CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2015/2016
Module Title: Mathematics for Technology
Module Code:
MATH 6023
School:
School of Building and Civil Engineering
School of Mechanical, Electrical & Process Engineering.
Programme Title:
Bachelor of Science (Honours) in Construction Management Year 1
Bachelor of Science (Honours) in Quantity Surveying - Year 1
Bachelor of Science in Construction - Year 1
Bachelor of Science in Craft Technology (Wood) with Business Year 1
Bachelor of Science in Craft Technology in Mechanical Services Year 1
Certificate in Food Processing Fundamentals – Year 1
Certificate in Equipment Maintenance Fundamentals – Year 1
Programme Code:
CCNMG _8_Y1
CQTSU_8_Y1
CCONS_7_Y1
ECTWB_7_Y1
ECTMS_7_Y1
EFDPF_6_Y1
EEQMF_6_Y1
External Examiner: Dr J. Cruickshank
Internal Examiners: Mr D. O’Shea, Mr P. Finch
Instructions: Answer Question 1 from Section A and any three questions from Section B.
Duration: 2 Hours
Sitting: Winter 2015
Requirements for this examination: Book of formulae and tables and Graph Paper
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have
received the correct examination. If in doubt please contact an Invigilator.
1
Section A
(Compulsory)
1.
(a)
The number of labourers hired by a building contractor to work on a building site
over the course of a 35 day job in July and August 2015 is shown in the
table below.
Number of labourers
3
4 5 6 7 8 9
Number of days
10 9 5 1 5 2 3
Determine:
(i) The mean number of labourers per day.
(ii) The median number of labourers per day.
(iii) The mode for this data.
(b)
(8 marks)
A nationwide survey was performed on 40 electricians in the construction
industry to determine their age. The results are shown in the table below:
Age of electrician (years) 21 to 25 26 to 30 31 to 35 36 to 40
Number of electricians
4
7
11
(i)
Represent this data on a Histogram.
(ii)
Calculate the mean age of the forty electricians.
(iii)
Calculate the standard deviation from the mean.
2
10
41 to 45
8
(17 marks)
Section B
2.
(a) Make C the subject of the formula: P 
K L

T C
(5 marks)
(b) The length of a rectangular pond is 1.1 metres longer than its width. The
perimeter of the pond is 14.2 metres. Determine its area, correct to three
significant figures.
(5 marks)
(c) Solve for x and y:
7 x  2 y  26
6 x  5 y  29
(5 marks)
(d) Solve for x in both of the following equations:
3.
(a)
(i)
3x 2  11x  4  0
(ii)
9 2 x  2  27 3 x2
(10 marks)
(i) Draw a graph of the function, f ( x)  2 x 2  x  10 for  3  x  3
(ii) Use the graph to solve: f ( x)  0
(12 marks)
(b) The table below gives values of F and C which are related by the law F  aC  b
where a and b are constants.
F
C
(i)
(ii)
(iii)
(iv)
59
15
77
25
113
45
167
75
Verify the law exists by drawing an appropriate graph.
Find approximate values of a and b.
State the law.
Find the value of C when F = 150
(13 marks)
3
4.
(a)
(i) The price of a cordless drill including 23% VAT was €295.20. What was
the price of the cordless drill before the VAT was included?
(ii) If the VAT rate increased to 24.5%, by how much would the price of the
drill increase?
(6 marks)
(b)
A sum of money was shared between Andy, Bill and Cathal in the ratio
2.4:3.5:4.6. If Bill got €283.50
(i) What was the sum of money?
(ii) How much did Cathal get?
(5 marks)
(c) The quadrilateral PQRS is shown below. QRS is a right angled isosceles triangle.
Calculate:
(i) The length of the side QS, correct to two decimal places.
(ii) The size of angle PQS, correct to the nearest minute.
(iii) The length of the side QR, correct to two decimal places.
(iv) The area of the quadrilateral.
4
(14 marks)
5. (a) A hotel is planning to construct a patio area which is shown in the diagram below. It
is to be made up of a square of side 12 metres in the middle with a semi-circle on one
end and an equilateral triangle on the other end.
(i)
(ii)
(iii)
Calculate the area of the patio.
Calculate the number square patio slabs, of side 1.2 metres, needed to
cover the patio. Allow 8% extra for waste.
The patio slabs are sold in bales of 16 at a cost of €140 per bale. What
will it cost to buy the patio slabs for the job?
(14 marks)
(b) A solid concrete bollard has a cylindrical base and a hemispherical top. The
bollard has a diameter of 1.2 metres and a total height of 1.5 metres.
(i)
(ii)
Calculate the volume of concrete needed to make one of these bollards.
Calculate the total surface area of the bollard.
5
(11 marks)
Statistical Formulae
Mean ( x )
 fx
x
f
Standard deviation (  )

 fx
f
2
  fx 


f 


2
or  
 f ( x  x)
f
6
2