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PreCalculus Midterm Name For each box you are to choose which question you want to answer and show all work for that prompt only. Answer only one of the questions in each section! 1. As a submarine at the surface of the ocean makes a dive, its path makes a 21º angle with the surface. If the submarine goes for 300 m along its downward path, how deep will it be? How many meters along this path must it go to reach a depth of 1000 m? 2. Determine the 201st term of the sequence: 79, 76, 73, 70, ... Solve the equation on the interval 0 2 : 2cos 2 3 0 List the next 3 terms of the sequence: 363 726 1089 , , 7 7 7 3. Determine the exact value of each expression: 3 tan sec1 3 4. After being struck with a hammer, a gong vibrates 22 vibrations in the first second and in each second 2 thereafter makes as many vibrations as in the 3 previous second. Find how many vibrations the gong makes before it stops vibrating. Find the exact value of the tan 870 (No decimals here, use an identity and unit circle knowledge) Consider an equilateral triangle with sides of 40 centimeters. Connect the midpoints of the sides of the triangle. Continue to connect midpoints of each successive triangle. List the perimeters of the first four triangles formed. What is the sum of the perimeters of the first n triangles? 5. Use a Double-Angle Formula to determine the exact 5 value of tan 2 given sec , sin 0 . 2 6. Determine the sum of the following series: a. 1 2 4 8 8192 5 5 5 5 5 Determine the exact value of cos( ) : 3 2 sin , ; cos , 0 . 5 2 5 2 Every March the NCAA holds their National Championship Women’s Basketball Tournament which allows 64 universities to participate. Each game consists of two teams and only the winner of each game advances to the next round of competition. 9 b. 100 (1.08) n 0 4 c. ( 2 n 4) n n 1 Write a sequence for the number of games played in each round. Is this arithmetic or geometric? Is this sequence finite or infinite? How many rounds are needed to crown a champion? Write the series related to your sequence? What is the sum of this series? What does this sum represent? 7. The roof of a house is being reconstructed to accommodate heavy snows. The current 32-foot roofline makes an 18.2 angle with the horizontal. The owner has decided to construct the new roof so that it makes a 50 angle with the horizontal. What will be the length of the new roofline? 8. A software program requires users to login with a case sensitive 6-character password with no spaces. Using a “QWERTY” keyboard (see handout), find the number of possible passwords the program will accept. A surveyor marks off measurements shown below for a triangle shaped courtyard in a new community. Determine the angle at C two different ways, then find the lengths of the distances marked a and b. A electrical outlet has a 98% reliability rating (meaning when an appliance is plugged in it will work 98% of the time.) Suppose you make toast each morning for one week using the same outlet. Find the probability of the outlet not working exactly 2 of these days.