Course Title: Apply mathematical techniques to scientific contexts

Part B: Course Detail

Teaching Period: Term1 2016

Course Code: MATH7064

Course Title: Apply mathematical techniques to scientific contexts

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C4327 - Certificate IV in Tertiary Preparation

Course Contact: Nancy Varughese

Course Contact Phone: +61 3 9925 4713

Course Contact Email: nancy.varughese@rmit.edu.au


Name and Contact Details of All Other Relevant Staff

Marjorie Furlan

marjorie.furlan@rmit.edu.au

Nominal Hours: 70

Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.

Pre-requisites and Co-requisites

None

Course Description

The purpose of this unit is to provide learners with knowledge and skills related to basic statistics, functions and their graphs, circular functions, exponents and logarithms.


National Codes, Titles, Elements and Performance Criteria

National Element Code & Title:

VU20934 Apply mathematical techniques to scientific contexts

Element:

1 Use unit circle definitions of trigonometric quantities, graphs of the three basic trigonometric functions and radian measure to solve mathematics problems

Performance Criteria:

1.1 sinx, cosx and tanx are defined in terms of the unit circle and symmetry properties are used to convert the function of a negative angle or an angle greater than 90 degrees to the function of an acute angle
1.2 Angles are converted between degrees and radian measure
1.3 The value of the three basic trigonometric ratios of any angle given in degrees or radians is determined 
1.4  The graphs of y= sin x, y= cos x and y = tan x, where x is measured in degrees or radians are sketched
1.5  The graphs of y= a sin bx and y =a cos bx, giving amplitude and wavelength are sketched   
1.6  Problems involving simple applications of circular functions are solved

 

Element:

2 Use simple algebraic functions and their graphs to solve mathematics problems

Performance Criteria:

2.1 Simple problems involving direct and inverse proportion are solved.
2.2 Given a graph, its general shape, rates of change, intercepts and asymptotes are described and its domain and range are given using set notation.
2.3 The graph of a quadratic function is sketched.
2.4 Given its graph, the set of co-ordinates which make up the relation or its equation determine whether a relation is a function.
2.5 Quadratic equations are solved both algebraically and graphically.
2.6 Equations are determined from graphs with known quadratic rules.         
2.7 Simultaneous equations are solved algebraically and graphically.

 

Element:

3 Determine non-linear laws by transforming them into a linear form

Performance Criteria:

3.1 A set of non-linear data is transformed to a linear form and the line of best fit is drawn.
3.2 The corresponding non-linear formula is determined.

Element:

4 Solve problems involving exponential and logarithmic functions

Performance Criteria:

4.1 Exponential expressions are simplified using the laws of indices.
4.2 Exponential equations are solved without using logarithms. 
4.3 Expressions are converted between exponential and logarithmic forms
4.4 Logarithms are evaluated.
4.5 Applied problems are solved using logarithms and simple exponential equations.
4.6 Graphs of exponential functions are drawn.

Element:

5 Collect and process numerical data to illustrate its statistical properties

Performance Criteria:

5.1 Statistical data is presented using tables and graphs.
5.2 Using frequency distribution curves, determine numbers and/or percentage values which have a particular characteristic.
5.3 Using cumulative frequency curves, determine percentiles for data.
5.4 Measures of central tendency are determined for a given set of data giving limitation of their use in isolation.
5.5 Determine measures of spread giving limitation of their use in isolation.
5.6 Properties of statistical data are determined


Learning Outcomes


By the end of this course, students will be able to:

  • Understand technical mathematical terminology.
  • Apply mathematical logic to a scientific context.
  • Use a scientific calculator for complex calculations.


