Final Exam Study Guide PDF (MATH 1113 Fall 2024)

Final Exam Study Guide (2% of your course grade) #1 Student Name: _____________________ Class Name: MATH 1113 Fall 2024 - TR - 2:00 PM - Bhat Number...

Final Exam Study Guide (2% of your course grade) #1 Student Name: _____________________ Class Name: MATH 1113 Fall 2024 - TR - 2:00 PM - Bhat Number of Questions: 50 Instructor Name: Bhat, Ashwini Question 1 of 50 The functions f and g are defined as follows. 2 7x − 3 f x =x −x−2 and g x = 5x − 1 x Find f x+7 and g. 2 Write your answers without parentheses and simplify them as much as possible. Question 2 of 50 The functions f and g are defined as follows. x+8 f x = 2 x − 64 x+7 g x = 2 x − 14x + 49 For each function, find the domain. Write each answer as an interval or union of intervals. Question 3 of 50 Find the domain of the function. x+1 f x = 2x − 2 Write your answer as an interval or union of intervals. Final Exam Study Guide (2% of your course grade) #1 Page 1 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 4 of 50 f x+h −f x Find the difference quotient , where h ≠ 0, for the function below. h 2 f x = − x − 4x + 1 Simplify your answer as much as possible. Question 5 of 50 f x+h −f x Find the difference quotient , where h ≠ 0, for the function below. h x f x = x+8 Simplify your answer as much as possible. Question 6 of 50 1 5 For the functions f x = and g x = , find the composition f ∘ g and simplify your answer as x−4 x much as possible. Write the domain using interval notation. f∘g x = ________________________ Domain of f ∘ g : ________________________ Final Exam Study Guide (2% of your course grade) #1 Page 2 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 7 of 50 Graph the rational function. 2 − 4x − 8x + 4 f x = 2x + 1 y 10 8 6 4 2 x -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 Question 8 of 50 Graph the rational function. 2 x − 10x + 24 g x = x−6 y 10 8 6 4 2 x -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 Final Exam Study Guide (2% of your course grade) #1 Page 3 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 9 of 50 The one-to-one function g is defined below. 7x g x = 6x − 1 −1 −1 Find g xis the inverse of g. , where g −1 Also state the domain and range of g in interval notation. Question 10 of 50 Use the properties of logarithms to expand the following expression. 2 x log 3 5 x+8 Your answer should not have radicals or exponents. You may assume that all variables are positive. Question 11 of 50 Solve for x. log5 x + 8 = log5 x + 4 + 1 Question 12 of 50 Solve for x. 2 x − 17x + 32 7 − 4x 8 = 64 Final Exam Study Guide (2% of your course grade) #1 Page 4 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 13 of 50 The number of bacteria P h in a certain population increases according to the following function, where time h is measured in hours. 0.06 h P h = 2900e How many hours will it take for the number of bacteria to reach 3600? Round your answer to the nearest tenth, and do not round any intermediate computations. Question 14 of 50 Find sec θ, sin θ, and tan θ, where θ is the angle shown in the figure. Give exact values, not decimal approximations. 17 θ 8 Question 15 of 50 A ladder leans against the side of a house. The angle of elevation of the ladder is 73°, and the top of the ladder is 14 ft from the ground. Find the length of the ladder. Round your answer to the nearest tenth. ? 14 73° Final Exam Study Guide (2% of your course grade) #1 Page 5 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 16 of 50 The length of a shadow of a building is 50 ft when the sun is 67° above the horizon. Find the height of the building. Round your answer to the nearest tenth. ? 67° 50 Question 17 of 50 A ramp 20 ft long rises to a platform. The bottom of the platform is 12 ft from the foot of the ramp. Find x, the angle of elevation of the ramp. Round your answer to the nearest tenth of a degree. Platform 20 x 12 Ground Final Exam Study Guide (2% of your course grade) #1 Page 6 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 18 of 50 13π Let θ=. Complete parts (a), (b), and (c) below. 