Microsoft Word - MATH 1151 Semester I Supplemental Exam 2020.docx
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Programme Code: DT6522, DT6524
Module Code: MATH1151
CRN: 29247, 29365
TECHNOLOGICAL UNIVERSITY DUBLIN
CITY CAMPUS
_____________
Programme Code: DT6522, DT6524
Programme Title:
Access Foundation Programme
International Foundation Programme
Year 1
______________
SEMESTER 1 SUPPLEMENTAL EXAMINATIONS 2019/20
______________
Module Title: Intermediate Mathematics 1
Internal Examiner: Dr. Theresa Hedderman-Bowe
Dr. Qi Wang
External Examiner: Sriyani Jayaweera
David McCann
Exam Duration: 3 hours
Instructions: Answer all the questions for full marks
Special Instructions/Handouts:
Use of non-programmable calculators is allowed
Use of mathematical tables and formulae book is allowed
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QUESTION XXXXXXXXXXmarks)
(a) Simplify: XXXXXXXXXX! 15+ 7 − 4+ 3(4! XXXXXXXXXXmarks)
(b) Find:
(i) The LCM of 6, 7 and XXXXXXXXXXmarks)
(ii) The HCF of 32 and XXXXXXXXXXmarks)
(c) Perform the following calculations:
(i) Increase 56 by 36% XXXXXXXXXXmarks)
(ii) Decrease 789 by 13% XXXXXXXXXXmarks)
(iii) Increase 152 by a factor of XXXXXXXXXXmarks)
(iv) Decrease 78 by a factor of XXXXXXXXXXmarks)
(d) Patrick is travelling from Dublin to Dundalk by train. The train journey takes 1 hour 45 mins. It
takes 35 minutes to get from Connolly station to Gormanstown station. It takes 1/5 of the total
time to get from Gormanstown station to Laytown station. And 30% of the total time to get from
Laytown station to Drogheda station. How long does it take to get from Drogheda to Dundalk
station? XXXXXXXXXXmarks)
(e) A certain mobile phone company is offering a deal to its domestic bill paying customers. The
offer is 225 free texts and 300 minutes of free calls to any network anytime in Ireland for €75 per
month. Additional texts messages cost 8 cent per message and phone calls cost 25 cent per
minute. Calculate the following monthly bills:
(i) 150 texts and 325 minutes of calls for the month of April (10 marks)
(ii) 5 hours and 30 minutes of calls and 11 texts each to 23 people for the month of May
XXXXXXXXXXmarks)
(iii) For the month of June an average of 20 minutes of calls and 35 texts per day were sent
(10 marks)
(f) A toy store owner is buying game consoles. Xbox comes in 8 per box, PS4 comes in 12 per box
and Nintendo Switch comes in 18 per box.
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(i) What is the smallest number of Xbox consoles the owner can order where there is an
equal number of all three consoles ? XXXXXXXXXXmarks)
(ii) The store owner wants to have at least 80 Nintendo Switches but also wants to have an
equal number of all consoles. How many boxes of each console must be ordered to
achieve this? XXXXXXXXXXmarks)
QUESTION XXXXXXXXXXmarks)
(a) Factorise the following alge
aic expressions by grouping: (4 marks each)
(i) 2?? − ?? + 12?? − 6??
(ii) 6?? + 3?? + 4?? + 2??
(iii) 5?? + 2?? − 6?? − 15??
(iv) −4?? + 28?? + 3ℎ? − 21ℎ?
(b) Solve the following simultaneous equations: XXXXXXXXXXmarks each)
(i) ? + 7? = 17
2? − 4? =  −2
(ii) −3? + 6? = 9
−4? − 4? =  −36
(c) Simplify each of the following using the rules of indices and logarithms: (4 marks each)
(i) 132 × 138
(ii)
!!!
511
(iii) log2 10 - log2 2
(iv)
log3 6
log3 5
(d) A tennis match in Wimbledon costs €50 for a premium ticket and €20 for a standard. For the
women’s final 14,800 people were recorded as present at the match. The total money earned from
ticket sales was €323,000. How many of each type of ticket were sold? (12 marks)
(e) In a construction company workers fall into four categories. These are plumber, electrician,
carpenter and painter as shown in the table below.
