MATH FOR LIBERAL ARTS FINAL REVIEW


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1 MATH FOR LIBERAL ARTS FINAL REVIEW Find the value of the annuity. Round to the nearest cent. A = P 1 + r n r n nt  1 P = A r n 1 + r n nt  1 1) Periodic Deposit: $100 at the end of each year Rate: 5% compounded annually Time: 9 years Determine the periodic deposit. Round to the nearest cent. A = P 1 + r n r n nt  1 P = A r n 1 + r n nt  1 2) Periodic Deposit: $? at the end of every six months Rate: 10% compounded semiannually Time: 8 years Financial Goal: $310,000 Solve the problem. 3) A real estate company borrowed $415,000 to develop some condos. It amortized the loan to pay monthly for 4 years at 7% interest. Find the amount of each monthly payment. Provide the following information. a. Name the vertex of the angle. b. Name the sides of the angle. c. Name the angle in three different ways. 4) Solve the problem. 5) The hour hand of a clock moves from 12 to 10 o'clock. Through how many degrees does it move? 6) The hour hand of a clock moves from 12 to 1 o'clock. Through how many degrees does it move? 1
2 Find the measure of the angle in which? appears. 7) 13 8) 71 Find the measure of the complement of the angle. 9) Find the complement of 40. Find the measure of the supplement of the angle. 10) Find the supplement of 127. Find the measures of angles 1, 2, and 3. 11) 113 Find the measure of angle A for the triangle shown. 12)
3 Find the measure of the angle. 13) Find the measure of angle 2 in the figure shown. Use similar triangles and the fact that corresponding sides are proportional to find the length of the side marked with an x. 14) 15 m 3 m 5 m 12 m 4 m Use similar triangles and the fact that corresponding sides are proportional to find the length of the segment marked with an x. 15) 10 in. 8 in. 10 in. Use the Pythagorean Theorem to find the missing length in the right triangle. Use a calculator to find square roots, rounding, if necessary, to the nearest tenth. 16) c 6 in. 9 in. 17) a 20 m 10 m Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding, if necessary, to the nearest tenth. 18) If you drive 16 miles south, then make a left turn and drive 12 miles east, how far are you, in a straight line, from your starting point? 3
4 Find the perimeter of the figure shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 19) 27 in. 9 in. 12 in. 3.5 in. 15 in. 5.5 in. Solve the problem. 20) Find the sum of the measures of the angles of a 6sided polygon. Use formulas to find the area of the figure. 21) 14 in in. 17 in. 22) 6 ft 10 ft 10 ft 9 ft Solve the problem. 23) What will it cost to tile a rectangular floor measuring 296 feet by by 36 feet if the tile costs $13 per square foot? Solve the problem. Round all circumference and area calculations to the nearest whole number. 24) How much fencing is required to enclose a circular garden whose radius is 70 m? 4
5 Use the given right triangle to find the trigonometric function. 25) cos B 26) sin A Find the measure of the side of the right triangle whose length is designated by the lowercase letter. Round your answer to the nearest whole number. 27) 129 in. 40 Use the inverse trigonometric keys on a calculator to find the measure of angle A, rounded to the nearest whole degree. 28) 12 m 27 m 5
6 Find the measures of the parts of the right triangle that are not given. Round your answers to the nearest whole number. 29) c a 31 b = 59 yd Solve the problem. 30) To find the distance across a large pond, a surveyor took the measurements in the figure shown. Use these measurements to determine how far it is across the lake. Round to the nearest foot feet Graph the equation. Select integers for x, 3 x 3. 31) y = 4x  2 Evaluate the function at the given values of the variable. 32) f(x) = 5x a. f(1) b. f(7) 6
7 Evaluate f(x) for the given values for x. Then use the ordered pairs (x, f(x)) from your table to graph the function. 33) f(x) = x x f(x) Use the x and yintercepts to graph the linear equation. 34) x  3y = 9 Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whether the line rises, falls, is horizontal, or is vertical. 35) (7, 3), (16, 7) Graph the linear function using the slope and yintercept. 36) y = 1 2 x  3 7
8 In the following problem: a. Put the equation in slopeintercept form. b. Identify the slope and yintercept. c. Graph the line. 37) 3x + 8y = 24 Graph the horizontal or vertical line. 38) x = 2 39) y = 5 8
9 The graph shows that the cost of the average college mathematics textbook has been rising steadily since ) a. What is the yintercept? b. What is the slope? c. What is the equation of this line, in slopeintercept form? d. Predict the cost of an average college mathematics textbook in Solve the system by graphing. Check the coordinates of the intersection point in both equations. 41) 3x + y = 11 3x + 5y = 5 Solve the system by the substitution method. Be sure to check all proposed solutions. 42) x  5y = 7 2x  4y = 14 Solve the system by the addition method. Be sure to check all proposed solutions. 43) x + 2y = 257x + 2y = 31 9
