[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-459501-105":59,"doc-detail-459501-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","qat-sample-questions-set-3","QAT - Sample Questions - SET 3","","A collection of exam-style multiple-choice questions covering calculus and related topics, including evaluating derivatives of defined functions, identifying level-curve functions from graphs, and finding tangent plane equations from surface definitions. The set also includes differential equation/integration style prompts, application problems such as candle burn rate and time-to-complete burning, and linear algebra questions about determinants of matrix powers and polynomial relationships. 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Let 􀝂 (􀝔) = ((􀯫􀯫21))~~ ~~((􀯫􀯫36)) . What is 􀝂′(0)?  \nA. 5/6  \nB. −4/3  \nC. 1  \nD. −1/3  \nE. 2/3  \n2. The following graph (solid lines only) shows level curves of which function? (A level curve of 􀝂(􀝔, 􀝕) is a set of points (􀝔, 􀝕) such that 􀝂 (􀝔, 􀝕) is constant.)  \n10  \n5  \n0  \n-5  \n-10  \ny  \n-10 -5 0 5 10  \nx  \nA. 􀝂 (􀝔, 􀝕) = |􀝕| − 􀝔  \nB. 􀝂 (􀝔, 􀝕) = |􀝔| + 􀝕  \nC. 􀝂 (􀝔, 􀝕) = |􀝔|􀝕  \nD. 􀝂 (􀝔, 􀝕) = 10|􀝔 + 􀝕|  \nE. 􀝂 (􀝔, 􀝕) = 10|􀝔 − 􀝕|  \n3. Suppose 􀝂(􀝔, 􀝕) = √2􀝔 + 􀝕 . Which of the following is the equation of the plane that is tangent to the graph of 􀝂 (plotted on the 􀝔, 􀝕, 􀝖 axes) atthe point (4,1)?  \nA. 􀝖 = 16 􀝔 + 13 􀝕 + 2  \nB. 􀝖 = 16 􀝔 + 13 􀝕 + 1.5  \nC. 􀝖 = 13 􀝔 + 16 􀝕 − 1.5  \nD. 􀝖 = 13 􀝔 + 169 􀝕 − 1.5  \nE. 􀝖 = 13 􀝔 + 16 􀝕 + 1.5  \n4. If dydx 􀀠 y sec2 x and y 􀀠 5 when x 􀀠 0 , then y =  \nA. etanx 􀀎 4  \nB. etanx 􀀎 5  \nC. 5etanx  \nD. tan 􀝔 + 5  \nE. tan x 􀀎 5ex  \n5. A candle is burning so that when its height is ℎ cm, it is burning at a rate of 3√ℎ cm per hour. If the initial height of the candle is 36 cm, how long will it take for the candle to burn down completely?  \nA. 4 hours  \nB. 5 hours  \nC. 6 hours  \nD. 7 hours  \nE. 8 hours  \n6. Let 􀜣 = [ − 21 − 21 ] . Let 􀜣􀯍 denote the transpose of 􀜣 .  \nWhat is the determinant of (􀜣􀯍 )2?  \nA. −2  \nB. −9  \nC. 0  \nD. 2  \nE. 3  \n7. Let 􀝂(􀝔) = 1 + 􀝔 and 􀝃 (􀝔) = 􀝔 2 . Which of the following polynomials is not a linear combination of 􀝂(􀝔) and 􀝃 (􀝔)?  \nA. 1 + 2􀝔 + 3􀝔2  \nB. 5 + 5􀝔 + 12 􀝔 2  \nC. 3 + 3􀝔 − 􀝔 2  \nD. −2 − 2􀝔 + 4􀝔2  \nE. 1 + 􀝔 − 􀝔 2  \n8. Two balls are chosen (without replacement) at random from an urn consisting of three red balls, two blue balls, and one pink ball. What is the probability that at least one blue ball is chosen?  \nA. 1/5  \nB. 2/5  \nC. 3/5  \nD. 2/15  \nE. 8/15  \n9. An urn consists of three white balls and two red balls. Frank and Jane alternately randomly choose a ball (with replacement) . The first person who gets the same color as the latest ball chosen by the other person wins the game. Assume that Frank starts first, and he cannot win from the first ball. What is the probability that Jane wins this game?  \nA. 13/19  \nB. 13/25  \nC. 19/25  \nD. 13/15  \nE. 1/2  \nProblem 10-11  \nAssume that the daily returns of an asset is normally distributed with mean 􀟤 and variance 􀟪 2 . Let 􀜺1, 􀜺2,…, 􀜺10 be ten independent sample of the asset returns. Define the sample average ̅􀜺 and the sample variance 􀜵 2 as follows:  \n̅􀜺 = 110 􀜺􀯜􀯜 = 1  \n, 􀜵 2 = 19 (􀜺􀯜 − ̅􀜺)2 􀯜 =1  \nAnswer the following questions.  \n10. What is the distribution of ̅􀜺?  \nA. Normal with mean 􀟤/10 and variance 􀟪2/10  \nB. Normal with mean 􀟤/10 and variance 􀟪 2  \nC. Normal with mean 􀟤 and variance 􀟪2/10  \nD. Normal with mean 􀟤 and variance 􀟪2/100  \nE. Normal with mean 􀟤/10 and variance 􀟪2/100  \n11. The sample variance 􀜵2 , after scaling by an appropriate constant , has which of the following distribution?  \nA. Normal  \nB. Chi-square, degree 9  \nC. Chi-square, degree 10  \nD. Student-t, degree 9  \nE. Student-t, degree 10  \n12. Let 􀜺 and 􀜻 be two random variables with variances 1 and 2 , respectively. If the covariance of 􀜺 and 􀜻 is -0.75, which of the following has the lowest variance?  \nA. 􀜺  \nB. −􀜺  \nC. 0. 5􀜺 + 0. 5􀜻  \nD. 0. 5􀜺 − 0. 5􀜻  \nE. 0. 6􀜺 + 0. 4􀜻  \n13. Many firms encourage employees to participate in assistance programs that enable employees, free of charge, to improve their physical fitness and reduce stress. These programs increase worker productivity, reduce absenteeism, and lessen insurance costs for employee health care. Therefore, these programs benefit both the company and the employee.  \nWhich of the following, if true, most significantly strengthens the conclusion above?  \nA. Physical fitness reduces employees’ risk of heart disease.  \nB. Physical fitness is the most popular program.  \nC. Employee assistance programs require company to hire more employees to monitor the programs offered.  \nD. Studies have shown that stress management course is not effective.  \nE. Physical injuri","cbCaieIgQX6k9a9I","https://ap.wps.com/l/cbCaieIgQX6k9a9I","pdf",586077,"English","# QAT Sample Questions (SET 3)\n## Questions 1-9\n## Questions 10-14\n## Questions 15-16\n## Questions 17+","[{\"question\":\"How do you compute 􀝂′(0) in Question 1?\",\"answer\":\"Question 1 defines 􀝂 (􀝔) in terms of an expression involving 􀝔, then asks for the derivative at 0 and provides multiple-choice options for the value.\"},{\"question\":\"Which method is used to identify the function from level curves in Question 2?\",\"answer\":\"Question 2 states that an A-level curve of 􀝂(􀝔, 􀝕) is the set of points where 􀝂(􀝔, 􀝕) is constant, and it asks which listed function matches the shown solid level curves.\"},{\"question\":\"What statistics concepts appear in Questions 10-12?\",\"answer\":\"Questions 10-12 use properties of the sampling distribution of the sample mean, the scaled sample variance distribution, and relate variances and covariance to find which linear combination has the lowest variance.\"}]","QAT - Sample Questions - SET 3 | PDF",1790756061]