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Unformatted text preview: , where 0 < a < b.
b + a sin x
(i) Show that dy
(b 2 + a 2 ) cos x
(b + a sin x ) 2
(4) (ii) Find the maximum and minimum values of y.
(4) (iii) Show that the graph of y a + b sin x , 0 < a < b cannot have a vertical asymptote.
b + a sin x
(2) 151 (b) For the graph of y = 4 + 5 sin x for 0 ≤ x ≤ 2π,
5 + 4 sin x
(i) write down the y-intercept; (ii) find the x-intercepts m and n, (where m < n) correct to four significant figures; (iii) sketch the graph.
(5) (c) The area enclosed by the graph of y = 4 + 5 sin x and the x-axis from x = 0 to x = n is
5 + 4 sin x
denoted by A. Write down, but do not evaluate, an expression for the area A.
(Total 17 marks) 221. The distribution of lengths of rods produced by a machine is normal with mean 100 cm and
standard deviation 15 cm.
(a) What is the probability that a randomly chosen rod has a length of 105 cm or more?
(2) (b) What is the probability that the average length of a randomly chosen set of 60 rods of this
type is 105 cm or more?
(Total 5 marks) 152 222. In a study to check whether nicotine and alcohol consumption may be related, a survey of 452
women was conducted. The data below gives the alcohol consumption against the nicotine
intake per day.
Alcohol (cl/day) None 16 or more 105
more than 30 1–15
17 Investigate whether the consumption of nicotine and alcohol are related to each other.
Use a 5% level of significance in your analysis and explain all your steps and conclusions.
(Total 9 marks) 223. Scientists have developed a type of corn whose protein quality may help chickens gain weight
faster than the present type used. To test this new type, 20 one-day-old chicks were fed a ration
that contained the new corn while another control group of 20 chicks was fed the ordinary corn.
The data below gives the weight gains in grams, for each group after three weeks.
Ordinary corn (Group A) New corn (Group B) 380 366 356 361 447 401 375 283 349 402 462 434 403 393 426 356 410 329 399 406 318 467 407 350 384 316 272 427 420 470 392 345 (a) 321 455 360 431 430 339 410 326 The scientists wish to investigate the claim that Group B gain weight faster than Group
A. Test this claim at the 5% level of significance, noting which hypothesis test you are
using. You may assume that the weight gain for each group is normally distributed, with
the same variance, and independent from each other. 153 (b) The data from the two samples above are combined to form a single set of data. The
following frequency table gives the observed frequencies for the combined sample. The
data has been divided into five intervals.
(6) Weight gain Observed 271–310 2 311–350 9 351–390 8 391–430 15 431–470 6 Test, at the 5% level, whether the combined data can be considered to be a sample from a
normal population with a mean of 380.
(Total 16 marks) 224. A–B is the set of all elements that belong to A but n...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.
- Fall '13
- The Land