formula, etc. Correct solution to given equation ( pt each) - each extra solution -0.5 did not carry the equals sign -0.5 incorrect notation -.5 per incorrect number in factoring - per incorrect sign in factoring -0.5 a substitution was used but never defined Page of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D 0. (5 pts.) Given that x = is a root of g(x) = x x, factor g( x) completely. Show all of your work in a clear, logical manner. x + x + x x + 0x x x x x x x x x x 0 Final Factored Form: g(x) = (x )(x + x + ) Awarded Use proper factor for division Correctly perform long division of polynomial Correct rewrite of polynomial Full credit for correct synthetic division -0.5 to.5 for each error in polynomial long division depending on the severity and cascading effect -0.5 to - for incomplete work in polynomial long division -.5 factoring the irreducible quadratcis - lack of work - no work at all Page of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D. (5 pts.) The height in feet of a baseball thrown into the air is given by h(t) = 6t + 0t + where t is the time in seconds after the ball was released ( t 0 ). Realizing that an object hits the ground when its height is zero, find out how long it takes the ball to hit the ground. Be sure to include units on your answer. 0 = 6t + 0t + ( ) 0 = 8t 5t ( )( t ) 0 = 8t + t = t = 8 sec Awarded Factor Set each factor equal to zero 0.5 0.5 for each factor solutions 0.5 each Eliminate negative 0.5-0.5 no units - factored incorrectly but solved it correctly -5 factoring = constant - trying to complete the square -5 guess and check OK to use the quadratic formula without complete simplification Page of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D. ( pts.) Compute the following. Fully simplify your answer and present your answer as a single fraction. x ( x( x + ) x + x) where x, x x ( + x) x x + x x + x = x ( ) x x + x(x ) ( ) x ( ) ( x + ) x = x x + x (x ) = = x x( x + ) x x = x ( ) x + Awarded Multiply by reciprocal 0.5 Factor out negative 0.5 Factor bottom term Two cancellations Correct final answer -0.5 to - algebra mistakes or not simplifying answer do not follow egregious errors x x x + = ( ) x ( + 6x) x x + x + 6 x ( x + x + 6) = x = x x( x + ) x x + 6x = x + x + 6 x + x +x Awarded Multiply by reciprocal 0.5 Expand the top Expand the bottom Factor the bottom Correct final answer 0.5-0.5 to - algebra mistakes or not simplifying answer do not follow egregious errors Page of 6
MATH 00 Test Fall 06. ( pts.) Use sin x + y QP-,8-, Calc.-.,App B-D ( ) = sin x cos y + cos xsin y to help prove the following: π sin x+ cos x= sin( x+ ) sin x + π = sin x cos π + cos xsin π = sin x = + cos x [ sin x + cos x] = sin x + cos x ( ) ( ) x. (6 pts.) State the domain of the rational function g(x) = x +. Also find all the x x real root(s) and the y-intercept. If there are no roots or if there is no y-intercept say so. ( g(x) = x +) ( x ) ( = x + )( x +) ( x ) x x x ( )( x +) x = and x = are NOT in the domain g(x) = 0 when x =, x =, and x = but x = does NOT count as a root because it is not in the domain g( 0) = ( ) = Awarded Apply addition formula.5 Value of sine and cosine at.5 pi/ Simplify -0.5 to - incorrect notation/bad form - to - incorrect proof techniques Domain Partial credit can be given for factoring denominator (0.5), solutions to denominator=0 (0.5), each interval (0.5 each) Roots Partial credit can be given for setting numerator = 0 (0.5), solving (0.5), eliminating root not in domain (0.5) Intercept Partial credit can be given for trying to calculate g(0) (0.5) Awarded.5.5-0.5 for brackets [] in the domain (one time deduction) - so many brackets that their answer is all reals - each extra root (for example did not eliminate -, or included ) -0.5 not having plus/minus ½ root -0.5 if incorrect sign in intercept work and/or minor error - if y-intercept was stated as (y,0) -0.5 if y-intercept was not stated as a point Domain use interval notation Roots list as x-value(s) y-intercept write as a point (, ) (,) (, ) x =, x = 0, Page 5 of 6
MATH 00 Test Fall 06 QP-,8-, Calc.-.,App B-D 5. ( pt.) Check to make sure your Scantron form meets the following criteria. If any of the items are NOT satisfied when your Scantron is handed in and/or when your Scantron is processed one point will be subtracted from your test total. My scantron: is bubbled with firm marks so that the form can be machine read; is not damaged and has no stray marks (the form can be machine read); has bubbled in answers; has MATH 00 and my Section number written at the top; has my Instructor s name written at the top; has Test No. written at the top; has Test both written at the top and bubbled in below my CUID; and shows my correct CUID both written and bubbled in (bubble in a 0 in place of the C). Page 6 of 6