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1113/2804 MATH Practice Test IV Spring 2007 Name: GTid (9xxxxxxxx): Instructor: Mitchel T. Keller Course (1113/2804): There are 29 questions on this exam on 4 pages (not counting this coverpage). Write your name at the top of each page. Answer each question in the space provided; if you need additional space, you may write on the back of the page, but clearly indicate by the appropriate problem that you have work on the back. Be sure to explain your answers, as answers that are not accompanied by explanations/work may receive no credit. You are to complete this exam completely alone, without the aid of notes, texts, calculators, cellular telephones, personal digital assistants, or any other mechanical or digital calculating device. By signing on the line below, you agree to abide by the Georgia Tech Honor Code, the principles of which are embodied by the Challenge Statement: I commit to uphold the ideals of honor and integrity by refusing to betray the trust bestowed upon me as a member of the Georgia Tech community. Failure to sign this cover page will not be considered evidence of academic misconduct. However, if the cover page is not signed, 5 points will be deducted from your raw total score on this exam. Student signature: Question: Points: Score: 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 0 11 0 12 0 13 0 14 0 MATH 1113/2804 Practice Test IV 18 April 2007 Name: This list of practice problems is longer than the actual test will be. Since you do not have calculators, you should write answers in exact form such as sin(42 ) where appropriate. Questions 1 through 16 are for MATH 1113 only. Questions 17 through 23 are for both classes. Questions 24 through 29 are for MATH 2804 only. Problems for MATH 1113 only. 1. Convert 315 to radians. 2. Convert 4 radians to degrees. 3 7 and coterminal? Why or why not? 4 4 3. Are the angles 4. A sprinkler system on a farm is set to spray water over a distance of 35 meters and to rotate through an angle of 140 . Draw a diagram that shows the region that can be irrigated with the sprinkler. Find the area of the region. 5. Evaluate cos 8 3 using the period of cosine to assist you. 6. For the right triangle below, nd the exact values of sin , cos , tan , and sec . 4 5 7. Solve for x in the right triangle below if = . 3 x 3 8. In which quadrant is tangent positive and secant negative? 9. Given that tan = 1 and sin < 0, nd cos . 2 1 5 10. Evaluate arcsin , cos 1 ( 1), and arccos cos . 2 4 Page 1 of 4 Points earned: out of a possible ?? points MATH 1113/2804 Practice Test IV 18 April 2007 Name: 11. Use identities fundamental to simplify (csc2 x)(1 cos2 x). 12. Solve the equation 3 3 tan u 3 = 0. (Be sure to give the general solution.) 13. Find all solutions of the equation 2 sin(2x) 2 = 0 in the interval [0, 2 ). 14. Find the exact value of sin(2u) given that sin u = 4 3 and < u < . 5 2 15. Use the power-reducing formulas to rewrite sin2 x cos2 x in terms of rst powers of the cosine. . What is the amplitude of f ? What is its 16. Consider the function f (x) = 2 sin 2x + 2 period? What is the phase shift of f ? Sketch the graph of f on the interval [ , ], given the graph of sin x on the interval [ , ] below. (You should make your sketch on the same set of axes used to plot sin(x) below.) 3 2 1 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 -1 -2 -3 Problems for both classes. 17. Solve the nonlinear system of equations below. x2 y 2 = 9 x y =1 18. Solve the system of equations below. 2x y = 10 x + 5y = 6 Page 2 of 4 Points earned: out of a possible ?? points MATH 1113/2804 Practice Test IV 18 April 2007 Name: 12 . x2 9 3x2 4 . x2 (x 2) x3 + x + 1 . Do not x(x 2)3 (x2 + 4)2 19. Find the partial fractions decomposition for 20. Find the partial fractions decomposition for 21. Give the form of the partial fractions decomposition for solve for the constants!! 22. Determine the order of the following matrices. 2 3 1 0 2 3 1 (a) 0 2 0 5 3 0 (b) 1 (c) 0 3 1 5 10 9.3 23. Perform the indicated matrix operations below. If the given operation is not possible, write unde ned and brie y say why you cannot perform the operation. 2 1 4 2 1 0 0 1 1 1 (b) 0 1 4 + 1 (a) 2 (c) 0 2 1 1 3 5 0 1 1 1 1 2 1 0 2 0 2 3 0 1 Problems for MATH 2804 only. 24. Solve the system of equations below. 2x + 4y = 5 16x + 50y = 55 1 1 3 2 (d) (e) 2 1 0 Page 3 of 4 Points earned: out of a possible ?? points MATH 1113/2804 Practice Test IV 18 April 2007 Name: 25. Sketch the graph of the solution set of the system of inequalities below. y < x+1 y > x2 1 26. Use back-substitution to solve the system of linear equations below. 85 x 7y + 8z = y 9z = 35 z = 3 27. Write the augmented matrix corresponding to the sytem of equations below. 2x + 3y + 3z = 3 6x + 6y 12z = 13 28. Solve the system of equations below. 1 x + 2y + 6z = 2x + 5y + 15z = 4 3x + y + 3z = 6 29. Solve the system of equations below. x + 2z = 1 2y = 4 x + 3y z = 4 Page 4 of 4 Points earned: out of a possible ?? points
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MATH 1501G1/G2/G3 Test II Fall 2006 Name: GTid (9xxxxxxxx): Instructor: Mitchel T. Keller Teaching Assistant and Section: There are 6 questions on this exam on 4 pages (not counting this coverpage). Answer each question on a separate solution sheet (...
