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