Version A QP1-14,18-24, Calc ,App B-D

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1 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D Student s Printed Name: Instructor: CUID: 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: 1. Show legible and logical (relevant) justification which supports your final answer.. Use complete and correct mathematical notation. 3. 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 Points Points Earned Free Response Problem Possible Points Free Response 66 8 Multiple Choice 3 Points Earned 9 5 Test Total 100 Page 1 of 1

2 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D Multiple Choice. There are 1 multiple choice questions. Each question is worth 3 points and has one correct answer. The multiple choice problems will count as 3% of the total grade. Use a number pencil and bubble in the letter of your response on the scantron sheet for problems 1 1. 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. 1. (3 pts.) If sin x = 5 5 a) and x π,π, then find tan x. b) 1 c) - 1 d) - e). (3 pts.) Evaluate and simplify π 11π π cos + cot sin 6 3. a) 1 b) 3 1 c) 1 d) e) 3 + Page of 1

3 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D 3. What are the real roots of x! + x + 1? ( pts.) a) x = 1± 5 b) x = 1 5 c) x = 1± 5 d) x = 1 e) There are no real roots of this equation.. Below are the graphs of four relations. How many of these relations are functions? ( pts.) a) b) 1 c) 0 d) e) 3 5. Expand x + 3 ( pts.) ( ) ( ) x 3x + 9 a) x b) x 3 7 c) x 3 3x + 9x + 7 d) x 3 6x 18x + 7 e) x 3 9x + 7 Page 3 of 1

4 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D 6. (3 pts.) Which is the graph of y = cos x π? a) b) c) d) e) Page of 1

5 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D 7. If we know f (g(x)) = x + x +1, and f (x) = x, which of the following is g(x)? ( pts.) a) g(x) = x +1 b) g(x) = x c) g(x) = x d) g(x) = x +1 e) g(x) = x + x Which of the following is a root of f x = x! + 7x! 3x 18? (3 pts.) a) x = b) x = 3 5 c) x = 3 d) x = 3 e) x = 6 9. Which of the following are even functions? I. f( x) = π + xsin x ( pts.) II. h(x) = 1 x III. jx () = x x a) II only b) I and II c) III only d) I only e) I and III Page 5 of 1

6 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D 10. Find the equation of the line containing an x -intercept of 8 and a y -intercept of 6. (3 pts.) a) b) c) d) e) y+ 6 = ( x 8) 3 3 y+ 6 = ( x 0) 3 y 0 = ( x 0) 3 y 6 = ( x 0) y+ 6 = ( x 0) ( pts.) What is the domain of g(x) = 3x 9 5 x 7? a) 7, b), 7 7, c) (, ) e), 7 7, d), 7 1. Which one of the following is equivalent to 0? ( pts.) a) c) π π radians b) 6 3 radians π 3 radians d) 5 π radians e) π 3 radians Page 6 of 1

7 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D 13. Which function gives the following graph? ( pts.) a) y = ( x ) + b) y = ( x +1) c) y = ( x + ) d) y = ( x + ) + e) y = ( x + ) 1. Solve the following equation for x. ( t+ ) x= t x+ 5 (3 pts.) a) x = t + 5 t + t + b) x = t c) x = t + t t 3 d) x = t 5 e) x = t + t+ 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 1

8 MATH 100 Test 1 Fall 016 QP1-1,18-, 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. 1. (7 pts.) Graph the following piecewise function: x 3 x < f (x) = 1 x < 1 x x > 1. (3 pts.) Given f (x) = x, g(x) = 1, and h(x) = x +1, find ( f! g! h)(x) = f (g(h(x))). x 3. (5 pts.) Find an equation of the line that passes through ( 1,3) and is perpendicular to x y + 3 = 0. Present your answer in slope-intercept form. Page 8 of 1

9 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D. ( pts.) Find the x -intercept(s) of the function f (x) = x x +1. State your answer(s) as point(s). 5. ( pts.) Sketch a graph of f (x) = 1+ 1 x a. (3 pts.) Place the following quadratic equation into the form y = a(x h) + k. y = 5x 10x + 3 b. (1 pt.) What is the vertex of the quadratic equation y = 5x 10x + 3? Page 9 of 1

10 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D 7. (5 pts.) Sketch the curves y = x +1 and y = (x +1). Shade the region enclosed by the two functions. Clearly mark the point(s) of intersection. 8. ( pts.) Write the equation of a circle with center (6, -1), that passes through the point (,) (5 pts.) Find all real solutions of the equation x 3 x 3 15 = 0. Page 10 of 1

11 MATH 100 Test 1 Fall 016 QP1-1,18-, Calc ,App B-D 10. (5 pts.) Given that x = is a root of g(x) = x 3 x, factor g( x) completely. Show all of your work in a clear, logical manner. Final Factored Form: 11. (5 pts.) The height in feet of a baseball thrown into the air is given by h(t) = 16t + 30t + 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. 1. ( pts.) Compute the following. Fully simplify your answer and present your answer as a single fraction. x 3 ( + 6x) where x 3, x x + x ( ) x Page 11 of 1

12 MATH 100 Test 1 Fall ( pts.) Use sin x + y QP1-1,18-, Calc ,App B-D ( ) = sin x cos y + cos xsin y to help prove the following: π sin x+ cos x= sin( x+ ) ( ) ( ) x 1 1. (6 pts.) State the domain of the rational function g(x) = x +1. Also find all the x x 3 real root(s) and the y-intercept. If there are no roots or if there is no y-intercept say so. Domain use interval notation Roots list as x-value(s) y-intercept write as a point 15. (1 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 1 bubbled in answers; has MATH 100 and my Section number written at the top; has my Instructor s name written at the top; has Test No. 1 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 1 of 1

Version B QP1-14,18-24, Calc ,App B-D

Version B QP1-14,18-24, Calc ,App B-D 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