Grade 12 - Comp. / Annales-others 3 exercises (100% corrected)

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−10−5310724−6Variationdegx 1. Unclassified financial years E.6975 This exercise is a multiple-choice questionnaire. For each of the following questions, only one of the four answers pro-vided is correct. No justification is required. A correct answer earns one point. An incorrect answer, mul-tiple answers, or no answer earns or loses no points. Indicate the question number and the corresponding answer on your answer sheet. 1 Let f be the function defined on 0 ; + ∞ by: f ( x )= x · ln( x ) − x . Let f be its derivative function. We then have : a f ( x ) = 0 b f ( x ) = ln( x ) c f ( x ) = 1 x − 1 d f ( x ) = 1 x − x 2 The natural integers n satisfying the inequality: 6 × 0.95 n − 1 2 belong to the interval: a −∞ ; ln3 ln(5.7) b −∞ ; ln 0.5 0.95 c −∞ ; ln(0.5) ln(0.95) d ln(0.5) ln(0.95) ; + ∞ 3 A company manufactures metal tubes of length 2 m . A metal tube is considered to be within the standard if its length is between 1.98 m and 2.02 m . A random sam-ple of 1 000 tubes is taken, and it is observed that 954 tubes are within the standard. The confidence interval for the proportion of tubes within the standard for this company at a confidence level of 95 % , with the limits rounded to 10 − 3 , is : a 0.922 ; 0.986 b 0.947 ; 0.961 c 1.98 ; 2.02 d 0.953 ; 0.955 4 For an archer, the probability of hitting the target is 0.8 . The shots are assumed to be independent. What is the probability that he will hit the target 3 times in a series of 6 shots? a 0.512 b 2.4 c 0.262 144 d 0.081 92 E.6982 This exercise is a multiple-choice questionnaire. For each question, only one of the four answers is correct. A correct answer earns one point. An incorrect answer, mul-tiple answers, or no answer earns or loses no points. Indicate the question number on your answer sheet and copy the answer you have chosen. No justification is required. 1 A random variable X follows a uniform distribution on the interval 1 ; 9 , then a P 1 < X < 9 = 1 8 b P 5 < X < 9 = 1 2 c P 1 < X < 3 = 3 8 d P 1 < X < 2 = 1 2 2 A health survey aims to estimate the proportion of people who comply with the vaccination schedule recommended by the High Council for Public Health. To obtain a con-fidence interval of amplitude 0.01 at the confidence level 0.95 for this proportion, it is necessary to survey: a 200 people b 400 people c 10 000 people d 40 000 people 3 The solution to equation x 23 =92 is equal to : a 4 b 1.2 c e ln(92) 23 d e ln(21) 92 4 Consider the function g defined on the interval − 10 ; 10 , whose table of variations is given below : Let I = 3 − 5 g ( x ) d x . We can say that : a − 5 I 3 b 2 I 4 c 16 I 32 d 4 I 8 https://chingmath.fr chapExoCorrec/6975 sacados/6975 chapExoCorrec/6982 sacados/6982 −10−5310724−6Variationdegx
E.6990 This exercise is a multiple-choice questionnaire () . For each question, only one of the four answers is correct. Copy the question number and the correct answer. No justification is required. A correct answer is worth 1 points, while an incorrect answer or no answer does not add or subtract any points. Multiple answers do not earn any points. 1 The correct solution to equation 1 2 x = 3 10 is : a 1.74 b ln 10 − ln 3 ln 2 c − ln 3 ln 5 d 0.5 2 f is the function defined for any real number x by: f ( x ) = 2 x · e x 2 the correct value of the integral 2 − 2 f ( x ) d x is : a 4 · e 4 − 4 · e − 4 b 4 · e 4 + e − 4 c 0 d 1 3 f is the function defined for all x in the interval 0 ; + ∞ by: f ( x ) = 2 x + 3 · ln x We assume that the function f is differentiable on the interval 0 ; + ∞ . Recall that f denotes the derivative of the function f . For any real number x in the interval 0 ; + ∞ , we have : a f ( x ) = 2 x + 3 x b f ( x ) = 2 x c f ( x ) = 2 · ln x + 3 x + 2 d f ( x ) = 2 · ln x + 3 x 4 A quantity was increased by 5 % in the first year, then by 7 % in the second year. Over these two years, the overall percentage increase is equal to : a 12 % b 35 % c 0.35 % d 12.35 % https://chingmath.fr chapExoCorrec/6990 sacados/6990