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MSS511S - MATHEMATICS AND STATISTICS FOR SPATIAL SCIENCES - 2ND OPP - JULY 2023 |
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nAmlBIA UnlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTY OF HEALTH, NATURAL RESOURCES AND APPLIED SCIENCES
SCHOOL OF NATURAL AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND ACTUARIAL SCIENCE
I QUALIFICATION:
QUALIFICATION
I CODE:
I COURSE CODE:
I SESSION:
I DURATION:
BACHELOR OF PROPERTY STUDIES/NATIONAL DIPLOMA IN
PROPERTY STUDIES/GEOMATICS
27DPRS, 27DLMR, I LEVEL: 5
27DLAD, 27BPRS
MSS511S
I I COURSE MATHEMATICS AND STATISTICS
NAME: FOR SPATIAL SCIENCES
JULY 2023
jPAPER: THEORY
I
3 HOURS
j MARKS 100
j
SUPPLEMENTARY/
I EXAMINAR
I MODERATOR
2ND OPPORTUNITY EXAMINATION
I Dr. Jacob Ong'ala
I Mr.Andrew Roux
QUESTION PAPER
INSTRUCTION
l. 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
PERMISSIBLE MATERIALS
Non-programmable calculator without cover
THIS QUESTION 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) 7 (12 - 5)
(ii) 3~3 X 14 -.'- 2~4
(b) Simplify the following expressions completely
(i) 8x 2 y - [3x2y + (2xy 2 + 4x 2y - (3xy 2 - 4x 2y))]
(ii) (a3 ,/Tr/~)( Ja,Wc 3)
QUESTION 2 - 13 MARKS
(a) Evaluate the angle 0 in the diagram below.
[2 mks]
[3 mks]
[3 mks]
[3 mks]
[2 mks]
(b) In the triangle given below, find;
A
(i) angle C
(ii) angle A
(iii) side BC
2
[3 mks]
[2 mks]
[3 mks]
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(iv) Area of triangle ABC
[3 mks]
QUESTION 3 - 13 MARKS
(a) Factorise 3x 2 + lOx - 8
(b) Solve for m
[3 mks]
(c) Solve the following systems of equation (You may use any method)
3x-6y=l0
9x+15y=-14
[6 mks]
QUESTION 4 - 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 2 , A= 7.02D. Determine
(i) Coefficient of proportionality k
[2 mks]
(ii) Cross sectional Area A when R = 4S1
[1 mks]
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SECTION B
QUESTION 5 - 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
[2 mks]
(b) Mode
[2 mks]
(c) Median
[2 mks]
(d) Arithmetic mean
[2 mks]
(e) Variance
[3 mks]
(f) Standard Deviation
[2 mks]
(g) coefficient of variation.
[2 mks]
QUESTION 6 - 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
Qualitative/Quantitative
a Height (short, tall medium)
b Weight (37kg, 74Kg, 300g)
C Names (Jane, Grace, Ben)
d No. of cars passing a junction (23, 5, 86)
e Temperature (13°C, 49°C, 0.74°C)
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 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
Oxford
Starksville
Danville
Athens
Holgate
Carey
Whistler
Woodville
No of police (X)
15
17
25
27
17
12
11
22
No. of Crime (Y)
17
13
5
7
7
21
19
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(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 -
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