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Sma 2104 Mathematics For Science Question Paper

Sma 2104 Mathematics For Science

Course:Mathematics And Computer 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 2011/2012

FIRST YEAR FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN MATHEMATICS AND COMPUTER SCIENCE

SMA 2104 : MATHEMATICS FOR SCIENCE

DATE: AUGUST 2011 TIME: 2 HOURS

INSTRUCTIONS: ANSWER QUESTION ONE (COMPULSORY) AND
ANY OTHER TWO QUESTIONS.
______________________________________________________________________

QUESTION ONE (30 MARKS)

(a) Write down the sixth term of the expansion . Find the value of the constant term of the expansion.
[5 marks]

(b) By re-arranging the function y = 3x2 – 14x + 18 in the form

y = a(x + b)2 + c where a, b, and c are constants, find the

minimum value of y. State the value of x when y is a minimum.
[5 marks]

(c) Write down and evaluate in surd form an expression for

(i) Sin750 [3 marks]
(ii) Cos 1350 [2 marks]
(d) A bag contains 5 red balls and 7 white balls. Find the probability of drawing 2 white balls in the draws such that:

(i) The balls drawn are not being replaced. [2 marks]

(ii) The balls being replaced after each draw. [3 marks]

(e) Calculate the mean and the standard deviation of the following measurements in centimetres 2.25, 2.29, 2.36, 2.39, 2.31, 2.33
[5 marks]

(f) The second term of a geometric series is 1 and the fifth term is

. Find the first term and the common ratio of the series.

Determine the sum to infinity of the series. [5 marks]

QUESTION TWO (20 MARKS)

(a) A committee of six is to be formed from 9 women and 3 men. In how many ways can the members be chosen so as to include at least one man? [8 marks]

(b) Write down and simplify the term in y5 in the expansion of

[5 marks]

(c) Use Binomial theorem to find the value of (0.99)12 correct to three places of decimals. [7 marks]

QUESTION THREE (20 MARKS)

(a) In an arithmetic progression the sum of the first five terms is 30 and the third term is equal to the sum of the first two terms. Write down the first five terms of the progression. [6 marks]

(b) Solve the equation sec2? = 3tan ? – 1 giving values of ? from ?0 to 3600 [7 marks]

(c) The roots of the equation 2x2 – 4x + 1 = 0 are ? and ß. Find an

equation with integral coefficients whose roots are , and

[7 marks]

QUESTION FOUR (20 MARKS)

(a) Write 3cos? + 4sin? in the form Rcos(? - ?), and hence solve the equation 3cos? + 4sin? = 2 [9 marks]

(b) The following frequency table gives the heights to the nearest centimetre of 100 school boys.

Height (cm) 152 153 154 155 156 157 158 159 160 161
Number of boys 1 2 3 4 6 8 16 23 14 11

162 163 164 165 Total
6 4 1 1 100

Find:

(i) The mode. [2 marks]
(ii) The mean. [2 marks]
(iii) The median. [3 marks]
(iv) The standard deviation. [4 marks]

Sma 2104 Mathematics For Science Question Paper

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