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MSS511S - MATHEMATICS AND STATISTICS FOR SPATIAL SCIENCES - 1ST OPP - JUNE 2022 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS
QUALIFICATION:
QUALIFICATION
CODE:
| COURSE CODE:
| SESSION:
| DURATION:
BACHELOR OF PROPERTY STUDIES/NATIONAL DIPLOMA IN
PROPERTY STUDIES/GEOMATICS
27DPRS, 27DLMR,
27DLAD, 27BPRS
MSS511S
JUNE 2022
| LEVEL:
NCAOMUER:SE
| PAPER:
5
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MFOARTHSEPMAATTIIALCSSCIAENNDCESSTATISTICS |
THEORY
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3 HOURS
| MARKS 100
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FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
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| EXAMINAR
| Dr. Jacob Ong’ala
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| MODERATOR
| Mr.Andrew Roux
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INSTRUCTION
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1. Answer all the questions
2. Show clearly all the steps in the calculations
3. All written work must be done in blue and black ink
THIS
QUESTION
PERMISSIBLE MATERIALS
Non-programmable calculator without cover
PAPER CONSISTS OF 5 PAGERS (including the front page)
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SECTION A
QUESTION 1 - 11 MARKS
(a) Evaluate the following expressions
(i) 7(23 — 18) + (12 — 5)
(ii) 332 x 13 + 2°
(b) Simplify the following expressions completely
(i) 8x?y — [8a2y + (2ay? + 4a?y — (32y? — 427y))]
(ii) (a Vovc5) (abc)
QUESTION 2 - 13 MARKS
(a) Factorise 3x? + 10x — 8
(b) Solve for m
1(3m ~ 6) — 2i (5m +4) + =(2m —9) = 8
[2 mks]
[3 mks]
[3 mks]
[3 mks]
[3 mks]
(4. anaes
(c) Use completing the square method to solve the following quadratic equations
22? + 92-9 =0
[6 mks]
(d) Solve the following systems of equation (You may use any method)
39xx-+61y5=y1=0-14
QUESTION 3 - 07 MARKS
(a) A drilling speed should be set to 400 rev/min. The nearest speed available on the machine
is 412 rev/min. Calculate the percentage over speed.
[2 mks]
(b) A map scale is 1:30000. On the map, distance between 2 schools is 6cm. determine the
actual distance between the schools giving your answer in Km
[2 mks]
(c) The electrical resistance R of a piece of wire is inversely proportional to the cross-sectional
area A when A = 5mm?, A = 7.020. Determine
(i) Coefficient of proportionality k
[2 mks]
(ii) Cross sectional Area A when R = 40
[1 mks]
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QUESTION 4 - 13 MARKS
(a) Evaluate the angle @ in the diagram below.
\\
\\ 640
10|8°39°
- _-$89 8
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(b) In the triangle given below, find;
c= ihse
b = 22.31
(i) angle C
(ii) angle A
(iii) side BC
(iv) Area of triangle ABC
[2 mks]
[3 mks]
[2 mks]
[3 mks]
[3 mks]
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SECTION B
QUESTION 5 - 17 MARKS
(a) Indicate whether each of the following variables is quantitative or qualitative.
measurement scale. (example of data is shown in the bracket)
State its
[5 mks]
Variable
Height (short, tall medium)
Weight (37kg, 74Kg, 300g)
Names (Jane, Grace, Ben)
No. of cars passing a junction (23, 5, 86)
Temperature (13°C, 49°C, 0.74°C)
Qualitative/Quantitative | Measurement scale
(b) Represent the following data sets in a frequency table
(i) Dataset 1: Blood groups;
[4 mks]
A; B; O; A; AB; O; O; A; O; B; A; A; A; O; O;
O; B; O; AB; B, O, B, O, A, A
(ii) Dataset 2: Height of male soldier
[8mks]
60; 60.5; 61; 61; 61.5; 63.5; 63.5; 63.5; 64; 64; 64; 64; 64; 64; 64; 64.5;
64.5; 64.5; 64.5; 64.5; 64.5; 64.5; 64.5; 66; 66; 66; 66; 66; 66; 66; 66; 66;
66; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 67; 67; 67;
67; 67; 67; 67; 67; 67; 67; 67; 67; 67.5; 67.5; 67.5; 67.5; 67.5; 67.5; 67.5;
68; 68; 69; 69; 69; 69; 69; 69; 69; 69; 69; 69; 69.5; 69.5; 69.5; 69.5; 69.5;
70; 70; 70; 70; 70; 70; 70.5; 70.5; 70.5; 71; 71; 71; 72; 72; 72; 72.5; 72.5;
73; 73.5; 74
QUESTION 6 - 16 MARKS
Trudy Green works for the True-Green Lawn Company. Her job is to solicit lawn-care business
via the telephone. Listed below are the numbers of appointments she made in each of the last
25 hours of calling. 5, 4,2,7,6,8,5,4,6,4,4,5,4,5,7,4,2,8,3,3,6,3,3 Calculate the following
(a) Range
[1 mks]
(b) Mode
[1 mks]
(c) Median
[1 mks]
(d) Arithmetic mean
[2 mks]
(e) Variance
(f) Standard Deviation
[2 mks]
[2 mks]
(g) coefficient of variation.
[2 mks]
QUESTION 7 - 23 MARKS
The city council of Windhoek is considering increasing the number of police in an effort to
reduce crime. Before making a final decision, the council asks the Chief of Police to survey
other cities of similar size to determine the relationship between the number of police and the
number of crimes reported. The Chief gathered the following sample information.
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City
No of police (X) | No. of Crime (Y)
Oxford
15
17
Starksville | 17
13
Danville
25
5
Athens
27
7
Holgate
17
7
Carey
12
21
Whistler
11
19
Woodville | 22
6
(a) Draw a scatter plot
(b) Interpret results in (a) above
(c) Find the correlation coefficient r
(d) Fit a regression model for the data
(e) Use the regression model above to find Y when X=30.
[4mks]
[2mks|
[9mks]
[6mks]
[2mks]
- END -