ETS MATH PRAXIS 5164 QUESTIONS AND ANSWERS 100% PASS

ETS MATH PRAXIS 5164 QUESTIONS AND ANSWERS 100% PASS Andre has driven 98 miles, which is 35% of the total distance he must drive on his trip. How many more miles does Andre have to drive on his trip? A.34 B. 182 C. 280 D. 378 182 Correct Answer: B Option (B) is correct. Since Andre has driven 35% of the total distance, he still has 65% of the total distance left to drive. The distance he has left to drive can be found using the proportion the fraction 98/0.35 = x/0.65 where x represents the distance, in miles, that Andre has left to drive. Thus, 0.35 = 63.7, and x = 182. Note that in most multiple-choice questions that ask for numerical values, the exact answer should be found, as it should be in this question. If a multiple-choice question includes a word like “approximately,” it generally indicates that the correct option will not be an exact value. Elizabeth owns x books. Kierra owns 5 more books than Elizabeth and 8 fewer than Ana. Which of the following expressions represents the total number of books the three girls own? 3x-3 3x+3 3x+13 3x+18 Correct Answer: D Option (D) is correct. Since it is given that Elizabeth owns x books, it can be determined that Kierra owns x+5+8 books. The total number of books the girls own is x+x+5+x+5+8 = 3x+18. A right triangle and a student's process for finding the length of the unknown side of the right triangle are given as follows. Based on the information given, which of the following skills is the most important to review with this student? A. Solving for a variable in a quadratic equation B. Finding the approximate value of a square root C. Determining whether a triangle is a right triangle D. Identifying which side of a right triangle is represented by each variable in the Pythagorean theorem Option (D) is correct. The student mistakenly switched the hypotenuse with the unknown leg length when using the Pythagorean theorem. Thus, it is most important to review which side of a right triangle is represented by each variable in the Pythagorean theorem with the student so the student can correctly apply the Pythagorean theorem. Note that the student correctly solved the equation 3 to the 2nd power + 5 to the 2nd power = x to the second power for x, it is not necessary to find a decimal approximation of square root of 34, and it is appropriate for the student to use the Pythagorean theorem, since the triangle is a right triangle. If f(x)=−x squared - 2x+4, what is the value of f (-2) ? . -4 -2 4 12 Option (C) is correct. To find the value of f of negative 2f (-2), substitute -2 for x and then follow the order of operations. Therefore, f(-2)=-2(-2)squared -2(-2)+4=-4+4+4+4=4 Note that in most multiple-choice questions that ask for numerical values, the exact answer should be found, as it should be in this question. If a multiple-choice question includes a phrase like “best approximates” or “is closest to,” it generally indicates that the correct option will not be an exact value. Which TWO of the following word problems can be answered by dividing 4 by one 1/5? A. A quilt requires one 1/5 square meter of purple cloth. How many square meters of purple cloth are needed for 4 of these quilts? B. A machine working at a constant rate takes an hour to sort 4 bins of mail. How many bins of mail does the machine sort in one 1/5 hour? C. Each person at a dinner was served one 1/5 of a fish fillet. A total of 4 fish fillets were served. How many people were served at the dinner? D. A roll of copper wire that was 4 meters long was cut into sections that were each one 1/5 meter long. How many sections were made from the roll of copper wire? E. Each of 4 people in a study group read one 1/5 of the total chapters in a book. No student read the same chapter as any other student. What fraction of the total chapters in the book did the study group read? Options (C) and (D) are correct. Problem (C) can be answered by dividing the number of fillets, 4, by the fraction of a fillet served per person, one 1/5 fillet per person, to determine that 20 people were served at the dinner. Problem (D) can be answered by dividing the length of the roll of wire, 4 meters, by the length per section, 1/5 meter per section, to determine that 20 sections were made from the roll. Leah wants to estimate the number of students in her eighth-grade class whose favorite color is green. She wants to survey 25 students who are likely to be representative of her entire eighth-grade class. From which of the following populations should Leah randomly select her sample of 25 students? A. Students at a basketball game B Students at an eighth-grade assembly C. Students arriving at her middle school one morning D. Students in her eighth-grade social studies class who are wearing green Option (B) is correct. A random sample of students at an eighth-grade assembly is likely to be representative of the entire eighth-grade class. The population in option (A) is not likely to be representative of the entire eighth-grade class because students from other grades are likely to be present and there are many eighth-grade students who are not likely to attend a basketball game. The population in option (C) is not likely to be representative of the entire eighth-grade class because students from other grades are likely to be present. The population in option (D) is not likely to be representative of the entire eighth-grade class because students who are wearing green