Sma2250:Maths For Biologists. Question Paper
Sma2250:Maths For Biologists.
Course:Bachelor Of Crop Protection
Institution: Meru University Of Science And Technology question papers
Exam Year:2012
QUESTION ONE (30 MARKS) a) If sin?? = 3 5 ?????? cos?? = 15 17 , where A is obtuse and B is acute, find the exact value of sin(?? + ??). (5 Marks) b) Find the derivative of the following functions i. (3?? + 2)4. (3 Marks) ii. 1 + ??2 (3 Marks) iii. (??-3)2 (??+2)2 (4 Marks) c) Find the area enclosed by the x-axis, ?? = 1,?? = 3 and the graph ?? = ??3.(5 Marks) d) Find the x-coordinates of the stationary points of the curve ?? = ??2 - 1 1 + ?? . (5 Marks) e) Let x be a normally distributed random variable with a mean of the and a standard deviation of 2. Find the probability that x lies between 11 and 13.6. (5 Marks)
QUESTION TWO (20 MARKS)
a) Find; sin3?? - ??2 ????. (4 Marks) ??5 - 3??2 4??3 - 3 ???? (4 Marks) b) Find the area enclosed by that part of ?? = ??2 for which ?? is positive, y axis and the lines ?? = 1 and ?? = 4. (8 Marks) c) Determine the integral of ??cos2??????. (4 Marks)
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QUESTION THREE (20 MARKS)
a) Evaluate the following derivatives i. 1 (2??+3)2 . (3 Marks) ii. (2x2 - 3 x2 ) 1 3 . (3 Marks) b) A container in the shape of a right circular cone of height 10cm and base radius 1cm is catching the drips from a tap leaking at the rate of 0.1cm3/s. Find the rate at which the surface area of water is increasing when the water is halfway up the cone. (14 Marks)
QUESTION FOUR (20 MARKS)
To determine whether taking Agricultural based subjects and Business related subjects affects 100 male students were drawn from the students body.
The grade point average for ??1 = 100 (Agriculture courses) had a mean of ??1 = 2.7 and variance of ??2 = 0.36. A second group of Business students ??2 = 100 had a mean ??2 = 2.54 and variance of ??2 = 0.40. Using ? ??????h?? = 0.05;
a) Construct a 95% confidence interval for the difference in average achievements between students taking Agricultural courses and those taking business courses. Using the confidence interval, can you conclude that there is a difference in the population means for the two groups of the students? (10 Marks) b) The average weekly earnings for female social workers is Ksh. 670. Do men in the same positions have average weekly earnings that are higher than those for women? A random sample of n=40 male social workers showed ?? = ????h 725 and ?? = ????h 102. Test the appropriate hypotheses using ?= 0.01. (10 Marks)
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