CLEP College Math Questions and Answers Graded A+

CLEP College Math Questions and Answers Graded A+ Carl deposited P dollars into a savings account that earned 8 percent annual interest, compounded semiannually. Carl made no additional deposits to or withdrawals from the account. After one year, the account had a total value of $10,816. What was the value of P? 10,000 Triangle DEF (not shown) is similar to ABC shown, with angle B congruent to angle E and angle C congruent to angle F. The length of side DE is 6 cm. If the area of ABC is 5 square centimeters, what is the area of DEF ? 45cm^2 m is an odd integer. For each of the following numbers, check if the number is odd. m^2 + m + 1 Which of the following statements is NOT true for all real numbers a and b ? a3-b3=(a+b2)(a2-b) For any positive integers a and b, the operation ^ is defined as a^b=(2a-1)^b-1 . What is the value of (2^2)^3? 25 A company manufactures electronic components that each must weigh from 29.5 grams to 30.5 grams, inclusive. Which of the following inequalities describes all acceptable weights x, in grams, for each component? |30-x| <= 0.5 When Bill makes a sandwich, he may choose from among 3 kinds of rolls, 4 varieties of meat, and 2 types of sliced cheese. If he chooses one roll, one meat, and one type of cheese, how many different kinds of sandwiches can he make? 24 Which of the following statements about an event A are true? I. The probability that the event A will occur can be less than 0. II. The probability that the event A will occur can be equal to 1. III. The sum of the probability that event A will occur and the probability that event A will not occur is equal to 1. II and III only The difference between the mean and the median of the numbers 27, 27, 29, 32, and 35 is 1 In a class with 50 students, 25 of the students are female, 15 of the students are mathematics majors, and 10 of the mathematics majors are female. If a student in the class is to be selected at random, what is the probability that the student selected will be female or a mathematics major or both? 0.6 On an exam for a class with 32 students, the mean score was 67.2 points. The instructor rescored the exam by adding 8 points to the exam score for every student. What was the mean of the scores on the rescored exam? 75.2 A new computer graphics company employs 10 programmers. The company decides to expand into digital animation and needs to transfer 3 of the programmers into the new department. How many different combinations of 3 programmers can be chosen to transfer to the new department? 120 The faces of a fair cube are numbered 1 through 6; the probability of rolling any number from 1 through 6 is equally likely. If the cube is rolled twice, what is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll? 7/12 A scientist estimated the number of bacteria in a sample every hour and recorded the estimates in the table above. Then the scientist used the data to create the scatterplot above. Based on the information, which of the following functions best models the number of bacteria,f(t) , at time t, in hours? f(t)=100(2^t) The width of a rectangular garden is x feet. If 300 feet of fencing is needed to enclose the garden, which of the following represents the length of the garden, in feet? 150-x Michael wishes to give his son a savings bond that will mature in 8 years. He would like the value of the savings bond to be $5,000 at maturity. If he can invest in a bond that has an annual interest rate of 4% compounded monthly, which of the following is the best approximation of the amount he should invest? 3650 The graph above shows the closing price of one share of stock of Company Y for each of the five business days last week. Which of the following is closest to the percent change in the closing price of one share of stock from Tuesday to Wednesday? 67% Let A be a nonempty set and let B and C be any two subsets of A. Which of the following statements must be true? B U C ( A The area of a rectangular field is the product of its length and width. If each dimension of the rectangular field is multiplied by 3, then the area of the enlarged field is how many times the area of the original field? 9 "If it snows, then school is closed." Which of the following is logically equivalent to the statement above? If school is not closed, then it does not snow An artist drew a rectangle. The artist then modified the rectangle so thatthe length ofthe rectawngle increased by 30 percent and the width of the rectangle decreased by 40 percent. After the modification, what was the percent decrease in the area of the rectangle? 22% The results of a survey of 200 college students showed that some students who were business majors were women and all students who were business majors took calculus. Which of the following is a valid conclusion from the survey? Some students who were women took calculus. A house was purchased for $140,000. Three years later, the value of the house was $155,000. If the value of the house increased linearly from the date it was purchased, which of the following represents the value, in dollars, of the house years after the date it was purchased? V=140,000 +5,000 t A painting was purchased for $22 million and sold one year later for $26.4 million. The profit on the most recent sale was what percent of the purchase price? 20% If x and y are nonzero integers, which of the following must be an integer? (x^2+xy)/x Which of the following ordered pairs is NOT in the Cartesian product A x B? b, a Each number in data set A is increased by adding 3 to each data point to form data set B. Which of the following is the same for sets A and B? Range Sam opened a restaurant. On the first day he had 100 customers. On the fourth day he had 160 customers. If the number of customers per day grew linearly, what was the number of customers on the second day? 120 In a group of 33 students, 15 students are enrolled in a mathematics course, 10 are enrolled in a physics course, and 5 are enrolled in both a mathematics course and a physics course. How many students in the group are not enrolled in either a mathematics course or a physics course? 