might be more likely to say that green is their favorite color. Following an introductory lesson on multiplying two binomials, Ms. Davis wants to follow up with a quick problem at the end of class to assess student proficiency. The students will write their final answers on slips of paper and hand them to Ms. Davis as they exit the class. Which of the following expressions would be LEAST useful for assessing student proficiency in multiplying two binomials? (x-3) (x-5) (x+3) (x-5) (x-5) (x+5) (x+5) (x+5) Option (C) is correct. A common error that students make when multiplying binomials is to multiply only the x terms and the constant terms, forgetting to multiply each of these by one another. Therefore, a useful assessment problem would be one where this common error would lead to an incorrect answer so that Ms. Davis would know whether a student is using incorrect reasoning. A student who makes this error when multiplying the binomials in option (C) will get an answer of xsquared-25, which is the same as the correct answer, so Ms. Davis would have no way of knowing whether the student is using this incorrect reasoning; consequently, this is not a useful problem for assessing student proficiency in this situation. A student who makes the same error when multiplying the binomials in options (A), (B), and (D) will get an incorrect answer, so these problems would be useful for assessing student proficiency in this situation. The length of a right rectangular prism is twice its height, and the height of the prism is twice its width. If the volume of the prism is 1,000 cubic inches, what is the height, in inches, of the prism? 5 10 15 20 Option (B) is correct. Let lℓℓ be the length of the prism, let h be the height of the prism, and let w be the width of the prism. Since the length of the prism is twice its height, l = 2h, and since the height of the prism is twice its width, h = 2w. By substitution, l =4w, since l= 2h= l = 2 (2w) = l =4w. Then, since the prism is a right rectangular prism, l w h equals 1,000 ℓwh = 1,000. Then, by substitution, (4w)(w)(2w) = 1,000 = 8w 3squared =1,000 w3squared =125 = w=5. Finally, by substitution, the height of the prism is 2w, = 2(5)=10 inches. Note that in most multiple-choice questions that ask for numerical values, the exact answer should be found, as it should be in this question. If a multiple-choice question includes a phrase like “best approximates” or “is closest to,” it generally indicates that the correct option will not be an exact value. Which of the following values can be represented by the preceding area model? Select ALL that apply. Answer the question by selecting the correct responses. 0.3% 3% 30% 0.3/10 3/10 30/10 The number of bacteria in a culture doubled every hour. The culture started with 10 bacteria. Which of the following functions models the number of bacteria in the culture after t hours? f(t)=10t f (t) = 10 +2t f (t) =10 power of t f (t) = 10(2) power of t Ms. Patel's students are working on summarizing data collected from measurements on a single variable. She asks them to make observations about the following list of the numbers of students in each mathematics class at Franklin Middle School. 16, 20, 21, 18, 28, 29, 22, 21, 26, 28, 22, 19, 25, 22, 28 Which of the following student statements provides evidence of statistically appropriate reasoning about the data? A. There are two numbers that show up three times in the list, so that means the list has two modes. B. outliers in the list are 16 and 29 because those are the smallest and largest numbers in the list. C. The median number of students in a math class is 21 because there are 7 numbers before it and 7 numbers after it in the list you showed us. D. Since there are 6 numbers in the list that are less than 22 and 6 numbers that are greater than 22, the mean number of students in a math class has to be 22. Company F charges a one-time fee of $85.00 to rent a truck plus $0.60 for every mile driven. Company G charges a one-time fee of $61.00 to rent a truck plus $0.90 for every mile driven. For what number of miles is the cost to rent a truck the same at both companies? _______ miles During a two-week period, a library reported that 6,590 people used the library. The following table shows the numbers of people in various categories of library use for that two-week period. Morning 1,420 adults 725 children Afternoon 870 adults 525 children Evening 2,100 adults 950 children Option (B) is correct. In order to calculate the percentage, you must know two things: the total number of people who used the library during the two-week period and the total number of people who used the library during the afternoon. The total number of people who used the library during the afternoon is 1,395. This number is determined by adding 870, the total number of adults who used the library during the afternoon, and 525, the total number of children who used the library during the afternoon. The total number of people, adults and children, who used the library during the two-week period, 6,590, is given in the problem. To calculate the percentage of the total, divide 1,395 by 6,590 to get approximately 0.21, and the option that is closest to this value is 20%. Another way to calculate the percentage is to set up and solve the proportion the fraction 1,395/6,590 = x/100. Note that when a word like “approximately” is used in a question, it generally indicates that the correct option will not be an exact value.