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MATH 1113/2804 Practice Test II Spring 2007 Name: GTid (9xxxxxxxx): Instructor: Mitchel T. Keller Course (1113/2804): There are 20 questions on this exam on 7 pages (not counting this coverpage). Write your name at the top of each page. Answer each...
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MATH 1113 FORMULAS SPRING 2007 Formulas to know for Test IV and the Final Reciprocal identities. 1 sin u = csc u 1 csc u = sin u Quotient identities. sin u cos u Pythagorean identities. tan u = sin2 u + cos2 u = 1 1 sec u 1 sec u = cos u 1 cot u 1 c...
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MATH 1113/2804 Practice Test Ia Spring 2007 Name: GTid (9xxxxxxxx): Instructor: Mitchel T. Keller Course (1113/2804): There are 8 questions on this exam on 4 pages (not counting this coverpage). Answer each question in the space provided; if you need...
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MATH 1501G1/G2/G3 Quiz #5 Name: 26 September 2006 1. (5 points) Take the Derivative using the Chain Rule y = tan3 sin(2x) + (x + 4)3/2 + 1 1 sin2 (x2 ) . Solution: We begin by noting that 1 sin2 (x2 ) = cos(x2 ), so the second term becomes 1 1/ ...
Georgia Tech >> MATH >> 073 (Fall, 2009)
MATH 1113/2804 Quiz #2 Name: 24 January 2007 1. (5 points) Solve the inequality below and sketch the solution on the real number line |9 2x| 2 < 1. Solution: We rst must isolate the absolute value expression on one side of the inequality by addi...
Georgia Tech >> MATH >> 1501 (Fall, 2008)
MATH 1501G1/G2/G3 Quiz #9 1. (5 points) Find the indefinite integral Name: 2 November 2006 (3 - csc x)2 + ex dx ex + 1 Solution: We begin by expanding the integrand and have that the indefinite integral we wish to find is (9 - 6 csc x + csc2 x +...
Georgia Tech >> MATH >> 1501 (Fall, 2008)
MATH 1501G1/G2/G3 Quiz #1 1. (5 points) Solve the inequality Name: 24 August 2006 (x2 + 1)(x2 4)(5x + 1)(x 1)2006 (x2 3)(4x 7) < 0 and express your answer in interval notation. Be sure to explain how you arrive at your answer in order to receiv...
Georgia Tech >> MATH >> 1501 (Fall, 2008)
MATH 1501G1/G2/G3 Quiz #2 1. (5 points) Using the , method, show that Name: 31 August 2006 2x2 - 5x - 3 = 7. x3 x-3 lim Solution: Let > 0. We seek a > 0 such that if 0 < |x - 3| < , then 2x2 - 5x - 3 - 7 < . x-3 To do this, we note that the num...
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MATH 1113/2804 Quiz #3 Name: 7 February 2007 1. (5 points) Consider the function g(x) = -(x + 10)2 + 5. a. Identify the parent function f of g. b. Describe the sequence of transformations from f to g. c. Sketch the graph of g. Solution: a. The par...
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BIOINFORMATICS REVIEW Vol. 14 no. 7 1998 Pages 551-561 Comprehensive, comprehensible, distributed and intelligent databases: current status Dmitrij Frishman 1, Klaus Heumann 2, Arthur Lesk 3 and Hans Werner Mewes 1 Information Center for Protein Se...
Georgia Tech >> CS >> 4440 (Fall, 2008)
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MEDICAL NEWS said Hendin. Hospitals should implement programs that train medical students and physicians to recognize depression in themselves, colleagues, and patients. M...
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$\"vgv\"jgc l }r$igji l uhqsgs\"0hcv$vc pgg\"8xxi@v\"qgvc # f c e i h ! t d c t t f c x i ! # ! c i i c x x i h c i ! e f i t ! # ! c d !x i e i i h # i i e # ! ! t # f d x t t i f x ! e i ! i h e x e qy t # f d !x t ...
