FDN020 Essential Mathematics Session 1. Arithmetic

1.

FDN020 Essential Mathematics
Session One
Arithmetic
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2.

Attendance
Every class in the Murdoch University Foundation Program plays an essential role in skills building for university study. Students
should therefore do their very best to attend all scheduled classes to ensure that they progress through the unit satisfactorily. For
this reason, students must meet an attendance requirement of at least 80% of all scheduled classes (in addition to
assessment requirements) in order to pass this unit and be eligible to receive an offer for continued study at Murdoch
University.
Any student who is absent for two successive class sessions will be contacted by student services for follow up and support.
Additional absences will trigger further contact and intervention efforts. If you are going to miss a class for any reason, it is
imperative that you communicate with your teacher as soon as possible via email (ideally before class).
Please note the following:
- Documentation (such as a medical certificate) is required to explain absenteeism;
- It is the responsibility of the student to follow up on missed work due to absences; and
- In the first three sessions of the course, tardy students will be given serious warnings for late arrival. From session 4 onwards,
students who arrive more than 10 minutes late for a class (or who leave early by the same margin) or do not return from a break
will be deemed to be absent from that session.
Where a student misses an 'in class' assessment due to absence, the student will need to negotiate with their teacher to arrange
an alternative place and time for the student to complete the task. Rescheduling tasks is not guaranteed and students will need to
provide good reasons for being absent (with evidence such as a medical certificate).
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3.

Key Assessment Information
Assessment
Weighting
When
Outline
Quiz Activities:
25%
In class
The concept tests will be conducted in a computer lab
under supervised and timed conditions.
Online
(10%)
Session 4
In class
(15%)
Session 9
Mid-Trimester Test
15%
Session 6
This test will cover everything that has been covered in
class so far.
Practical Assignment
25%
Session 12
The practical assignment and presentation will be
undertaken partly during the students own time and
presented in class. The topic will be distributed in Week
3.
Final Exam
35%
Week 13 or 14
The final exam will be for 2 hours and held in the exam
period (week 14). It will be a problem-solving based
exam addressing Learning Outcomes 1 & 3.
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4.

No Supplementary Assessments
Please note that supplementary assessments are not offered in
Murdoch Dubai Foundation units.
The foundation program is a pathway into undergraduate university
study. As such, it is absolutely imperative that we ensure this pathway
provides you with adequate preparation for the transition to your
undergraduate course. We have tried to achieve this goal by
strengthening the overall curriculum of the program and the content
and assessments within the individual units that make up the program.
Students who have previously completed foundation studies on the
basis of supplementary examinations have generally struggled more in
their undergraduate studies. The elimination of supplementary
assessments will provide you with a higher likelihood of success when
you move to your undergraduate course.
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5.

Base Arithmetic
• The aim of this lecture is to revise and reinforce basic number
work.
• Background and discussion:
– Our modern counting (decimal) system is base 10.
– Base 2 (or binary system) is used in boolean algebra and from 1950
onwards has played
– a central role in computing machines. The number 1 typically represents
`on' and 0 represents `o'.
– Babylonians used base 60.
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6.

What are some uses of binary numbers?
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7.

1.1 Base 2
1.1 Base 2
(a) converting between base 2 and base 10
(b) addition and subtraction in base 2
(c) multiplication in base 2
Example 1.2. (base conversion)
1. Convert these numbers from base 2 to base 10.
(a) 101
(b) 11010
2. Convert these numbers from base 10 to base 2.
(a) 7
(b) 15
(c) 140
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8.

1.1.1 Adding and subtracting in base 2
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9.

How to add large numbers:
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10.

Example 1.3. Calculate these binary numbers:
1. (a) 11 + 11
1. (b) 111 + 10
1. (c) 1100 + 1101
2. (a) 11 - 10
2. (b) 100 - 10
2. (c) 1111 - 11
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11.

1.1.2 Multiplication in base 2
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12.

1.1.2 Multiplication in base 2
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13.

Example 1.4. Calculate these binary numbers:
• (a) 110 x 10
• (b) 1101 x 11
• (c) 1111 x 110
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14.

1.2 Other bases
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15.

Example 1.6. (base conversion)
1. Convert these numbers to base 10.
(a) 33 in base 4
(b) 331 in base 4
(c) 42032 in base 4
2. Convert these numbers to base 4.
(a) 16 in base 10
(b) 91 in base 10
(c) 364 in base 10
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16.

2 Roman Numerals
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17.

Rules
1. Smaller numerals follow larger.
2. add up all the numerals to find its value.
3. I, X, C, M can be repeated up to 3 times in a row.
4. In certain cases a smaller number may come before a larger
number. In such cases we subtract the smaller from the larger.
Example 2.1.
DCCLXVII is 500 + 100 + 50 + 10 + 5 + 1 + 1 = 767
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18.

Roman Numerals
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19.

Write the Roman numerals for
(a) The numbers 1-10.
(b) The numbers 11-20.
(c) The numbers 100, 200, 300, . . . ,1000.
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20.

Exercises
1. Write these numbers in Roman numeral form.
(a) 22
(b) 25
(c) 99
(d) 101
(e) 36
(f) 347
(g) 349
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21.

Exercises
2. Work out these Roman numerals.
(a) XXVIII
(b) XXXIX
(c) XLI
(d) CLXI
(e) CCCXLV
(f) DCIX
(g) DCCL
(h) DXCIX
(i) LXIX
(j) DXLIX
(k) DCCCLXXXVIII
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22.

Exercises
3. Write these years in Roman numeral.
(a) 1960
(b) 2013
(c) 1666
(d) 1870
(e) 1066
(f) 2020
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23.

Exercises
4. What years do these numerals represent?
(a) MMXV
(b) MDLXV
(c) MM
(d) MDCCCL
(e) MCMXC
(f) MCDL
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