Get premium membership and access revision papers, questions with answers as well as video lessons.
Mathematics For Science Question Paper
Mathematics For Science
Course:Diploma In Information Technology
Institution: Kca University question papers
Exam Year:2012
UNIVERSITY EXAMINATIONS: 2011/2012
STAGE I EXAMINATION FOR THE DIPLOMA IN INFORMATION
TECHNOLOGY
DIT 107 MATHEMATICS FOR SCIENCE
DATE: MARCH, 2012 TIME: 1½ HOURS
INSTRUCTIONS: Answer Any Three Questions
Question One
a) Solve the equation 3x2 – 7x – 2 = 0 to 2 decimal places (2 Marks)
b) You are given the following statistical samples:
SAMPLE 1
Mean 21
Number 20
Standard deviation 2.0
SAMPLE 2
Mean 15
Number 10
Standard deviation 1.5
SAMPLE 3
Mean 20
Number 15
Standard deviation 1.7
1) The 3 samples are now mixed. What is the new:
i. Mean (2 Marks)
ii. Standard deviation (2 Marks)
2) 15 is now added to each of the data items in sample 1. What is the new
i. Mean (2 Marks)
ii. Standard deviation (1 Marks)
c) Find the 9th term of the sequence 5, 7, 9, 11, ….. (2 Marks)
d) Two events A and B are such that P(A)= 3/7 and P(~B) = 5/8 and P(AnB) = 1/10 .
Calculate
i.P(AUB) (2 Mark)
ii.P(A / ~ B) (2 Marks)
e) Solve the equation 2cos2 ? = cos ? for 0 =? = 3600 (4 Marks)
f) Add the following surd and simplify as much as possible (2 Marks)
3v2 + v8
Question Two
Consider the data below:
SCORE x f d ? f ? f ?2
25-29 5
30-34 20
35-39 6
40-44 10
45-49 4
50-54 7
55-59 2
60-64 11
65-69 8
70-74 1
TOTALS
You are further given the following additional information:
X = class mid-points
d= x – 52
? = d / 5
a) Using the above information fill in the columns above (5 Marks)
b) Using the values you have filled in the table, calculate
i.Mean (4 Marks)
ii.Variance (4 Marks)
iii.Standard deviation (2 Marks)
c) Plot the cumulative frequency curve for the data above (3 Marks)
d) Simplify the following without using tables (2 Marks)
log8 + log12.5
Question Three
a) The 20th term of an arithmetic sequence is 60 and 16th term is 20. Find the first term and the
common difference (6 Marks)
b) A student has a constant probability of 0.7 of coming early for a ‘Math for Science’ lesson. For 8
lessons, what is the probability that the student was?
i. Late for 2 lessons (2 Marks)
ii. In time for more than 75% of the lessons (3 Marks)
c) Solve the following quadratic equations by (6 Marks)
i. Factorization
3x = 2x2 - 2
ii. By use of formula
4x2 – x – 3 = 0
d) A business woman wants to raise her capital to Shs. 20,000. She opens an interest free account with
initial deposit of shs. 1500. She decides to deposit shs. 500 every month. After how many years will
she be able to raise the capital (Hint: Using Arithmetic Sequences) (3 Marks)
Question Four
a) If the mean of the values 14, y, 17, 16 and y is y+0.4, find the value of y. (2 Marks)
b) A bag contains 8 ripe apples and 5 raw apples. If two apples are drawn from the bag one at a time.
Find the probability of drawing a ripe apple and a raw apple if there is no replacement (4 Marks)
c) The sum of an Arithmetic Progression of 8 terms is 90 and the first term is 6. What is the last term?
What is the common difference? (5 Marks)
d) If the mean weekly wage of 86 employees is £172.45 and employee number 87 earned £158.80. What is the
mean wage of all 87 employees? (3 Marks)
e) A committee of 4 must be chosen from 3 women and 4 men.
Calculate (6 Marks)
i. In how many ways the committee can be chosen
ii. In how many ways 2 men and 2 women can be chosen
iii. Probability that the committee consists of 2 men and 2 women
Question Five
a) Simplify v(4 – x2 ) where x = 2sin? (3 Marks)
b) if log2 = 0.30103 and log3 = 0.47712, find without using tables or calculator (4 Marks)
i. log30
ii. log72
c) Given that the first and last terms of an arithmetic sequence are 7 and 157 respectively and that the
sum of all the terms of the series is 2542. Calculate the common difference of the sequence and the
twenty first term of the sequence. (6 Marks)
d) An airplane has 2 engines which function independently of one another. The probability that engine
A fails in flight is 0.02 while the probability that engine B fails in flight is 0.05. Assuming that the
plane fly with at least one engine functioning, determine the probability that the airplane has a
successful flight (3 Marks)
e) Solve for x in the following equations (4 Marks)
i. 32x-1 = 2187
ii. 2x = 5
More Question Papers
Popular Exams
Return to Question Papers