10 Solve the problem. 44) A couple have bought a new house and are comparing quotes from two moving companies for moving their furniture. Company A charges $80 for the truck and $55 per hour for the movers. Company B charges $70 for the truck and $65 per hour for the movers. Create a cost equation for each company where y is the total cost and x is the number of hours of labor. Write a system of equations. Graph the linear inequality. 45) 2x + 4y 8 Graph the system of inequalities. 46) x  2y 2 x + y 0 Express the set using the roster method. 47) the set of odd natural numbers less than 19 Write or in the blank so that the resulting statement is true. 48) {red, blue, green} {blue, green, yellow, black} Use,,, or both and to make a true statement. 49) {9, 10, 11} {9, 10, 11} 50) {11, 12, 13} {11, 12, 13} 10
11 Calculate the number of subsets and the number of proper subsets for the set. 51) {1, 3, 5, 7, 9, 11} Consider below the branching tree diagram based on the number per 3000 American adults. Let T = the set of Americans who like classical music R = the set of Republicans who like classical music D = the set of Democrats who like classical music I = the set of Independents who like classical music Determine whether the statement is true or false. 52) Let M = the set of Democratic men who like classical music W = the set of Democratic women who like classical music M T 53) Let M = the set of Republican men who like classical music W = the set of Republican women who like classical music If x M, then x R. Use the Venn diagram to list the elements of the set in roster form. 54) List the elements of B. 11
12 Use the Venn diagram to list the elements of the set in roster form. 55) The set of students who studied Saturday and not Sunday Let U = {21, 22, 23,..., 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27,..., 39}, and D = {22, 24, 26, 28,..., 40}. Use the roster method to write the following set. 56) A' Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 57) C' A' 58) (A B)' 59) A B' 60) C' A' 61) A' 62) A (B C) Solve the problem by applying the Fundamental Counting Principle with two groups of items. 63) In how many ways can a girl choose a twopiece outfit from 5 blouses and 6 skirts? 64) How many different fourletter secret codes can be formed if the first letter must be an S or a T? Use the Fundamental Counting Principle to solve the problem. 65) There are 7 performers who are to present their acts at a variety show. One of them insists on being the first act of the evening. If this request is granted, how many different ways are there to schedule the appearances? Evaluate the factorial expression. 66) 5! 3! 12
13 67) 6! (62)! Use the formula for n P r to evaluate the expression. 68) 10 P 7 Use the formula for n P r to solve. 69) A club elects a president, vicepresident, and secretarytreasurer. How many sets of officers are possible if there are 13 members and any member can be elected to each position? No person can hold more than one office. In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is not necessary to solve the problem. 70) How many different user ID's can be formed from the letters W, X, Y, Z if no repetition of letters is allowed? 71) A record club offers a choice of 7 records from a list of 45. In how many ways can a member make a selection? Use the formula for n C r to evaluate the expression. 72) 5 C 4 Solve the problem. 73) To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 55 numbers (one through 55). The order in which the selections is made does not matter. How many different selections are possible? Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 74) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 6. 75) You are dealt one card from a standard 52card deck. Find the probability of being dealt an ace or a 7. 76) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that the arrow will land on 3 or 4. 13
