SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Transcription

1 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) {10, 12, 14,..., 68} 1) Are the sets equivalent? 2) A = {25, 27, 29, 31, 33} B = {26, 28, 30, 32, 34} 2) Are the sets equal? 3) A is the set of residents age 25 or older living in the United States B is the set of residents age 25 or older registered to vote in the United States 3) Write or in the blank so that the resulting statement is true. 4) {x x is a tree} {x x is a spruce tree} 4) Calculate the number of subsets and the number of proper subsets for the set. 5) the set of natural numbers less than 10 5) 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. 6) A' 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) C' A' 7) 1

2 Use the given cardinalities to determine the number of elements in the specific region. 8) n(u) = 125, n(a) = 40, n(b) = 60, n(c) = 36, n(a B) = 15, n(a C) = 18, n(b C) = 14, n(a B C) = 8 Find VIII. 8) Solve the problem by applying the Fundamental Counting Principle with two groups of items. 9) An apartment complex offers apartments with four different options, designated by A through D. 9) 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? Use the formula for n P r to solve. 10) In a contest in which 10 contestants are entered, in how many ways can the 4 distinct prizes be awarded? 10) 11) A signal can be formed by running different colored flags up a pole, one above the other. Find the number of different signals consisting of 7 flags that can be made if 3 of the flags are white, 2 are red, and 2 areblue. 11) Use the formula for n C r to evaluate the expression. 12) To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 50 numbers ( one through 50.) The order in which the selections is made does not matter. How many different selections are possible? 12) 2

3 Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 13) Use the spinner below to answer the question. Assume that it is equally probable 13) 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. 14) You are dealt one card from a standard 52-card deck. Find the probability of being dealt an ace or a 9. 14) 15) The ages of 30 swimmers who participated in a swim meet are as follows: 15) 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, For the given data set, find the a. mean b. median c. mode (or state that there is no mode) d. midrange. 16) A company advertised that, on the average, 98% of their customers reported "very high 16) satisfaction" with their services. The actual percentages reported in 15 samples were the following: 98, 98, 94, 60, 71, 98, 94, 71, 98, 98, 60, 94, 94, 98, 60 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. 17) 3, 9, 18, 24, 12, 16, 5, 8, 22, 14, 7, 36, 19, 7, 6, 22 17) Find the standard deviation for the group of data items (to the nearest hundredth). 18) 3, 9, 18, 24, 12, 16, 5, 8, 22, 14, 7, 36, 19, 7, 6, 22 18) The scores on a driver's test are normally distributed with a mean of 100. Find the score that is: 19) Find the score that is 2 standard deviations below the mean, if the standard deviation is ) 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. 20) data item: 78; standard deviation: 12 20) 3

4 Express the fraction as a percent. 21) ) Write the decimal as a percent. 22) ) Express the percent as a decimal. 23) 43.8% 23) 24) A dress regularly sells for $137. The sale price is $101. Find the percent decrease of the sale price from the regular price. 24) 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. Round answer to the nearest cent. 25) P = $600 25) 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. 26) principal: $ ) rate: 4% compounding periods per year: 4 time: 5 years 27) A mother invests $2000 in a bank account at the time of her daughter's birth. The interest is compounded quarterly at a rate of 7%. What will be the value of the daughter's account on her twentieth birthday, assuming no other deposits or withdrawals are made during this period? 27) Solve the problem using the present value formula P = A (1 + r n )nt. 28) How much money should be deposited today in an account that earns 5% compounded semiannually so that it will accumulate to $8000 in 11 years? 28) Find the measure of the complement of the angle. 29) ) Find the measure of the supplement of the angle. 30) ) 4

5 Find the measures of angles 1, 2, and 3. 31) 31) 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. 32) 32) 23 Find the measure of 3. Find the measure of the angle. 33) Find the measure of angle 4 in the figure shown. 33) Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding, if necessary, to the nearest tenth. 34) A square sheet of paper measures 28 centimeters on each side. What is the length of the 34) diagonal of this paper? 5

6 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. 35) Rectangle 7 cm 35) 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. 36) 18 cm 36) 6 cm 9 cm 2 cm 9 cm 4 cm Use formulas to find the area of the figure. 37) 13 in. 5 in. 37) 20 in. Find the circumference and area of the circle. Round the answer to the nearest whole number. 38) 38) 18 ft 39) At a certain time of day, the angle of elevation of the sun is 64. To the nearest foot, find the height of a pole whose shadow at that time is 13 feet long. 39) ft 6

7 Graph the equation. Select integers for x, -3 x 3. 40) y = x2-2 y 10 40) x Find f of each given value of x. 41) f(x) = 9x - 6 a. f(-5) b. f(-7) 41) The graph shows that the cost of the average college mathematics textbook has been rising steadily since ) 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 ) 43) The quadratic function y = x2-0.41x models the median, or average, age, y, at which U.S. men were first married x years after In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.) 43) 7

8 Use a calculator with a yx key or a ^ key to solve the problem. 44) Research suggests that the probability of a certain fuse malfunctioning increases exponentially as the concentration of an impurity in the fuse increases. The probability is modeled by the function y = 2(257,949)x, where x is the impurity concentration, and y, given as a percent, is the probability of the fuse malfunctioning. Find the probability of the fuse malfunctioning for an impurity concentration of Round to the nearest percent. 44) 8

9 Answer Key Testname: MATH 1332 EX REVF12 1) 30 2) Yes 3) No 4) 5) 512; 511 6) A' = {26, 27, 28,..., 40} 7) {r, t} 8) 28 9) ) ) ) ) ) 2 13 Age Number of Swimmers ) ) a. mean = 85.73, median = 94, mode = 98, midrange = 79 b. mode c. mean 17) 33 18) ) 56 20) ) 40% 22) 840% 23) ) 26.3% 25) $ ) amount in account: $10,981.71; interest earned: $ ) $ ) $ ) ) ) m 1 = 36, m 2 = 144, m 3 = 36 32) ) ) 39.6 cm 35) 18 cm 36) 48 cm 37) 50 in.2 38) 113 ft, 1017 ft2 39) 27 feet 9

10 Answer Key Testname: MATH 1332 EX REVF12 40) 10 y x ) -51, ) a. 46 b. 6 c. y = 6x + 46 d ) 1954, 25.1 years old 44) 11% 10