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(i) Express the number of workers in each category as a percentage of the total number of
workers in the company XXXXXXXXXXmarks)
(ii) With construction projects increasing next year, the company have decided to increase the
work force by 14%. How many electricians will have to be taken on? Give your answer to
the nearest whole number XXXXXXXXXXmark)
(iii) What will be the total number of workers next year after the additional workers are hired?
Give your answer to the nearest whole number XXXXXXXXXXmark)
(f) Calculate the following amounts:
(i) How much will be earned in interest on an investment of €876 left sitting in an account for
9 years at 4% simple interest? XXXXXXXXXXmarks)
(ii) A car loan was taken out for €24,500 over 5 years at 6% which is compounded annually.
How much interest will the bo
ower pay? XXXXXXXXXXmarks)
QUESTION XXXXXXXXXXmarks)
(a) Graph the following on a number line: XXXXXXXXXXmarks)
{ x | -2 < x ≤ 9, x ∈ R }
(b) Solve the following alge
aic equations for x: XXXXXXXXXXmarks each)
(i XXXXXXXXXXx) + 3(5x + 4) – 2x + 14
(ii) 4x +16 = 30 – 3x
(c) Solve the following quadratic equations by factorisation or by using the quadratic formula
(the ‘–b’ formula) and state whether the quadratic has real roots or not. (8 marks each)
Category Number of
students Plumber 29
Electrician 35
Carpenter 31
Painter 26
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(i) x2 + 9x + 18= 0
(ii) 12x2 - 10x - 5 = 0
(iii) 2x2 – 12x - 9 = 0
(d) In an election, candidate A got 65% of the total valid votes. If 21% of the total votes were
declared invalid and the total numbers of votes is 463,000, find the number of valid votes polled
in favour of candidate A XXXXXXXXXXmarks)
(e) Max scored 6 marks more than what he did in the previous examination in which he scored 30. Maria
scored 30 marks more than she did in the previous examination in which she scored 60. Who showed
less improvement?
(i) By what percent did Max do better in the second exam compared to the first?
XXXXXXXXXXmarks)
(ii) By what percent did Maria improve on the second exam compared to the first?
(8 marks)
(iii) How much better did Maria do compared to Max? XXXXXXXXXXmarks)
(iv) How many more marks did Max need so that his level of improvement equalled Maria’s?
XXXXXXXXXXmarks)
(f) Tina has a gross yearly income of €54,200. She has a standard rate cut off point of € 22,000 and a
tax credit of € 3,080. The standard rate of tax is 22% of income up to the standard rate cut off
point and 41% on all income above the standard rate cut-off point. Calculate:
(i) Tina’s gross tax for the year XXXXXXXXXXmarks)
(ii) Tina’s net tax paid for the year XXXXXXXXXXmarks)
(iii) The total USC Tina must pay XXXXXXXXXXmarks)
(iv) Tina’s net pay per year XXXXXXXXXXmarks)
XXXXXXXXXXUSC rates
END OF PAPER
Income Rate
First €10,036 2%
Next €5,980 4%
On the balance 7%
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MATH1151 — Intermediate Mathematics — Useful Formulae
International Foundation Programme / Semester 1
Access Foundation Programme 2017–2018
Rules of Indices
a
p⇥ aq = ap+q
a
p
a
q
= ap�q
�
a
p
�
q = ap⇥q
a
0 = 1
a
�p =
1
a
p
a
p
q =
q
p
a
p
a
1
q = q
p
a
(ab)p = apbp
✓
a
â—†
p
=
a
p
p
Quadratic Formula
ax
2+ bx+ c = 0
=) x = �b±
p
2�4ac
2a
Financial Mathematics
Compund Interest :
F = P(1+ i)t
Amortisation (loans) :
R = A
i(1+ i)t
(1+ i)t �1
Rules of Logs
a
x = y () log
a
y = x
log
a
(ax) = x
log
a
x+ log
a
y = log
a
(x⇥ y)
log
a
x� log
a
y = log
a
x
y
!
log
a
�
x
q
�
= q
�
log
a
x
�
log
a
1
x
!
= � log
a
x
log
a
x
log
a
= log
x
Number Sets
N Naturals = {0, 1, 2, 3, 4, 5, 6, · · · }
Z Integers =