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Math 001: Mathematics For Sciences Question Paper
Math 001: Mathematics For Sciences
Course:Certificate In Computer Science
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF
CERTIFICATE IN COMPUTER SCIENCE
MATH 001: MATHEMATICS FOR SCIENCES
STREAMS: CERT (COMP SCI) TIME: 2 HOURS
DAY/DATE: FRIDAY 16/8/2013 8.30 AM – 10.30 AM
INSTRUCTIONS:
Answer Question ONE and any other TWO Questions
(a) Distinguish between descriptive statistics and inferential statistics [2 mark]
(b) Consider the following data set x={11,13,15,16,19,22,13,20}. Calculate:
(i) Arithmetic mean [2 marks]
(ii) Harmonic mean [2 marks]
(iii) Geometric mean [2 marks]
(c) Determine the number of permutations of the letters of the word “HALLUCINATIONS” [3 marks]
(d) If a=?log?_b C,b=?log?_c a and ?C log?_a b, then prove that abc=1 [4 marks]
(e) Five percent of all TVs manufactured by a large electronic company are defective. A quality control inspector randomly selected three TVs from the production line. What is the probability that exactly one of these three TVs is defective? [4 marks]
(f) Solve for x in the equation ?Ax?^2+Bx+C=0 by completing the square method.
[3 marks]
(g) A geometric progression has the third term as 81 and the 6th term as 3.
Determine:
(i) The common ratio [3 marks]
(ii) The first term [2 marks]
(h) Prove that ?sin?^2 ?+?cos?^2 ?=1 where ? is an acute angle in a right angled triangle.
[3 marks]
Question Two (20 Marks)
(a) Given that f(x)=?3x?^2-?2x?^2+kx+9 and that when f(x) is divided by x+2, there is a reminder of -35.
(i) Find the value of the constant k [4 marks]
(ii) Find the reminder when f(x) is divided by (3x-2) [3 marks]
(b) (i) Express 1/v32 as a power of 2. [2 marks]
(ii) Express (64)^(1/x) as a power of 2. [2 marks]
(iii) Hence or otherwise solve the equation
(64)^(1/x)/2^(1/x) =1/v32 [4 mark]
(c) (i) Expand (1+3x)^8 in ascending powers of x up and including the term x^3 (simplify each coefficient in the expression) [3 marks]
(ii) Hence use your expansion in c(i) above to approximate the value of (1.09)^8
[2 marks]
Question Three (20 marks)
(a) Solve the equation. If cos?=2?sin?^2 ?, for values of ? between 0° to 360° [5 marks]
(b) Prove that sin??3A=3 sin??A-4?sin?^3 A.? ? [6 marks]
(c) (i) Find the sum of the following series
[4 marks]
(ii) Find the sum of the first n terms of the G.p 2+1/2+1/8+ · · · and find also the least value of n for which this sum exceeds 2.65. [5 marks]
Question Four (20 Marks)
(a) Sixteen players scored goals for AFC Leopard’s as recorded below for each player.
10,8,3,13,24,1,31,16,33,10,24,2,21,16,26,20. Construct a stem – and – leaf diagram to show this information. [4 marks]
(b) (i) State three measures of central tendency. [3 marks]
(ii) The following are wages in K£ of a group of people in a firm.
Yearly wages Number of people
501 - 550 120
551 – 600 60
601 – 650 25
651 – 700 20
701 – 750 15
751 - 800 8
Calculate the mean wage and the median wage. [7 marks]
(c) The following table shows the number of children per family in a housing estate.
No. of children 0 1 2 3 4 5 6
No. of families 1 5 11 27 10 4 2
Calculate:
(i) Variance
(ii) Standard deviation for the distribution. [6 marks]
Question five (20 Marks)
(a) (i) What is the difference between permutations and combinations? Give an examples. [4 marks]
(ii) A team of 4 children is to be selected from a class of 20 children to compete in a quiz game. In how many ways can the team be chosen? [3 marks]
(b) A survey of attitudes about one’s job yields the data in the following table.
Happy Unhappy Total
Bus drivers 50 75 125
Lawyers 40 35 75
Total 90 110 200
A person form this group is selected at random. Give that the selected person is a bus driver, find the probability that he or she is happy. [3 marks]
(c) A customer made a deposit of sh. 25,000 in an account which pays compound interest at the rate of 5 percent per annum. How much is his investment worth ten years later? [4 marks]
(d) Sketch the graph of the function y=4sin 3x with x in the domain 0°=x=240°
[4 marks]
From the sketch or otherwise determine:
(i) The amplitude [1 mark]
(ii) The period of the function [1 mark]
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