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Sma 2104 Mathematics For Science Question Paper
Sma 2104 Mathematics For Science
Course:Bachelor Of Science
Institution: Jomo Kenyatta University Of Agriculture And Technology question papers
Exam Year:1
W1-2-60-1-6
JOMO KENYATTA UNIVERSITY
OF AGRICULTURE AND TECHNOLOGY
University Examinations 2012/2013
EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN MATHEMATICS AND COMPUTER SCIENCE/ ANALYSTICAL CHEMISTRY/ BIOCHEMISTRY/ INDUSTRIAL CHEMISTRY/ CONTROL AND INSTRUMENTATION/ BIOTECH/ MMB
SMA 2104: MATHEMATICS FOR SCIENCE
DATE: AUGUST 2012 TIME: 2 HOURS
INSTRUCTIONS: ANSWER QUESTION ONE (COMPULSORY) AND ANY OTHER TWO QUESTIONS
ALL THE NECESSARY WORKING MUST BE CLEARLY SHOWN
QUESTION 1
a) i) Find the minimum value of x2 – 5x – 7 and state the value of x
when the minimum value occurs. (3 marks)
ii) Rationarise the denominator of (2 marks)
b) i) If are the roots of the equation 2x2 – 5x – 1 = 0, find the value of . (2 marks)
ii) The expression ax4 + bx3 – x2 + 2x + 3 has remainder 3x + 5 when
it is divided by x2 – x – 2. Find the values of a and b. (3 marks)
c) Find the sum of odd numbers between 11 and 199 inclusive. (4 marks)
d) Given that sin Find the value of (i) sin 2 (3 marks)
e) Eliminate from the equations x = 2 tan and y = tan 2 . (3 marks)
f) i) Find the probability of getting three heads in five tosses of unfair
coin in which the probability of getting a head is (3 marks)
ii) Find the mean and standard deviation of the numbers 2, 3, 4, 5, 6 and 7(3 marks)
g) How many arrangements can be made of the letters in the word
TROTTING? In how many of these are N and G next to each other? (3 marks)
QUESTION 2
a) Find an equation with integral co-efficients, whose roots are the squares
of the roots of the equation 2x2 + 5x – 6 = 0 (5 marks)
b) Find the greatest value of:
-10 + 14x – 2x2 and state the value of x at which it occurs. Sketch the curve
of y = -10 + 14z -2x2. Showing clearly the line of symmetry of the curve.(5 marks)
c) Solve by factorization the equation 2x2 – 5x + 3 = 0 (5 marks)
d) The sum to infinity of a geometrical progression with a positive common
ratio is 9 and the sum of the first two terms is 5. Find the first four terms
of the progression. (5 marks)
QUESTION 3
a) A committee of six is to be formed from nine women and three men. In how
many ways can the members be chosen so as to include at atleast one man?(6 marks)
b) i) Find the middle term in the expansion of (6x + (4 marks)
ii) What is the value of the constant term in the expansion of:
(4 marks)
c) Express 24 sin x + 7cosx in the form R sin (x + and hence solve the
equation 24 sin x + 7 cos x + 15 = 0 (7 marks)
QUESTION 4
a) The length in centimeters of twelve rods are as follows: Find the mean
value and standard deviation. 5.33, 5.31, 5.33, 5.22, 5.29, 5.34, 5.35, 5.31,
5.27, 5.28, 5.32, 5.25 ( 7 marks)
b) Four fair coins are thrown and the number of heads are counted. What are
the chances that 0, 1, 2, 3, and 4 heads are obtained?
The experiment is repeated 128 times. Draw a table to show the numbers
of throws one could expect to give 0, 1, 2, 3 and 4 heads. (8 marks)
c) Ten percent of articles from a machine are defective. In a sample of 12
what is the chance that there will be three defectives? (5 marks)
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