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Bit 1110 Mathematics For Sciences – Distance Learning Question Paper
Bit 1110 Mathematics For Sciences – Distance Learning
Course:Bachelor Of Science In Information Technology
Institution: Kca University question papers
Exam Year:2014
UNIVERSITY EXAMINATIONS: 2013/2014
ORDINARY EXAMINATION FOR THE BACHELOR OF SCIENCE
IN INFORMATION TECHNOLOGY
BIT 1110 MATHEMATICS FOR SCIENCES - DISTANCE
LEARNING
DATE: AUGUST, 2014
TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and any other TWO
QUESTION ONE [30MARKS]
(a) What is the number of terms of the arithmetic progression, 15 + 21 +27 + ..., that will give a
sum of 960?
[3 Marks]
(b) The third term of a G.P. is 18, and the last term is 486. If the sum of the progression is 728,
find the number of terms and the common ratio.
(c) Differentiate between a sequence and a series.
[3 Marks]
[2 Marks]
(d) Given that log102 = 0.3010 and log103 = 0.4771 and without using a calculator or logarithm
tables find:-
(i) log1015552
(ii) log10
[2 Marks]
81
8
(e) Express 7 4 3 in the form
[2 Marks]
4
p where p is an integer.
[2 Marks]
(f) How many even numbers, greater than 3000, can be formed with the digits 1, 2, 4, 8, if each
digit may be used only once in each number?
(g) Find the remainder when f(x) = 4x – x + x - 3 is divided by 2x – 1
5
3
2
3
(h) Expand (2a + 3b) using binomial theorem
[3 Marks]
[2 Marks]
[3 Marks]
(i) Calculate the remaining side and angles of triangle PQR in which p = 15.9 cm, r = 18.6 cm
and P = 570.
[4 Marks]
(j) Give two advantages and two disadvantages of observation as a data collection method.
[4 Marks]
1
QUESTION TWO [20 MARKS]
(a) Given that log102 = 0.3010 and log103 = 0.4771, without using tables or logarithm
function in your calculator, find:-
(i) log10864
(ii) log10
32
81
[4 Marks]
(b) Solve the following equation for x
(i) Log2(10x + 2) – log2(x + 1) = 3
(ii) - 3 log5 + log x2 = log
[4 Marks]
1
125
[3
Marks]
(iii) 3x(72x+1) = 37
(c) Solve for the equation,
[5 Marks]
log x 2
48
14
log x 2
[4 Marks]
QUESTION THREE [20 MARKS]
(a) Differentiate between the following terms as used in statistics.
(i) Continuous and discrete data. [2 Marks]
(ii) Primary and secondary data. [2 Marks]
(iii) Quantitative and qualitative data. [2 Marks]
(b) Explain the main sources of secondary data.
[5 Marks]
(c) Give two advantages and two disadvantages of each of the following methods of data
collection
(i) Personal Observation.
[3 Marks]
(ii) Interviewing method. [3 Marks]
(iii) Self-Completion Questionnaires. [3 Marks]
QUESTION FOUR [20 MARKS]
(a) If Cos ? =
(b) Express
4
, find (i) Cosec ? (ii) tan ?
5
[4 Marks]
1 tan 600
in surd form, then rationalize the denominator
1 tan 600
Marks]
2
[4
(c) The captain of a clipper ship C spots two other ships on the ocean. Ship A is about 5 km
away and ship B is about 5.2 km away. The angle between the two sightings is 200. How
far apart are the ships A and B?
[ 4 Marks]
(d) At a criminal trial, the witness gave the following testimony: “The defendant was 20
meters from the victim. I was 50 meters from the defendant and 75 meters from the
victim when the shooting occurred. I saw the whole thing.” Use cosine rule to show the
testimony has errors.
[4 Marks]
0
(e) A rocket with a range of 200 km is launched at sea with a bearing of 30 . (A bearing is
the angle measured clockwise form due north).
(i) How far north of its original position will the rocket land?
(j) How far east of its original position will the rocket land?
[4 Marks]
QUESTION FIVE [20 MARKS]
(a) Obtain the expansion of 3x
1
2
3
, in descending powers of x.
[4 Marks]
(b) Eight girls are running a race. In how many ways can the first three places be filled, if
there are no dead heats?
[3 Marks]
(c) The 15th term of an A.P. is 59 and the sum of the first fifteen terms is 465. What is the
sum of the first twenty terms?
[4 Marks]
(d) In how many ways can four letters of the word SCHOOL be arranged in a row, if no
letter is repeated?
[3 Marks]
(e) Show that the sum of the first n terms of the geometric progression with first term a, and
common ratio r, is given by the following formula.
sn
a ( r n 1)
r 1
[6 Marks]
3
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