Georgia Tech >> CS >> 3451 (Fall, 2008)
CS3451: Project 1, Ray Tracing 1 Goal Implement ray-tracing. Your programs should be able to render triangles and spheres lit by a single white light source (no attenuation) and viewed from any point and with any screen location. All the necessary...
Georgia Tech >> CS >> 2007 (Fall, 2009)
Recall: symmetric setting Public-key (asymmetric) setting A K K pkR A skR S R S R 1 2 Asymmetric encryption schemes A scheme AE is specified a key generation algorithm encryption algorithm K, an E, and a decryption algorithm D. AE=(K,E,...
Georgia Tech >> CS >> 6260 (Fall, 2008)
Recall: symmetric setting Public-key (asymmetric) setting A K K pkR A skR S R S R 1 2 Asymmetric encryption schemes A scheme AE is specified a key generation algorithm encryption algorithm K, an E, and a decryption algorithm D. AE=(K,E,...
Georgia Tech >> CS >> 4400 (Fall, 2008)
Chapter 11 Relational Database Design Algorithms and Further Dependencies Copyright 2004 Ramez Elmasri and Shamkant Navathe Chapter Outline 0. Designing a Set of Relations 1. Properties of Relational Decompositions 2. Algorithms for Relational Dat...
Georgia Tech >> CS >> 6400 (Fall, 2008)
Chapter 11 Relational Database Design Algorithms and Further Dependencies Copyright 2004 Ramez Elmasri and Shamkant Navathe Chapter Outline 0. Designing a Set of Relations 1. Properties of Relational Decompositions 2. Algorithms for Relational Dat...
Georgia Tech >> CS >> 4440 (Fall, 2008)
CS 4440 Emerging Technologies and Applications TAKEHOME EXAM 1 (Assigned October 26, due in class- hardcopy October31) (Grade Weight 25%) (No late exams accepted) NOTE: Please allocate your time in proportion to the points assigned to the questions a...
Georgia Tech >> CS >> 3451 (Fall, 2008)
Drawing Bezier Curves 1 General polynomial curves Let B(t) (t [0, 1]) be a polynomial curve. A simple way to draw it would be to compute several points along it, like B(0), B(t), B(2t). . . B(N t) = B(1) (where t = 1/N ) and join each pair of conse...
Georgia Tech >> CS >> 2200 (Fall, 2008)
CS 2200 Fall 2006 Test 1 Name:_GT Number: gt_ Please indicate your GT number in the grid below so we have some chance of being able to read it. G t 0 0 0 0 a 1 1 1 1 B 2 2 2 2 c 3 3 3 3 d 4 4 4 4 e 5 5 5 5 F 6 6 6 6 G 7 7 7 7 h 8 8 8 8 i 9 9...
Georgia Tech >> CS >> 7470 (Fall, 2008)
The Memory Glasses: Subliminal vs.Overt Memory Support with Imperfect Information Richard W. DeVaul, Alex Sandy Pentland Massachusetts Institute of Technology Media Laboratory {rich,sandy}@media.mit.edu Abstract Wearables are frequently designed to s...
Georgia Tech >> CS >> 3451 (Fall, 2008)
cs3451 Test 1 - Spring 2007 Solutions 1. Let O = (0, 0, 0). The triangle ABC is visible from O if O and D are on dierent sides of the plane passing through A, B and C. Equivalently, it is visible if and only if (AB AC) AO and (AB AC) AD are not o...
Georgia Tech >> CS >> 3451 (Fall, 2008)
P12 P1 t : 1t t:1 t P123 P2 t: 1 t t: P01 1 t t 1 t:1 t P23 P0123=B(t) t: P012 P0 P3 Figure 1: De Casteljau algorithm. The control points P0 , P1 , P2 and P3 are joined with line segments (shown in red; those red intervals form somethin...
Georgia Tech >> CS >> 6262 (Fall, 2008)
Computer and Network Security via Program Analysis (Malware Analysis) Monirul Sharif Guest Lecture CS-4803 (CNS) College of Computing Georgia Institute of Technology Date: 09/22/2006 Introduction Program analysis techniques are used for malware det...
Georgia Tech >> CS >> 3451 (Fall, 2008)
Practice problems - set 5 1. Let\'s say that someone gave you a function LookU pColor(x1, y1, x2, y2) which, when called with floating point arguments x1, y1, x2, y2, returns the intensity of light arriving at (x1, y1, 0) from the direction of (x2, y2...
Georgia Tech >> CS >> 3451 (Fall, 2008)
1. You are clipping a triangle with respect to a rectangular viewport. Can the result have: a) b) c) d) e) 3 edges? 4 edges? 5 edges? 6 edges? 7 edges? For each case, either explain why or draw an example. 2. You are drawing two triangles, blue and ...
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