14 Solve the problem. 77) The government of a town needs to determine if the city's residents will support the construction of a new town hall. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the town's residents? A) Survey every 6th person who walks into city hall on a given day. B) Survey a random sample of persons within each geographic region of the city. C) Survey the first 200 people listed in the town's telephone directory. D) Survey a random sample of employees at the old city hall. 78) A random sample of 30 high school students is selected. Each student is asked how much time he or she spent watching television during the previous week. The following times (in hours) are obtained: 6, 14, 8, 11, 8, 6, 8, 7, 5, 11, 9, 7, 7, 6, 9, 8, 5, 5, 10, 7, 5, 7, 14, 9, 6, 10, 6, 9, 8, 7 Construct a frequency distribution for the data. 79) Which one of the following is true according to the graph? A) The graph is based on a sample of approximately 62 thousand people. B) The percent of people with years of higher education greater than those shown by any rectangular bar is equal to the percent of people with years of education less than those shown by that bar. C) If the sample is truly representative, then for a group of 50 people, we can expect about 32 of them to have one year of education beyond high school. D) More people had 4 years of education beyond high school than 3 years. Find the mean for the group of data items. Round to the nearest hundredth, if necessary. 80) 78, 78, 87, 71, 91, 78 Find the median for the group of data items. 81) 97, 97, 91, 47, 72, 97 Find the mode for the group of data items.if there is no mode, so state. 82) 1.3, 2.3, 1.5, 2.9, 1.3, 2.3, 1.3, 8.1, 8.1,
15 Find the midrange for the group of data items. 83) 96, 96, 93, 44, 71, 96 Find the range for the group of data items. 84) 11, 11, 11, 19, 23, 23, 23 A group of data items and their mean are given. Find a. the deviation from the mean for each of the data items and b. the sum of the deviations in part a. 85) 46, 46, 48, 51, 51, 51, 52, 53, 56, 56; Mean = 51 Find the standard deviation for the group of data items (to the nearest hundredth). 86) 15, 16, 17, 18, 19 Solve the problem. 87) 25% of 28 is what number? 88) What number is 22% of 17? 89) 22 is 5% of what number? 90) Jeans with an original price of $44 are on sale at 25% off. What is the sale price of the jeans? (Round to the nearest cent, if necessary.) 91) A dress regularly sells for $130. The sale price is $84. Find the percent decrease of the sale price from the regular price. The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year and round answer to the nearest cent. 92) P = $6700 r = 4.5% t = 21 months The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t. Round answer to the nearest cent. 93) P = $ r = 5% t = 9 months The principal P is borrowed and the loan's future value, A, at time t is given. Determine the loan's simple interest rate, r, to the nearest tenth of a percent. 94) P = $170 A = $ t = 3 years 15
16 Determine the present value, P, you must invest to have the future value, A, at simple interest rate r after time t. Round answer to the nearest dollar. 95) A = $5500 r = 10% t = 1 year Solve the problem. 96) Lonnie needs extra money to buy a truck to start up a delivery service. He takes out a simple interest loan for $ for 6 months at a rate of 7.25%. How much interest must he pay, and what is the future value of the loan? Solve the problem. A = P 1 + r n nt P = A 1 + r n nt A = Pe rt Y = 1 + r n n ) How much money should be deposited today in an account that earns 10% compounded semiannually so that it will accumulate to $1000 in 12 years? 98) James and Susan wish to have $10,000 available for their wedding in 2 years. How much money should they set aside now at 6% compounded monthly in order to reach their financial goal? 99) A passbook savings account has a rate of 7%. Find the effective annual yield if the interest is compounded monthly. 16
17 Answer Key Testname: SPR2015 FINALREVIEW 1) $ ) $13, ) $ ) a. point A b. AB and AC c. A, BAC, CAB 5) 300 6) 30 7) 77 8) 109 9) 50 10) 53 11) m 1 = 67, m 2 = 113, m 3 = 67 12) 41 13) ) 9 m 15) 2.5 in. 16) 10.8 in. 17) 17.3 m 18) 20 mi 19) 72 in. 20) ) in. 2 22) 240 ft 2 23) $138,528 24) 440 m 25) ) ) 99 in. 28) 24 29) a = 35 yd; c = 69 yd; B = 59 30) 167 feet 31) 32) 10, ) x f(x) ) 36) 37) a. y = x + 3 b. slope =  3 8, yintercept = 3 c. 38) 35) 10 23, rises 17
18 Answer Key Testname: SPR2015 FINALREVIEW 39) 40) a. 46 b. 6 c. y = 6x + 46 d ) {(5, 4)} 42) {(7, 0)} 43) {(7, 9)} 44) y = 55x + 80 y = 65x ) 47) {1, 3, 5,..., 17} 48) 49) 50) 51) 64; 63 52) True 53) True 54) {12, 13, 15, 16, 17} 55) {Karen, Charly} 56) A' = {26, 27, 28,..., 40} 57) {r, t} 58) {r, t, v, x} 59) {u, w} 60) {q, r, s, t, u, v, x, z} 61) {r, t, v, x, z} 62) {q, s, u, w, y, z} 63) 30 64) 35,152 65) ) 20 67) 30 68) 604,800 69) ) Permutations, because the order of the letters matters. 71) Combinations, because the order of the records selected does not matter. 72) 5 73) 28,989,675 74) ) ) ) 94 82) ) 70 84) 12 85) 5, 5, 3, 0, 0, 0, 1, 2, 5, 5; 0 86) ) 7 88) ) ) $ ) 35.4% 92) $ ) $ ) 7% 95) $ ) interest: $ ; future value: $ ) $ ) $ ) 7.2% 46) 76) ) B 78) Hours Number of of TV HS Students ) D 18
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