nr—‘IITIIBIR UNIVERSITY -...
Transcript of nr—‘IITIIBIR UNIVERSITY -...
nr—‘IITIIBIR UNIVERSITY
OF SCIEI'ICE FII'ID TECHI‘IOLOGY
FACULTY OF HEALTH AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of Regional and Rural Development, Bachelor of Communication,
Bachelor of Technology Public Management, Bachelor of Supply Chain Management, Bachelor of
Office Management and Technology, Bachelor of Natural Resources Management, Bachelor of
Emergency Medical Care, Diploma In Vocational and Training, Bachelor of HOSpitality Management
QUALIFICATION CODE:07BRRD,07BAC0,07BPMN,
07BLSM,07BOMT,07BNTC,O7BEMC,06DVET,07HMN
LEVEL: 4
COURSE CODE: BMS411$ COURSE NAME: BASIC MATHEMATICS
SESSION: NOVEMBER 2017 PAPER: THEORY
DURATION: 3 HOURS MARKS: 100
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER(S) Mr] Amunyela, Mrs A Sakaria, Ms Y Shaanika, Mr F Ndinodiva,
Mr E Mwahi, Mr R Mumbuu
MODERATOR: Mrs S Mwewa
INSTRUCTIONS
.wxve. Answer ALL the questions.
Write clearly and neatly.
Number the answers clearly.
1.
THIS QUESTION
PERMISSIBLE MATERIALS
Non-Programmable Calculator without the cover
PAPER CONSISTS OF 5 PAGES (Including this front page)
Section A [22 Marksl
Question 1
(Write down the letter corresponding to your best option for each question in the answer
booklet provided)
1.1
1.1.1
1.1.2
1.1.3
1.2
1.3
1.4
1.5
1.6
1.7
Given a list of numbers: 2,3,4,15,16,14,7,8,9,21. Answer 1.1.1 through to 1.1.3
How many prime numbers are in the list
A. 1 B. 2 C. 3
How many numbers are factors 21?
A. 1 B. 2 C. 3
[2]
D.4
[2]
D. 4
If W = 2, What is the value of x from the list
A. 4 B. 15 C. 16 D. 21
Find the Lowest Common Multiple (LCM) 36,75 & 4O [2]
A. 1800 B. 10800 C.180 D. 1
Calculate the value ofm = —3xy2 ifx = 3 ,y= —2
A. 36 B. 12 C. ~36 D. -6
The expression (a + b)2 + Zab — b2 simplifies to? [2]
A. a2 + 4ab B. 5a2 + b2 C.—4a2—b2 D. 1
Factorize the expression xy—
mx + km —
ky completely [2]
A. (x—k)(y—m) B. (y—m)(k—2m)
C-(x-m)(y-k) D-(x-y)(—m+y)
If a, b, m and n are real numbers with a and b positive, which one of the following is
not true?
Solve the equation —3(3x — 1) = 12
A.x=—11 B.x=—4
[2]
C. a X 0 = a D.(ab)m = ambm
C.x=2 D.x=—1
1.8
1.8.1
1.8.2
The following sets are given:A = {1,2345} ,B = {2,3,4} ,
C = {7,11,8}.Answer
question 1.8.1 and 1.8.2.
Which of the following is not true about these sets? [2]
A.AmC={} B.AnB=B
C.AUB=A D.CisasubsetofB.
n(A U B) is : [2]
A. 5 B. {1,2,3,4,5} C. 4,3 &2 D. 8
SECTION B (Show all your work)
Question 2 (33 marks)
2.1
2.2
2.2.1
2.3
2.3.1
2.3.2
2.4
2.5
2.5.1
2.5.2
2.5.3
Boxes that are 12 cm tall are being stacked to boxes that are 18 cm tall. What is the
shortest height at which the two stacks will be the same height? [4]
There are 40 girls and 32 boys who want to participate in 8th grade intramurals. If
each team must have the same number of girls and the same number of boys, what
is the greatest number of teams that can participate in intramurals? [4]
How many girls are in each team and how many boys are in each team? [2]
Solve the linear equations:
2_ 1
2x_x+1
H
8m—2=6—2m [2]
The sum of two consecutive positive integers is 123. Express each of these numbers
in terms of x and find the numbers. [5]
Simplify the following expressions without using the calculator
2 1
azb3
a5b6[3]
3a(2 — 2a) -—
(6a— 6a2) [2]
2.6 Factorize the following expressions completely
2.6.1 4m2y2 — 12x23! [3]
2.6.2 hm — b3m + hn — b3n [4]
Question3 (18 marks)
3.1 In the Venn diagram
n(A) = 432 ,n(B) = 518 ,n(S) = 1010
S
AB
252y
X
Find
3.1.1 w [2]
3.1.2 y [2]
3.1.3 x [2]
3.2 It is given that the universal set S = {x: x is an integer, 2 S x S 19}
A = {xzx is an integer, 7 S x S 12}
B = {x: x is an integer,x S 12}
C = {x:x is an integer,x < 6}
3.2.1 List the elements of set A, B and C [6]
3.2.2 Find the set A n C [2]
3.2.3 Find the set B U C [2]
3.2.4 Find the set Ac [2]
Question 4 (27 marks)
4.1 GivenA = (1 2),B = (4
3) ,C = (2x 2) ,D = (g), calculate:3 4 ——2 6 3 4
4.1.1 33 — A [5]
4.1.2 determinant of matrix B [2]
4.1.3 AB [4]
4.2 Find the value of the letters in the following matrix equation [6]
(y—é—s ”‘2?th 2H3; 1165)
4.3 Mr. Junias would like to invest his money for 12 years to raise money for his
daughters’ university education. CFS Bank offers him an interest of 7.5%
compounded quarterly while NMB Bank offers him an interest of 10% p.a
compounded semi-annually.
4.3.1 If Mr. Junias chooses to invest N$5200 with CFS Bank, how much money will he
have in his account after 8 years. [3]
On maturity at CFS Bank he withdraws the matured value and moves it to NMB Bank
where he tops up the amount by N$2000 from his savings.
4.3.2 What amount of money will be available for his daughter’s university education after
12 years correct to 2 decimal places. [5]
4.4 John bought a BMW at N$185 000 beginning of 2010 from a local car dealer. He was
informed that the value of his car depreciates by one-third each year from the year
of purchased. Calculate the value of the BMW in year 2011 [3]
END EXAMINATION QUESTION PAPER