NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
13 Storch Str eet
Pri va t e Bag 13388
Windho ek
T: +26 4 207 2543
E: rmumbuu@nust.na
W: www.nust.na
NA MIBI A
Faculty of Health and Applied Sciences
DEPARTMENT OF MATHEMATICS & STATISTICS
Course Title: BASIC MATHEMATICS
Course Code: BMS411S
Assignments 1 AND 2 (FULL TIME AND PART-TIME ONLY EXTENDED DUE DATE: 05 APRIL 2019
Information and Instructions:
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Please use this page as your assignment COVER PAGE.
All students in any particular assignment group are expected to participate fully.
All students in the same assignment group will earn the same marks.
After submitting the assignment, the group may be asked to defend the submission before
the course lecturer (or his nominated representative). The lecturer may nominate any
member of a group to defend the submission on behalf of the group. In other words, it is
not advisable for any group to condone a non-contributing colleague.
Each group should have a minimum of 5 students and a maximum of 8 students.
This assignment is weighing 20% towards your CA marks.
The submission should indicate the names and student numbers of the members of the
group.
Where a group member is not contributing, an advance report should be lodged with the
lecturer in writing. The lecturer will counsel the affected student. This will again be
discussed during the defense / presentation of the submission.
A group member found guilty of not contributing to a submission will score a zero for that
assignment.
GROUP MEMBERS
ST.NUMBER
SURNAME
INITIALS
Signature
TAKE NOTE: All assignments should be typed (F12, Calibri or Arial), No hand-written assignments
will be accepted
1
Assignment 1: EXTENDED DUE DATE: 05 April 2019(FT and PT ONLY)
60
1.
From the set of numbers : 20, 21, 22, 23,
22
7
, 𝜋, √14, √36,
3
a)
b)
c)
d)
e)
f)
2.
√−8, -10, 0, 10, 25, 30, 29, 27, 26, 25, 24
Write down:
A multiple of 8
An the irrational number
A cube number
All the integers
A square root of 784
Two numbers whose product is 567
The mass of the earth is
24
1
95
52
13
Marks:
,
[9 marks]
(1)
(1)
(4)
(1)
(2)
of the mass of the planet Saturn. The mass of the earth
is 5.97 × 10 kilograms. Calculate the mass of the planet Saturn, giving your answer
in standard form , correct to 2 significant figures.
[5 marks]
3.
In 1997 the population of China was 1.24 × 109 and in 2002 the population of China
was 1.28 × 109 . Calculate the percentage increase from 1997 to 2002.
[5 marks]
4.
Three lectures of NUST entered to race around a track. Mr Mumbuu takes 60 seconds to
complete one lap, Mr Jonas takes 48 seconds to complete one lap and Mr Gift takes 45 seconds to
complete one lap. If all three lecturers start the race at the same time at 07:10, when will they be
at the same point again?
[5 marks]
.
5.
6.
NUST choir has 120 sapranos, 50 altos and 60 tenors. If the coordinator wants to separate the choir
into smaller groups,
[7 marks]
a) what is the greatest number of groups that can be formed?
(4)
b) how many sapranos, altos and tenors will be in each group?
(3)
Simplify the following algebraic expressions:
[17 marks]
a) 8𝑥 2 𝑦 − 𝑦𝑥 2 + 5𝑦 2 + 8𝑥 − (5 + 5𝑥𝑦 2 − 5𝑦 2 + 6)
(4)
b) (3𝑥)3 × (2𝑥)3 × (−3𝑥 2 )3
(4)
4
5
4𝑎
c) √(9𝑏6 )
𝑑)
7.
(4)
6𝑥 5 𝑦 2 + 2𝑥4 𝑦 3 − 3𝑥3 𝑦 4 −5𝑥 2 𝑦5
−𝑥 2 𝑦 2
Factorise completely:
(5)
[7 marks]
𝑎) 16𝑎2 𝑏 − 24𝑎4 𝑏 2 𝑐
(3)
b) 3𝑦 + 4 𝑝𝑞 − 3𝑝 − 4𝑦𝑞
(4)
2
8.
Solve for y in the following equation
-
2𝑦
3
+
𝑦
2
=−
[5 marks]
5
4
Assignment 2; EXTENDED DUE DATE: 05 April 2019(FT and PT ONLY)
1. Given S= {a, b, c, d, e}, find P(S)
Marks: 75
[3 marks]
2. If Ω={x: x∈N, x < 20} and
A= {x| x∈N, x < 10, x is prime}
B= {3, 5, 7, 9, 11, 13, 15}
C= {x| x∈N, 15 < x ≤ 17}
Find:
a. Ω𝑐
b. Ac
c. A∩B
d . ̅̅̅̅̅̅̅̅̅
A∩B
e. ̅̅̅̅̅̅̅
A∪B
f. Ac ∩ Bc
g. Compare answers from question (e) and (f) and give a comment.
h. A⊕B
i. n(A⊕B)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(1)
[17 marks]
3. Represent the following set notations on appropriate Venn diagrams by shading the indicated
regions.
(Use set A, B and C)
3. 1. (𝐴⋃𝐵)ˈ
(2)
3.2. { } or φ
(2)
3.3. 𝐴 − 𝐵 𝑜𝑟 𝐴/𝐵
(2)
3.4. 𝐴 ⊕ 𝐵
(2)
𝐴⋂𝐵 𝑐
(2)
3. 6. 𝐴𝑐 ⋂𝐵 𝑐
(2)
3.5.
3
3.7. 𝐴⋃𝐵 𝑐
3.
(2)
[14 marks]
A group of 50 students at the Namibia University of Science and Technology, take at least on of
these subjects: Calculus(C) and ANOVA(A). 17 take both subjects, 9 take Calculus 1 only, 8 take
ANOVA only and 𝑥 take neither subjects.
4.1 Represent this information on a venn diagram.
(4)
NB: For questions 4.2 to 4.4 use appropraite set notations.
4.2 Find the value of 𝑥.
(3)
4.3 Find the number of students taking Calculus or ANOVA.
(3)
4.4 Find the number of students taking ANOVA.
(3)
4.5 Find the number of students who are not taking Calculus.
(3)
[16 marks]
2𝑥
7
5. Given marices 𝐷 = (
3
−2 4
−2 4
−2
), 𝐶 = (
), 𝐸 = (
) and 𝐹 = ( )
3 5
3 5
3
1
5.1 Find if possible
a) 𝐶 + 𝐸
(4)
b) 𝐶𝐸
(4)
c) 𝐹𝐸
(4)
5.2 Find the value of x if the determinant of matrix D is 10.
(3)
[15 marks]
6. Solve for Y in the following matrix equation.
−10
−7
−2𝑌 − 3 (
24
−5
)=(
19
−11
−7
)
5
[4 marks]
7. Tyson obtained a loan from the bank at 7.5% simple interest for 2.5 years. If the simple interest was
N$347.50, how much did he borrow?
[3 marks]
8. Hilma invested N$20 000 on 01/01/2018 at 9.5 % interest p.a compounded semi-annually.
How much will she receive by 01/01/2022?
[3 marks]
4
5