4 (a) Sketch θ in standard position. y x (b) Find an angle between − 2π and 0 that is coterminal with θ. Write your answer in radians in terms of π. _______ (c) Find an angle between 0 and 2π that is coterminal with θ. Write your answer in radians in terms of π. _______ Final Exam Study Guide (2% of your course grade) #1 Page 7 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 19 of 50 Answer the following. (a) Find an angle between 0° and 360° that is coterminal with − 225°. 10π (b) Find an angle between 0 and 2π that is coterminal with. 3 Give exact values for your answers. Question 20 of 50 5π Sketch θ= in standard position. Then show its reference angle. 4 y x Question 21 of 50 28π Find the reference angle for −. 9 Final Exam Study Guide (2% of your course grade) #1 Page 8 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 22 of 50 8 Let θ be an angle such that csc θ = and tan θ > 0. 5 Find the exact values of cot θ and cos θ. Question 23 of 50 5π Find the exact value of sin −. 6 Question 24 of 50 Find the exact values below. sec 30° tan 30° Question 25 of 50 Find the exact values below. cos 420° csc − π Question 26 of 50 If θ = 150°, find the exact value of each expression below. (a) cos 2θ = __ (b) cos − θ = __ (c) cos 2 θ = __ Final Exam Study Guide (2% of your course grade) #1 Page 9 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 27 of 50 Graph the trigonometric function. 2 y = sin x 3 y 3 2 1 x π 2π 3π 4π -1 -2 -3 Question 28 of 50 Graph the trigonometric function. 1 2 y=− cos x −3 2 3 y 4 3 2 1 x -π π 2π 3π 4π -1 -2 -3 -4 Final Exam Study Guide (2% of your course grade) #1 Page 10 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 29 of 50 Write an equation of the form y = a sin b x or y = a cos b x to describe the graph below. y 3 2 1 x 2π π π 2π π 4π 5π 2π − − 3 3 -1 3 3 3 3 -2 -3 Final Exam Study Guide (2% of your course grade) #1 Page 11 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 30 of 50 Final Exam Study Guide (2% of your course grade) #1 Page 12 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  What are the domains and ranges of the following functions? Final Exam Study Guide (2% of your course grade) #1 Page 13 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Function The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Domain 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. y = csc x The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Range 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Domain 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. y = cot x The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Range 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. y = cos x The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Domain 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. Range The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. 2 The set of all real numbers. Final Exam Study Guide (2% of your course grade) #1 Page 14 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. Question 31 of 50 3 Find the exact value of sin − 1 −. 2 Write your answer in radians in terms of π. Question 32 of 50 5 Find the exact value of sin cos − 1 −. 6 Question 33 of 50 −1 3π Find the exact value of tan sin. 2 Write your answer in radians in terms of π. Question 34 of 50 Rewrite cot sin − 1 5v as an algebraic expression in v. Question 35 of 50 Simplify. csc x sin x cot x Use algebra and the fundamental trigonometric identities. Your answer should be a number or use a single trigonometric function. Final Exam Study Guide (2% of your course grade) #1 Page 15 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 36 of 50 Simplify. 