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Math 0121: General Mathematics Question Paper
Math 0121: General Mathematics
Course:In Animal Health And Production & Diploma In Tourism And Hotel Management
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF
DIPLOMA IN ANIMAL HEALTH AND PRODUCTION &
DIPLOMA IN TOURISM AND HOTEL MANAGEMENT
MATH 0121: GENERAL MATHEMATICS
STREAMS: DIP. (ANHE), DTHM TIME: 2 HOURS
DAY/DATE: TUESDAY 7/8/2013 8.30 A.M. – 10.30 A.M.
INSTRUCTIONS:
Answer Question ONE and any other TWO Questions.
Question One (30 Marks)
Define the following:
A set (and give an example) [2 marks]
Union of two sets [1 mark]
Intersection of two sets [1 mark]
Represent the universal set
S = {a,b,c,d,e,f,g} and the union of sets A = (a,b,c) and B = (d,e) in a Venn diagram.
[3 marks]
A nutritionist wishes to prepare a food mixture that contains 40g of vitamin A and 50g of vitamin B. the two mixtures that are available contain the following percentage of vitamin A and B.
Vitamin A Vitamin B
Mixture I 10% 4%
Mixture II 5% 12%
How many grams of each mixture should be used to obtain the desired diet? [4 marks]
(i) Solve for x in the equation ?ax?^2+bx+c=0 by completing the square method.
[3 marks]
(ii) For the function f(x)=?4x?^2-3x+1, obtain the coordinates of the vertex and state whether it is a maximum or minimum. [3 marks]
Given that A = [¦(4&2@3&2)] and B = [¦(3&2&-1@1&6&2)], find AB and (AB). [3 marks]
Evaluate [3 marks]
A farm manager estimates that when x thousand people are employed at her farm, the profit will be P(x) million Shs, where P(x)=-x^2+4x. What level of employment maximizes profit? What is the maximum profit? [4 marks]
Evaluate [3 marks]
Question Two (20 Marks)
Given the sets;
A = {1,2,3,4}, B = {7,8,9}, C = Ø
Find;
A?B [2 marks]
(ii) A?Ø [2 marks]
(iii) AnØ [2 marks]
A survey of 100 randomly selected students gave the following information.
45 Students are taking Mathematics
41 Students are taking English
40 Students are taking History
15 Students are taking Mathematics and English
18 Students are taking Mathematics and History
17 Students are taking English and History
7 Are taking all the three subjects.
Let M = Students taking Mathematics
E = Students taking English
H = Students taking History
(i) Draw a Venn diagram to illustrate the above information. [4 marks]
(ii) Find how many students are;
Taking only Mathematics [2 marks]
Taking only English [2 marks]
Taking only History [2 marks]
Not taking any of these courses [2 marks]
Not taking Mathematics [2 marks]
Question Three (20 Marks)
A company manufactures two products, A and B. Each unit of A requires 3 labour hours and each unit of B requires 5 labour hours. Daily manufacturing capacity is 150 labour hours.
(i) ifx units of product A and y units of product B are manufactured each day and all labour hours are to be used, determine the linear equation that requires the use of 150 labour hours per day. [3 marks]
(ii) How many units of A can be made each day if 21 units of B are manufactured each day? [2 marks]
(iii) How many units of A can be made each week if 12 units of B are manufactured each day? (Assume a 5-day work week). [3 marks]
Solve the system of linear equations
2x+3y-z=1
3x+5y+2z=8
x-2y-3z=-1 [6 marks]
Determine whether the given quadratic equation has real roots classify as repeated or two distinct roots.
(i) x^2-6x+9=0 [2 marks]
(ii) ?5x?^2+4x-6=0 [2 marks]
(iii) ?3x?^2+x+5=0 [2 marks]
Question Four (20 Marks)
Solve 3x+4y=7 by finding
x+2y=2
The inverse of the matrix
A = (¦(3&4@1&2)) [4 marks]
(i) State whether the matrices given below are symmetric about the leading diagonal
or not
A = (¦(2&3&7@4&9&1@8&5&6)), B = (¦(1&2&5@2&8&9@5&9&4)) [2 marks]
(ii) If I is 3×3 identity matrix, show that A.I = I.A = A, where A is as in (i) above.
[4 marks]
Given Q = (¦(4&2&6@1&8&7))
Determine
(i) QT [1 mark]
(ii) Q.QT and state the order of the product matrix. [3 marks]
Solve the systems of equations by Cramer’s rule.
2a + 3b – c = 1
3a + 5b + 2c = 8
a – 2b – 3c = 1 [6 marks]
Question Five (20 Marks)
Differentiate
(i) y=?(x^2-6x+5)?^3 [2 marks]
(ii) y=x^2/(2-x) [3 marks]
If y=x^3-6x^ -5x+3, find y^4. [4 marks]
Integrate the following functions with respect to x.
(i) ?¦?(?3x?^2+4)dx.? [2 marks]
(ii) ?_1^2¦?(4x-x^2)? [3 marks]
Given the functions f(x)=3x and g(x)=x+1, find and .
[4 marks]
Find the gradient of the curve y=?3x?^2-x^3 at (1, 2). [2 marks]
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