13 A drawer contains exactly 5 red, 4 blue, and 3 green pencils. If two pencils are selected at random one after the other without replacing the first, what is the probability that the first one is red and the second one is green? 5/44 A rectangular flat-screen computer monitor has a diagonal that measures 20 inches. The ratio of the length of the screen to the width of the screen is 4 to 3. What is the perimeter of the screen, in inches? 56 A circular pizza with a 16-inch diameter is cut into 12 equal slices. What is the area, in square inches, of each slice? 16/3 pi A square tablecloth lies flat on top of a circular table whose area is π square feet. If the four corners of the tablecloth just touch the edge of the circular table, what is the area of the tablecloth, in square feet? 2 A box contains 12 red tickets and 8 blue tickets. One ticket was chosen at random and not replaced. A second ticket will be chosen at random. If the first ticket chosen was red, what is the probability that the second ticket chosen will be blue? 8/19 In 2010 the world population was about 6,800,000,000 and the population of the United States was about 310,000,000. Approximately what percent of the world population was the population of the United States? 4.6% If the annual interest rate for an investment is 20 percent, compounded 4 times a year, which of the following is closest to the effective annual yield? 21.6% The regular price of a pair of jeans was $50. The regular price was discounted by x percent during a sale, and the discounted price was $30. What was the value of x? 40 Which of the following is an irrational number? sqrt 14 A glass bowl was manufactured at a cost of $100.00. The glass bowl was priced 30 percent above the manufacturing cost. After one month, the price was discounted 25 percent. What was the discounted price? $97.50 What is the future value of $10,000 invested for one year at an annual interest rate of 2 percent, compounded semiannually? $10,201 Audrey deposited $10,000 into a 3-year certificate of deposit that earned 10 percent annual interest, compounded annually. Audrey made no additional deposits to or withdrawals from the certificate of deposit. What was the value of the certificate of deposit at the end of the 3-year period? $13,310 If P dollars is invested in a savings account that pays 5 percent annual interest, compounded continuously, in how many years will the account value be equal to 2P dollars? In 2^20 years From 1950 to 1990 the population of Country W increased by 40 percent. From 1990 to 2012 the population of Country W increased by 10 percent. What is the percent increase in the population of Country W from 1950 to 2012 ? 54 Let P(E) represent the probability of event E. Let A and B be events with P(A) = 0.3 , P(B) = 0.7, and P(AB) = 0.2 . What is the value of P(AB) ? 0.8 The chart below shows the number of teachers in City A, City B, City C, and City D in 2005 and 2010. Which city had the greatest percent increase in the number of teachers from 2005 to 2010? City B There are 220 seniors at a certain school. Among all seniors, 45 took calculus, 55 took physics, and 10 took both. How many seniors took neither calculus nor physics? 130 The rates below show the currency exchange rates on a certain day last year. Based on the values given in the table, which of the following is closest to the value of one euro in Mexican pesos? Exchange Rates 1 U.S. dollar = 0.72 euros 1 U.S. dollar = 13.21 Mexican pesos 18.35 Mexican Pesos Which of the following pairs of lines are perpendicular? 7y=x-2, 7x=3-y Roll two dice. What is the probability of getting a five or higher on the first roll and getting a total of 7 on the two dice. 1/18 Suppose $10000 is invested today at a 4% interest rate for 10 years. How much more will be under if the interested is compounded continuously, than if it is compounded monthly? $9.92 Suppose a colony of mushrooms triples in size every 10 days. If there are 10 mushrooms to start, how many days until there are 1000 mushrooms? 41.9181 days What is the circumference of a circle with area A=11 11.7571 Suppose a car cost $4000 in 1970. If the inflation rate is constant at 4%, what is the cost of the car in 2000? $12974 Suppose the weight of mice is normally distributed with mean 10 and standard deviation 2. Which of the following is the most accurate approximation to the probability a mouse has weight less than 8? 0.16 Which of the following statements is false? The product of two rational numbers cannot be an integer. Suppose a trapezoid has base lengths 8 and 14. What does its height need to be in order for the trapezoid to have area 30? 2.7273 Which of the following does not have a well-defined inverse function, defined on its range? f(x) = x^4 +1 Which of the following functions exhibits odd symmetry? f(x) = x^5 + 3x^3 Suppose one wishes to have exactly in 20 years. How much should one invest today, assuming a 5% interest rate compounded continuously? 36788 Suppose a right triangle has one leg length equal to 10 and the hypotenuse is equal to 15. What is the area of the triangle? 55.9 Suppose there are 50 possible dancers. How many trios may be formed, assuming the order within a trio does not matter? 19600 Which of the following number is largest? 7 x10^6 Suppose the largest number in a list of at least 3 numbers is 10. Suppose 10 is replaced by 100 in the list. Which of the following statistics must be unchanged? median