DIT 107 – MATHS FOR SCIENCE KCA Past Paper

UNIVERSITY EXAMINATIONS: 2021/2022
SCHOOL OF TECHNOLOGY
ORDINARY EXAMINATION FOR THE CERTIFICATE & DIPLOMA IN
INFORMATION TECHNOLOGY
DIT 107: MATHEMATICS FOR SCIENCE EXAM
DATE: DECEMBER 2021 TIME: 2 HOURS
INSTRUCTIONS:
ANSWER QUESTION ONE (compulsory) AND ANY OTHER TWO
QUESTIONS

QUESTION ONE (20 MARKS)
(a) Distinguish between a sample and population. [4 Marks]
(b) Mutually exclusive events and conditional probability [2 Marks]
(c) In a company, a certain computer has 20 folders of which 15 folders contains files with
accounting information and the rest are folders containing files with marketing information 2
folders are selected at random with replacement.
Using a tree diagram, what is the probability that,
(i) They both contain accounting information. [2 Marks]
(ii) One has accounting information while the other contains marketing information.
[3 Marks]
(d) A deck of 52 cards has 13 spades. If two cards are drawn from the deck at random, what is the
probability that both have spades? [3 Marks]
(e) A fair coin is tossed twice. Write down the sample space and find the probability of getting exactly
two heads. [3 Marks]
(f) Highlight THREE features of a good questionnaire as a tool used in data collection.
[3 Marks]
QUESTION TWO (15 MARKS)
(a) Solve for x given that
l
(b) Solve for x in the following expression
[2 Marks]
(c) The following data relates to the height of students in a class.
Height (Centimeters). Number of students (Frequency)
150 –                                   155 3
155 –                                   160 4
160 –                                   165 7
165 –                                   170 9
170 –                                   175 6
175 –                                   180 5
180 –                                  185 4
185 –                                   190 2
Required:
(i) The mean height of the students [3 Marks]
(ii) The median height of the students [2 Marks]
(iii) Standard deviation and variance of the height of students [3 Marks]
(iv) Coefficient of variation and make a comment [2 Marks]
QUESTION THREE (15 MARKS)
(a) Out of a group of 85 people, 30 invested in stock market, 45 had certificates of deposits (CD’s) and
44 had savings bonds. Furthermore, 23 had both CD’s and bonds 13 had CD’s and stocks and 13 had
stocks and bonds. Finally 10 of the people had no investment. Use Venn diagram to determine how
many of the people had

i. All the 3 types of investments. [2 Marks]
ii. At least two investments [2 Marks]
iii. At most two investment [2 Marks]
iv. Savings bonds only [1 Mark]
(b) i. what is a venn diagram? [1 Mark]
i. if A and B are two sets, present their intersection in a venn diagram [1 Mark]
(c) If p, q and r are the propositions
p You get an A on the final exam

QUESTION FOUR (15 MARKS)
(a) Using an example in each case, distinguish between a sequence and a series. [2 Marks]
(b) In the following Arithmetic progression, 22,27,32, ……………… determine the 8th term and
10th term. [3 Marks]

(c) Get the sum of the first 7 terms in the following Geometric progression,
4, 12, 36, …………… [2 Marks]

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