2 2 cos x 1 + tan x Use algebra and the fundamental trigonometric identities. Your answer should be a number or use a single trigonometric function. Question 37 of 50 Prove the identity. csc 2 x 1 − cos 2 x = 1 Question 38 of 50 Prove the identity. tan 2 x sec x − 1 2 = sec x + 1 sec x + 1 Question 39 of 50 Prove the identity. sin x + y = tan x + tan y cos x cos y Question 40 of 50 Prove the identity. tan 2π − x = − tan x Question 41 of 50 15 Find sin 2x, cos 2x, and tan 2x if tan x = and x terminates in quadrant III. 8 Final Exam Study Guide (2% of your course grade) #1 Page 16 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 42 of 50 Prove the identity. 2 cot x = sin 2x csc 2 x Question 43 of 50 Find all solutions of the equation in the interval 0 , 2π. sec θ + 1 = 0 Write your answer in radians in terms of π. Question 44 of 50 Find all solutions of the equation in the interval 0 , 2π. 3 cot 2 x − 1 = 0 Write your answer in radians in terms of π. Question 45 of 50 Find all solutions to the equation. cos 2x + 1 = 0 Write your answer in radians in terms of π. π π Example: x= + 2k π, k ∈ ℤ or x = + k π, k ∈ ℤ 5 7 Final Exam Study Guide (2% of your course grade) #1 Page 17 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 46 of 50 Find all solutions in the interval 0 , 2π. − 2 3 cosθ 27 = 3 Give your answer(s) in radians in terms of π. If there is more than one solution, separate them with commas. If there is no solution, click "No solution". θ= Question 47 of 50 Consider a triangle A B C like the one below. Suppose that A = 102°, C = 34°, and a = 47. (The figure is not drawn to scale.) Solve the triangle. Round your answers to the nearest tenth. B c a A C b Final Exam Study Guide (2% of your course grade) #1 Page 18 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 48 of 50 A ski resort has a lift fromA to C, as shown in the figure below. Angle D A C measures 37°. Mountain officials want to build a new ski lift from B to C. The base B will be 870 feet from A, and the new lift will be 1800 feet long. What will be the measure of angle B ? Round your answer to the nearest tenth of a degree. C 1800 ft 37° D A B 870 ft Question 49 of 50 Consider a triangle A B C like the one below. Suppose that C = 128°, a = 41, and b = 24. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. B a c C A b Final Exam Study Guide (2% of your course grade) #1 Page 19 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 50 of 50 Yoko wants to know the length of a tunnel built through a mountain. To do so, she makes the measurements shown in the figure below. Use these measurements to find the length of the tunnel. ? 234 m 109 m 71° Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth of a meter. Final Exam Study Guide (2% of your course grade) #1 Page 20 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Final Exam Study Guide (2% of your course grade) #1 Answers Class Name: MATH 1113 Fall 2024 - TR - 2:00 Number of Questions: 50 PM - Bhat Question 1 of 50 2 f x + 7 = x + 13x + 40 x 7x − 6 g = 2 5x − 2 Question 2 of 50 Domain of f: − ∞, − 8 ∪ − 8 , 8 ∪ 8 , ∞ Domain of g: − ∞ , 7 ∪ 7 , ∞ Question 3 of 50 − 1, 1 ∪ 1, ∞ Question 4 of 50 f x+h −f x = − 2x − h − 4 h Question 5 of 50 f x+h −f x 8 = h x+h+8 x+8 Question 6 of 50 x f∘g x = − 4x + 5 5 5 Domain of f ∘ g : − ∞, 0 ∪ 0 , ∪ , ∞ 4 4 Final Exam Study Guide (2% of your course grade) #1 Page 21 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 7 of 50 y 10 8 6 4 2 x -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 Question 8 of 50 y 10 8 6 4 2 x -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 Question 9 of 50 −1 x g x = 6x − 7 −1 7 7 Domain of g : − ∞, ∪ , ∞ 6 6 −1 1 1 Range of g : − ∞, ∪ , ∞ 6 6 Final Exam Study Guide (2% of your course grade) #1 Page 22 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 10 of 50 2 x 5 log 3 = 2 log x − log x + 8 5 3 x+8 Question 11 of 50 x = −3 Question 12 of 50 x = 3, 6 Question 13 of 50 3.6 hours Question 14 of 50 17 sec θ = 8 15 sin θ = 17 15 tan θ = 8 Question 15 of 50 14.6ft Question 16 of 50 117.8 ft Question 17 of 50 x = 53.1° Final Exam Study Guide (2% of your course grade) #1 Page 23 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 18 of 50 (a) y x (b) 3π − radians 4 (c) 5π radians 4 Question 19 of 50 (a) 135° 4π (b) radians 3 Final Exam Study Guide (2% of your course grade) #1 