Math 1332 Exam Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the cardinal number for the set. 1) {8, 10, 12,..., 66} 1) Are the sets equal? 2) A is the set of residents age 43 or older living in the United States B is the set of residents age 43 or older registered to vote in the United States 2) Are the sets equivalent? 3) A = {25, 27, 29, 31, 33} B = {26, 28, 30, 32, 34} 3) 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. 4) A' 4) Write or in the blank so that the resulting statement is true. 5) {red, blue, green} {blue, green, yellow, black} 5) Use the formula for the number of subsets of a set with n elements to solve the problem. 6) Pasta can be ordered with tomato sauce and some, all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli, shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for ordering pasta with tomato sauce? 6) 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. 7) (A B)' 7) 8) (A B)' C 8) 1
Use the Venn diagram shown to answer the question. 9) Which regions represent set D E? 9) Use sets to solve the problem. 10) A survey of 260 families showed that 10) 99 had a dog; 76 had a cat; 34 had a dog and a cat; 98 had neither a cat nor a dog nor a parakeet; 8 had a cat and dog and a parakeet. How many had a parakeet only? Plot the point in the rectangular coordinate system. 11) (-5, -4) 11) 6 y 4 2-6 -4-2 2 4 6-2 x -4-6 Find f of each given value of x. 12) f(x) = 9x - 6 a. f(-5) b. f(-7) 12) 2
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. 13) (-3, -4), (4, -1) 13) The graph shows that the cost of the average college mathematics textbook has been rising steadily since 1990. 14) a. What is the y-intercept? b. What is the slope? c. What is the equation of this line, in slope-intercept form? d. Predict the cost of an average college mathematics textbook in 2015. 14) Solve the system by the substitution method. Be sure to check all proposed solutions. 15) x + y = 8 y = 3x 15) Solve the system by the addition method. Be sure to check all proposed solutions. 16) x + 5y = -14 2x + 4y = -10 16) 3
Graph the linear inequality. 17) x + y 5 10 y 17) 5-10 -5 5 10 x -5-10 Express the fraction as a percent. 18) 2 5 18) Write the decimal as a percent. 19) 8.4 19) Express the percent as a decimal. 20) 43.8% 20) 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. 21) P = $600 21) r = 5.75% t = 4 months The principle represents an amount of money deposited in a savings account subject to compound interest at the rate shown. Use the formula A = P(1 + r n )nt to find how much money will be in the account after the given number of years and how much interest was earned in that period. 22) principal: $6500 22) rate: 4% compounding periods per year: 4 time: 4 years 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. 23) A = $12,000 23) r = 13.1% t = 2 years Find the measure of the complement of the angle. 24) 20.3 24) 4
Find the measure of the supplement of the angle. 25) 104.3 25) Find the measures of angles 1, 2, and 3. 26) 26) 144 The figure shows two parallel lines intersected by a transversal. One of the angle measures is given. Find the measure of the indicated angle. 27) 27) 23 Find the measure of 3. Find the measure of the angle. 28) Find the measure of angle 4 in the figure shown. 28) Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding, if necessary, to the nearest tenth. 29) A 20-foot pole is supported by two wires that extend from the top of the pole to points that 29) are each 15 feet from the base of the pole. Find the total length of the two wires. 5
Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 30) Rectangle 7 cm 30) 2 cm 2 cm 7 cm Find the perimeter of the figure shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 31) 21 in. 31) 7 in. 10 in. 2.5 in. 11 in. 4.5 in. Use formulas to find the area of the figure. 32) 13 in. 5 in. 32) 20 in. Find the area of the figure. 33) 33) 4 ft 10 ft 10 ft 10 ft Find the circumference and area of the circle. Round the answer to the nearest whole number. 34) 34) 18 ft 6
