# Course Title: Use a range of techniques to solve mathematical problems

## Part B: Course Detail

Teaching Period: Term2 2018

Course Code: MATH7081

Course Title: Use a range of techniques to solve mathematical problems

School: 174T School of VE Engineering, Health & Science

Campus: City Campus

Program: C4386 - Certificate IV in Tertiary Preparation

Course Contact: Namrita Kaul

Course Contact Phone: +61 3 9925 4387

Course Contact Email: namrita.kaul@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Rauha Quazi

+61 3 9925 4277

rauha.quazi@rmit.edu.au

Nominal Hours: 110

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

This unit describes the skills and knowledge to use a range of specialist techniques and concepts to solve mathematical problems.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: VU22074 Use a range of techniques to solve mathematical problems Element: 1. Use ratio, proportion and percent to solve problems Performance Criteria: 1.1 Determine a ratio from information in a practical problem and express it in simplest form 1.2 Divide a quantity into a given ratio 1.3 Convert between fractions, decimals and percent forms 1.4 Calculate a percentage increase or decrease of a quantity Element: 2. Use trigonometry to determine lengths Performance Criteria: 2.1 Use Pythagoras' Theorem to determine an unknown side of a right angled triangle 2.2 Use Pythagoras' Theorem and trigonometric ratios to find unknown side lengths and angles in triangles Element: 3. Use indices to solve problems Performance Criteria: 3.1 Evaluate index form expressions 3.2 Simplify exponential expressions using the first two index laws 3.3 Convert between decimal numbers and numbers expressed in Standard Notation 3.4 Perform calculations with numbers expressed in Standard Notation, using a calculator Element: 4. Use measurements to solve mensuration problems in two and three dimensions Performance Criteria: 4.1 Determine lengths and perimeters of rectangles, triangles, circles and simple combined shapes using appropriate and correct units 4.2 Determine areas of rectangles, triangles, circles and simple combined shapes using appropriate and correct units 4.3 Determine volumes of prisms and pyramids with rectangular, triangular and circular cross-sections and with simple combined shapes as cross sections using appropriate and correct units Element: 5. Substitute into and transpose equations and formulae Performance Criteria: 5.1 Substitute given values into equations and formulae 5.2 Write equations to solve problems 5.3 Transpose formulae 5.4 Solve linear equations Element: 6. Solve problems by plotting points Performance Criteria: 6.1 Plot given points and points determined from the general formula y = mx+c on the Cartesian plane 6.2 Determine the gradient of a straight line 6.3 Determine the equation of a straight line, where the equation has the general form y = mx+c, y = a and x = b 6.4 Use interpolation and extrapolation to make predictions from the line of best fit, noting limitations Element: 7. Present and evaluate statistical information Performance Criteria: 7.1 Collect, organise and graphically represent statistical data 7.2 Interpret and analyse statistical information Element: 8. Identify connections between formulae and graphical representations Performance Criteria: 8.1 Use graphical techniques to draw linear and non-linear graphs 8.2 Develop equations for given linear graphs, including lines of best fit Element: 9. Use algebraic techniques to analyse and solve problems Performance Criteria: 9.1 Develop formulae to describe relationships between variables and substitute into formulae to find particular values 9.2 Use a range of techniques to solve a range of algebraic problems and perform algebraic manipulations

Learning Outcomes

Details of Learning Activities

- discussion of mathematical concepts relevant to each topic
- discussion of the mathematical routines and procedures for solving problems related to each topic
- working independently or in groups in solving problems on exercise and work sheets
- working in groups to solve more challenging problems requiring interpretation and evaluation of results

Teaching Schedule

 Week Week starting Topic Assessment 1 2 July Order of operation Directed numbers Different types of fractions 2 9 July Convert between fractions, decimals and precent Significant figures Rounding of numbers 3 16 July Index laws Simplify expressions using index laws 4 23 July Ratio and proportion Percentage increase and decrease Quiz 1 5 30 July Introduction to basic algebra Substitution and transposition 6 6 Aug Simplify algebraic expressions Algebric techniques to solve problems Solving linear equations 7 13 Aug Graphing Linear equations Determining Linear equations Quiz 2 8 20 Aug Application of linear equations and graphs Simple non-linear graphs and their equations Semester break: 27 Aug – 31 Aug 9 3 Sept Scatter plot Line of best fit Workbook due 10 10 Sept Introduction to Statistics: Types of Data Collecting and Representing Statistical Data 11 17 Sept Interpret and analyse statistical information: Mean, Median, Mode, 5-Figure summary Assignment hand out 12 24 Sept Data collection for assignment and working on assignment 13 1 Oct Pythagoras Theorem Trigonometric ratios and applications Assignment due 14 8 Oct Perimeter and area of basic shapes and combined shapes 15 15 Oct Total surface area and volume of basic shapes and combined shapes 16 22 Oct Revision 17 29 Oct Exam week Exam

Learning Resources

Prescribed Texts

References

Other Resources

Online Learning materials will be provided during the course via canvas.

A basic scientific calculator is needed to solve problems.

An exercise book to complete exercises.

Overview of Assessment

Assessment in this course may include:
Worksheets
Quizzes
Assignments
Tests

 Assessments Topics covered Weighting Date Assessment 1: Quiz 1 Number skills, fractions and decimals and percent, indices 10% Week 4 Assessment 2: Quiz 2 Ratio and proportion, Percent increase/decrease, Substitution and transposition, Basic algebra, linear equations 20% Week 7 Assessment 3: Workbook Fractions and decimals Indices Ratio and proportion Percent increase/decrease Substitution, transposition Graphing and solving linear equations Simple non-linear graphs and their equations 20% Week 9 Assessment 4: Assignment Collecting and representing data Analyse and describe statistical information 20% Week 13 Assessment 5: Exam Scatter plot Line of best fit Statistics Trigonometry and geometry 30% Week 17

Assessment Matrix

Other Information

This course is graded in accordance with competency-based assessment, but which also utilise 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
DNS Did Not Submit for assessment

• To pass the course you need to pass, on average, each type of assessment (test, assignments etc.) For example, if there are two quizzes you need to have an average of 50% to pass and you also need to have passed the other assessment types. You can’t make up marks from one type of assessment to another (e.g. pass the quizzes but fail the assignment component).
• Late work that is submitted without an application for an extension (see below) will not be corrected.
• APPLICATION FOR EXTENSION OF TIME FOR SUBMISSION OF ASSESSABLE WORK - A student may apply for an extension of up to 7 days from the original due date. They must lodge the application form (available online http://www1.rmit.edu.au/students/assessment/extension) at least 24 hours before the due date. Students requiring longer extensions must apply for SPECIAL CONSIDERATION.
• For missed assessments such as quizzes and exam- you (& your doctor if you are sick) must fill out a special consideration form. This form must be lodged online with supporting evidence prior to, or within, five working days of the scheduled time of the assessment. http://www1.rmit.edu.au/students/specialconsideration

Plagiarism is the presentation of the work, idea or creation of another person as though it is your own. It is a form of cheating and is a very serious academic offence that may lead to expulsion from the University. Plagiarised material can be drawn from, and presented in, written, graphic and visual form, including electronic data and oral presentation. Plagiarism occurs when the origin of the material used is not appropriately cited. It also occurs through enabling plagiarism, which is the act of assisting or allowing another person to plagiarise or to copy your own work. Please make sure you consider this carefully in completing all your work and assessments in this course and if you are unsure about whether you might have plagiarised, seek help from your teacher.

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