Page 24 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 20 of 50 y x Question 21 of 50 π 9 Question 22 of 50 39 cot θ = 5 39 cos θ = 8 Question 23 of 50 5π 1 sin − =− 6 2 Final Exam Study Guide (2% of your course grade) #1 Page 25 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 24 of 50 2 3 sec 30° = 3 3 tan 30° = 3 Question 25 of 50 1 cos 420° = 2 csc − π Undefined Question 26 of 50 1 (a) cos 2θ = 2 3 (b) cos − θ =− 2 3 (c) cos 2 θ = 4 Question 27 of 50 y 3 2 1 x π 2π 3π 4π -1 -2 -3 Final Exam Study Guide (2% of your course grade) #1 Page 26 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 28 of 50 4 y 3 2 1 x -π π 2π 3π 4π -1 -2 -3 -4 Question 29 of 50 5 3 y= sin x 2 2 Final Exam Study Guide (2% of your course grade) #1 Page 27 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 30 of 50 Final Exam Study Guide (2% of your course grade) #1 Page 28 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Function The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Domain 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. y = csc x The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Range 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Domain 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. y = cot x The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Range 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. y = cos x The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. Domain 2 The set of all real numbers. The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. Range The set of all real numbers less than or equal to − 1 or greater than or equal to 1. π The set of all real numbers, except odd integer multiples of. 2 The set of all real numbers. Final Exam Study Guide (2% of your course grade) #1 Page 29 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  The set of all real numbers, except integer multiples of π. The set of all real numbers from − 1 to 1. Question 31 of 50 −1 3 π sin − =− 2 3 Question 32 of 50 11 6 Question 33 of 50 π − 4 Question 34 of 50 2 −1 1 − 25v cot sin 5v = 5v Question 35 of 50 tan x Question 36 of 50 1 Final Exam Study Guide (2% of your course grade) #1 Page 30 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 37 of 50 Statement Rule csc 2 x 1 − cos 2 x 1 = 2 1 − cos 2 x Reciprocal sin x 1 2 = 2 sin x Pythagorean sin x = 1 Algebra Question 38 of 50 Statement Rule 2 tan x 2 sec x + 1 2 sec x − 1 = 2 Pythagorean sec x + 1 sec x − 1 sec x + 1 = 2 Algebra sec x + 1 sec x − 1 = Algebra sec x + 1 Final Exam Study Guide (2% of your course grade) #1 Page 31 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 39 of 50 Statement Rule sin x + y cos x cos y sin x cos y + cos x sin y Sum and Difference cos x cos y sin x cos y cos x sin y + Algebra cos x cos y cos x cos y sin x sin y + Algebra cos x cos y tan x + tan y Quotient Question 40 of 50 Statement Rule tan 2 π − x sin 2 π − x = Quotient cos 2 π − x sin2 π cos x − cos 2 π sin x = Sum and Difference cos 2 π cos x + sin2 π sin x 0 ⋅ cos x − 1 ⋅ sin x = Evaluation 1 ⋅ cos x + 0 ⋅ sin x − sin x = Algebra cos x sin x = − Algebra cos x = − tan x Quotient Final Exam Study Guide (2% of your course grade) #1 Page 32 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 41 of 50 240 sin 2x = 289 161 cos 2x = − 289 240 tan 2x = − 161 Question 42 of 50 Statement Rule 2 cot x csc 2 x 2 cot x = 1 Reciprocal 2 sin x = 2 cot x sin2 x Algebra cos x = 2 sin2 x Quotient sin x = 2 sin x cos x Algebra = sin2 x Double-angle Question 43 of 50 θ=π Question 44 of 50 π 2π 4π 5π x= , , , 3 3 3 3 Final Exam Study Guide (2% of your course grade) #1 Page 33 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation  Question 45 of 50 π x= + k π, k ∈ ℤ 2 Question 46 of 50 5π 7π θ= , 6 6 Question 47 of 50 B = 44°, b = 33.4, c = 26.9 Question 48 of 50 20.1° Question 49 of 50 A = 33.3° , B = 18.7° , c = 58.9 Question 50 of 50 223.7 meters Final Exam Study Guide (2% of your course grade) #1 Page 34 / 34 Copyright © 2024 McGraw Hill - ALEKS® is a registered trademark of ALEKS Corporation