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. 35) 35) 129 in. 36 Solve the problem by applying the Fundamental Counting Principle with two groups of items. 36) An apartment complex offers apartments with four different options, designated by A through D. 36) A = number of bedrooms (one through four) B = number of bathrooms (one through three) C = floor (first through fifth) D = outdoor additions (balcony or no balcony) How many apartment options are available? 37) A person can order a new car with a choice of 11 possible colors, with or without air conditioning, with or without heated seats, with or without anti-lock brakes, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered in terms of these options? 37) Use the formula for n P r to evaluate the expression. 38) 10 P 7 38) Use the formula for n P r to solve. 39) A church has 10 bells in its bell tower. Before each church service 4 bells are rung in sequence. No bell is rung more than once. How many sequences are there? 39) In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is not necessary to solve the problem. 40) How many different user ID's can be formed from the letters W, X, Y, Z if no repetition of 40) letters is allowed? Use the formula for n C r to evaluate the expression. 41) 8 C 4 41) 42) 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? 42) 7
Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 43) Use the spinner below to answer the question. Assume that it is equally probable 43) 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 an odd number. 44) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is greater than 10. 44) Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express the probability as a decimal, rounded to the nearest thousandth, if necessary. 45) In 1999 the stock market took big swings up and down. A survey of 996 adult investors 45) asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily? How frequently? Response Daily 222 Weekly 281 Monthly 292 Couple times a year 140 Don't track 61 Solve the problem. 46) The ages of 30 swimmers who participated in a swim meet are as follows: 46) 23, 41, 35, 38, 45, 23, 55, 64, 24, 48, 56, 24, 31, 33, 46, 25, 34, 25, 63, 54, 29, 42, 51, 58, 38, 27, 27, 46, 35, 54 Construct a grouped frequency distribution for the data. Use the classes 23-32, 33-42, 43-52, 53-62, 63-72. For the given data set, find the a. mean b. median c. mode (or state that there is no mode) d. midrange. 47) A company advertised that, on the average, 95% of their customers reported "very high 47) satisfaction" with their services. The actual percentages reported in 15 samples were the following: 95, 95, 94, 52, 79, 95, 94, 79, 95, 95, 52, 94, 94, 95, 52 a. Find the mean, median, mode and midrange. b. Which measure of central tendency was given in the advertisement? c. Which measure of central tendency is the best indicator of the "average" in this situation? Find the range for the group of data items. 48) 3, 9, 18, 24, 12, 16, 5, 8, 22, 14, 7, 36, 19, 7, 6, 22 48) 8
Find the standard deviation for the group of data items (to the nearest hundredth). 49) 3, 9, 18, 24, 12, 16, 5, 8, 22, 14, 7, 36, 19, 7, 6, 22 49) A set of data items is normally distributed with a mean of 60. Convert the data item to a z-score, if the standard deviation is as given. 50) data item: 63; standard deviation: 2 50) Solve the problem. 51) A student scores 56 on a geography test and 279 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 20. The mathematics test has a mean of 300 and a standard deviation of 14. If the data for both tests are normally distributed, on which test did the student score better? 51) Use a table of z-scores and percentiles to find the percentage of data items in a normal distribution that lie between: 52) z = -2 and z = -0.2 52) 9
Answer Key Testname: MATH 1332 EX REVS11 1) 30 2) No 3) Yes 4) A' = {26, 27, 28,..., 40} 5) 6) 256 7) {r, t, u, v, w, x, z} 8) {v, x} 9) II, V 10) 21 11) 12) -51, -69 13) 3 7, rises 6 4 2 y -6-4 -2 2 4 6-2 14) a. 46 b. 6 c. y = 6x + 46 d. 136 15) {(2, 6)} 16) {(1, -3)} 17) -4-6 10 5 y -10-5 5 10-5 x x 23) $9509 24) 69.7 25) 75.7 26) m 1 = 36, m 2 = 144, m 3 = 36 27) 155 28) 120 29) 50 ft 30) 18 cm 31) 56 in. 32) 50 in.2 33) 240 ft2 34) 113 ft, 1017 ft2 35) 104 in. 36) 120 37) 352 38) 604,800 39) 5040 40) Permutations, because the order of the letters matters. 41) 70 42) 28989675 43) 3 5 44) 1 12 45) 222 996 ; 0.223 Age Number of Swimmers 23-32 10 46) 33-42 8 43-52 5 53-62 5 63-72 2 47) a. mean = 84, median = 94, mode = 95, midrange = 73.5 b. mode c. mean 48) 33 49) 8.89 50) 1.5 51) The student scored better on the geography test. 52) 39.79% -10 18) 40% 19) 840% 20) 0.438 21) $11.50 22) amount in account: $7621.76; interest earned: $1121.76 10