Details of Learning Activities

  • discussions about the theory of mathematical concepts and their real world applications.
  • exercises to consolidate knowledge


Teaching Schedule

 

 

Week

Date

Unit

Topic

 

Assessment

 

1
9th February

 

1: Algebra


1.1: Linear Equations
1.2: Quadratic Equations

 

 

2
16th Feb

 

 

1.3: Simultaneous Quadratic and Linear Equations
1.4: Cubic Equations

 

 

3

23rd Feb

 


2: Functions



2.1: Function and Set Notation
2.2: Linear Functions

  
 

4

1st March

 

 

2.3: Quadratic Functions
2.4: Cubic Functions

 

 

5
8th March

 

2.5: Linearizing Functions

Assignment 1 Algebra and Functions (20%) Due 22nd March

 

6
15th March

 

 

3: Indices and Logarithms



 




3.1: Index Laws
3.2: Solving Indicial Equations
3.3: The Relationship between Indices and Logarithms



 

  

7

22nd March

3.4: Exponential Graphs
3.5: Applications of Exponentials and Logarithms

 

 

29th March

 


Mid Semester Break (no class)

 

 

8

5th April

 

3: Indices and Logarithms

Quiz One 

 

Quiz One – Indices and Logarithms (15%)

 

10

12th April

Quiz feedback

 

 

 

4: Statistics
4.1: Classification and Organisation of Data 

 

4.2: Representing Data
4.3: Measures of Central Tendency – Ungrouped Data

 

 

11

19th April

 

12

26th April

4.4: Measures of Central Tendency – Grouped Data
4.5: Measures of Dispersion 

Assignment Two – Statistics (20%)
 
 

13
3rd May

 

5: Circular Functions

 

5.1: Radians and the Unit Circle

 

 

 

14

10th May

 

5.2: Unit Circle, Symmetry, Exact Values and Identities

 

 

15

17th May

 

5.3: Circular Functions
5.4: Applications of Circular Functions

 



 
 

16

24th May

Exam Revision

Quiz 2
Exam Revision

Quiz 2 Circular Functions (15%)

 

17

31st May

 

EXAM

Final exam

Final exam (30%)
 

 

 

 

 


Learning Resources

Prescribed Texts


References


Other Resources

A scientific calculator is recommended for this course.


Overview of Assessment

Assessments for this course may include the following:
assignments, quizzes and written exams

  •    


Assessment Tasks

           

·         Assignment 1 – Algebra and Functions (20%)

·         Quiz 1 – Indices and Logarithms (15%)

·         Assignment 2 – Statistics (20%)

·         Quiz 2 – Circular Functions (15%)

·         Final Exam – Algebra, Functions, Indices and Logarithms, Statistics and Circular Functions (30%)

 


Assessment Matrix

Other Information

This course is graded in accordance with competency-based assessment, but also utilises graded assessment
CHD: Competent with High Distinction (80-100%)
CDI: Competent with Distinction (70-79%)
CC: Competent with Credit (60-69%)
CAG: Competency Achieved – Graded (50-59%)
NYC: Not Yet Competent (0-49%)
DNS: Did Not Submit for Assessment

Late work that is submitted without an application for an extension will not be corrected.

APPLICATION FOR EXTENSION OF TIME FOR SUBMISSION FOR ASSESSABLE WORK:

o    A student may apply for an extension of up to 7 days from the original due date.

o    They must lodge the application form (available online http://www1.rmit.edu.au/students/assessment/extension) at least 24 hours before the due date.

o    The application is lodged with the School Admin Office on Level 6, Bdg 51, or emailed to the Coordinator (nancy.varughese@rmit.edu.au).

o    Students requiring extensions longer than 7 days must apply for Special Consideration (see the “Help Me” link in blackboard, via myRMIT studies or http://www1.rmit.edu.au/students/specialconsideration).

§  For missed assessments such as exams – you (& your doctor if you are sick) must fill out a special consideration form.

§  This form must be lodged online with supporting evidence (eg. Medical certificate), prior to, or within, 48 hours of the scheduled time of examination.

§  If you miss an assessment task due to unavoidable circumstances, you need to follow the procedures of special consideration and apply within the allowed time frame.

 

Course Overview: Access Course Overview