MATH 2 - PROBLEM SETS

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Ashlynn Russell
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1 MATH - PROBLEM SETS Problem Set 1: 1. Simplify and write without negative eponents or radicals: a. c d p 5 y cd b. 5p 1 y. Joe is standing at the top of a 100-foot tall building. Mike eits the building and walks along a straight path away from the building. At a certain point in time the distance between Mike and Joe is 700 feet. When Mike has walked an additional 00 feet, Joe calls out to Mike and Mike stops. a. How far did Mike walk after he left the building? Give the eact answer and the answer rounded to the nearest tenth of a foot. b. What is the distance between Mike and Joe? Give the eact answer and the answer rounded to the nearest tenth of a foot.. A ladder 1 feet long leans against a wall with its base 8 feet away from the wall. A person pushes the ladder toward the wall at the rate of 1 foot per second. After 5 seconds have passed, how much higher is the ladder on the wall?. Find all solutions for t + 5t = The endpoints of the diameter of a circle are, and 5,. Find the center and radius of the circle. Write the general equation of this circle.. Show that the line containing the points a, b and b, a is perpendicular to the line y =. What is the equation of the line? Problem Set : 1. a.sketch the graph of f = 1 by plotting points. b.use the graph of f to sketch the graph of each of the following functions. i.y = 1 ii.y = 1 iii.y = iv.y = A function is said to be even if it is symmetric with respect to the y ais. A function is said to be odd if it is symmetric with respect to the origin. Determine if the following functions are even, odd, or neither. a.f = b.f = + c.f = + 1 d.f = + 1. Let f = + and g = a. Find fg0. b. Find f f. c. Find the domain of the function f. Give you answer using interval notation. g ga d. Find and simplify. a

2 f + h f. Find and simplify h where f = + 1. Problem Set : 1. The graph of a quadratic function is the parabola with verte 10, 00 that passes through the point, 50. Draw the graph and find the function.. Let f = + 1. For what values of is f 0? For what values is f < 0? Write your answer in interval notation.. Solve for : a = 0 b. 5 + > 0. What is the domain of the function defined by f = interval form. Hint: Use a table of signs.? Write your answer in + Problem Set : 1. In parts a-d, state whether the function is a polynomial or not. If the function is not a polynomial, give a reason; if it is a polynomial, give its degree and leading coefficient. a. p = 5 + π 10 b. q = c.hz = z 7 z d. kt = Graph each of the following polynomials without using a calculator. Label the intercepts clearly with their values. a. p = + 1 b. q = Graph each of following rational functions without using a calculator. Find the intercepts and equations of asymptotes for each function. You may also want to use a table of signs. a. f = b. g = + 5 Problem Set 5: 1. Draw the graph of a third degree polynomial with -intercepts 1 and and y-intercept. Write a function that could have your graph.. Find the equation of a rational function r that satisfies all of the following conditions: horizontal asymptote y = 0 vertical asymptotes = and = y-intercept 0, no -intercepts. List all potential rational zeros of f =

3 . Find all real solutions of = 0. Problem Set : 1. Let f = + 1 and k = 5. a. Find f 1. What is the range of f 1? b. Find the inverse of k.. Find the function of an eponential graph with horizontal asymptote y =, y-intercept 0, and that goes through the point, 8.. Describe the transformations needed to transform the graph of y = e to the graph of g = 50e + 5. Give the equation of any asymptote and graph g.. Evaluate the following epressions: a.log 5 5 b. log 1 7 c. log 9 7 d. e ln π 5. Graph y = log 1 using transformations. Problem Set 7: 1. Compute each of the following without using a calculator. Answers should be eact. a. log 1 b. log 8 c. log +log 8 5 d. e.5 ln 1 e. log 8 log 8 + log 8 1 f. ln g. log 8 e log a. Write log a as a sum and/or difference of simpler logarithms. The epressions y inside the logarithms should not contain any products, quotients or powers. a. Suppose log a = 1. and log a y = 0.. Evaluate log a. y. Solve each of the following equations algebraically: a. log + + log = 1 b. = e c. e + e = 5 5. After three days a sample of radon- decayed to 58% of its original amount. a. What is the half-life of radon-? b. How long would it take for 90% of radon- to decay? Problem Set 8: 1. Let t = 15π and s = π 5. a. Find two numbers eact values, one between 0 and π and one between π and 0, which have the same terminal point as t. b. Find two numbers eact values, one between 0 and π and one between π and 0, which have the same terminal point as s. What are the reference number and quadrant for s?

4 . Without using a calculator, find the eact value of the si trigonometric functions evaluated at the given number q. If the value doesn t eist, write DNE. a. q = 17π b. q = π c. q = 19π d. q = 11π e. q = 9π. Compute the eact value: a. πcsc 157θ πcot 157θ b. logcos0 c. e lntan π. Find the eact value of each of the following without a calculator: a. cos 5π b. tan π c. sin π d. cos π e. tan π f. sec π g. csc 5π h. cot 7π 17π i. sec 5. Let sin t = 5 1 and 0 < t < π. Find cos t and tan t. Problem Set 9: 1. Suppose tan t = 5 and cos t < 0. Find each of the following: a. cos t b. sin t c. cott + π d. sect + π. Suppose csc t = 5 and sec t < 0. Find each of the following: a. cost + π b. tan t + π c. sinπ t. Graph each of the following functions without a calculator. Your graph should include two periods and portions to the left and to the right of the y-ais. a. f = cos b. g = sin π c. h = tan + π d. k = cos + π. Give the amplitude, the period, and the magnitude and direction of the phase shift for the function defined by f =. sin5 + π 7. Problem Set 10: 1. Find the eact value of the each epression without using a calculator. a. cos 1 b. sec tan 1 c. sin tan 1 d. sin 1 cos π. Simplify cos sec tan. Establish the identity: 1 cos θ 1 + sin θ = sin θ. Show that tan sin 1 v = to an epression containing at most one trigonometric function. v 1 v. Problem Set 11: 1. Let tan = 1 and sin > 0. Find sin + 5π and cos.

5 . Verify the identity: sin t + sin t = tan t. cos t + cos t + 1. Find all solutions for eact values: a. sin = 1 b. tan = c. cos = 1 d. sin = Problem Set 1: 1. A person walks on a straight path toward a building. At a certain moment, the person notices that the angle of elevation to the top of the building is 7. When the person is 50 feet closer to the building, the angle of elevation to the top of the building is 5. How tall is the building?. Identify each equation by name line, circle, parabola, ellipse or hyperbola. Graph the equation and label your graph with all pertinent information. e.q. center, verte or vertices, asymptotes a. + y = 1 b. y = c. y + = 1 d. y + = 0 e. + y + = 5 f. + y = Problem Set 1: 1. Find a formula for the nth term of each sequence. a. 1,, 5, 7 8,... b.,, 8, 1,,.... Find the sum of: 8 k + k + k=1. Use induction to show that n + n is divisible by for all natural numbers.. Find the coefficient of 10 in the epansion of Problem Set 1: 1. Solve the following system: y = y =. Graph each equation and find the points of intersection, if any: The circle 1 + y + = Parabola y + y + 1 = 0

Math 1160 Final Review (Sponsored by The Learning Center) cos xcsc tan. 2 x. . Make the trigonometric substitution into

Math 1160 Final Review (Sponsored by The Learning Center) cos xcsc tan. 2 x. . Make the trigonometric substitution into Math 60 Final Review (Sponsored by The Learning Center). Simplify cot csc csc. Prove the following identities: cos csc csc sin. Let 7sin simplify.. Prove: tan y csc y cos y sec y cos y cos sin y cos csc