mcc further maths course outline

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Last Updated: January 31 2010 MURRAYVILLE COMMUINITY COLLEGE Further Mathematics Unit 3 & 4 Subject description: Students complete four topics. One core topic – univariate and bivariate data, geometry & trigonometry, matrices, and functions and graphs. To satisfactorily complete each unit, students are required to demonstrate achievement of three outcomes in each of the above topics. Assessment tasks are to be part of the regular teaching and learning program and should be completed mainly in class and within a limited timeframe. Duration of subject: (7-12) 16 weeks Outcome 1 Define and explain key terms and concepts as specified in the content from the areas of study, and use this knowledge to apply related mathematical procedures to solve routine application problems. Assessment Outcome 2 Apply mathematical processes to analyse and discuss these applications of mathematics. . Outcome 3 Select and appropriately use technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem- solving,

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Page 1: Mcc Further Maths Course Outline

Last Updated: January 31 2010

MURRAYVILLE COMMUINITY COLLEGE

Further Mathematics Unit 3 & 4

Subject description: Students complete four topics. One core topic – univariate and bivariate data, geometry & trigonometry, matrices, and functions and graphs.To satisfactorily complete each unit, students are required to demonstrate achievement of three outcomes in each of the above topics.Assessment tasks are to be part of the regular teaching and learning program and should be completed mainly in class and within a limited timeframe.

Duration of subject: (7-12) 16 weeks

Outcome 1

Define and explain key terms and concepts as specified in the -content from the areas of study, and use this knowledge to apply related mathematical procedures to solve routine application problems.

AssessmentOutcome 2

Apply mathematical processes to analyse and discuss these applications of mathematics..

Outcome 3

Select and appropriately use technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.

Page 2: Mcc Further Maths Course Outline

Week (Lesson

Sequence)

Learning Focus(concepts / knowledge / skill)

Teaching and Learning activities & strategies

Resources(hyperlinked / texts /

embedded documents)

Assessment

11/2)

MatricesRevision

Chapter 16

Revision Exercise at end of Chapter

Practice SAC

Math Quest Further Math 12 2nd Edition Unit 3

Checkpoints VCE Further Math

VCAA website: practice exams

NEAP Practice exams

Lisachem practice exams

TSSM practice exam

Heffernan practice exams

Practice SAC

NEAP questions from Exam One and Exam Two

2

7/2

CORE - DATA ANALYSIS

Displaying, summarising and describing univariate data

types of data, numerical and categorical

review of methods for displaying univariate numerical data (stemplots, bar charts, including bar charts segmented appropriately using percentages, and frequency histograms), shape including symmetry and skewness (positive & negative), and outliers if appropriate

Quest.1 select’n of Qu’s

1A 1abde;

WE 4,5,6,7,8

1B 1abc;

WE 1,2,3A-D

1C 1, 2, 5

1E WE 9

1D 1adef, 3, 5, 8, 9, 13, 14

Ch.1 REVIEW

3

14/2

SAC 1 Matrices SAC 1 Matrices

4 review of summary statistics (mean and

standard deviation, median and WE 10,11,12

Page 3: Mcc Further Maths Course Outline

21/2interquartile range, range) for describing the centre and spread and conditions for their use; the use and interpretation of boxplots

MEAN

giving meaning to the standard deviation for bell shaped data sets using the 68-95-99.7% rule, boxplots with outliers

using random numbers draw a simple random sample from a population, display, summarise and describe the sample

1E 1abcf, 2, 3, 6, 8, 10, 13; 16F all;

WE13,14,15,16,17A-D

1F

WE 18,19

1G

WE 20,21

1H

WE 232-27

1I

5

28/2

POPULATIONS Quest Ch.1

1J

Students to do an independent investigation and relevant exercises.

6

7/3

Labour Day Holiday 8/3

Displaying, summarising and describing relationships in bivariate data

identification of dependent and independent variables

back to back stemplots and parallel boxplots

describing the relationship between a numerical variable and a categorical variable using summary statistics

Quest Ch 2

Dependent and independent variables (page 72)

WE 1a-b

Ex 2A Dependent and independent variables (page 73)

Back-to-back stem plots (page 75)

WE 2, 3

Ex 2B Back-to-back stem plots (page 78)

Page 4: Mcc Further Maths Course Outline

using a table(including two way) and or associated bar charts segmented appropriately using percentages

using a scatterplot to display and describe, in terms of direction (positive, negative), form (linear, non-linear) and strength (strong, moderate, weak); the association between two numerical variables

Parallel boxplots (page 80)

WE 4

Ex 2C Parallel boxplots (page 82)

Two-way frequency tables and segmented barcharts (page 84)WE 5, 6, 7

Ex 2D Two-way frequency table and segmented barcharts (page 88)

Scatterplots (page 90)

WE 8, 9

Ex 2E Scatterplots (page 94)

7

14/3

estimation of Pearson’s product-moment correlation from a scatterplot and use of calculator to calculate this correlation coefficient

use and interpretation of Pearson’s product-moment correlation

correlation and causation

calculation of the coefficient of determination (r2) from Pearson’s product-moment coefficient and interpretation of this coefficient in terms of explained variance

Pearson’s product-moment correlation coefficient (page 96)

WE 10a-c

Ex 2F Pearson’s product-moment correlation coefficient (page 98)Calculating r and the coefficient of

determination (page 99)

WE 11 a-c, 12

Ex 2G Calculating r and the coefficient of determination (page 103

Summary (page 106)

Page 5: Mcc Further Maths Course Outline

Chapter review (page 108)

8

21/3

Introduction to regression

Fitting lines to bivariate numerical data, by eye, the three median line (graphically) and the least squares methods, interpretation of slope and intercepts, and use of lines to make predictions; extrapolation and interpolation; residual analysis to check the quality of fit;

Estimation of the equation of an appropriate line of best fit from a scatter plot and use a calculator with bivariate stats to determine least squares regression line;

Fitting a straight line by eye (page 116)WE 1Ex 3A Fitting a straight line by eye (page 118)Fitting a straight line – the 3-median method (page 118)

WE 2

Ex 3B Fitting a straight line – the 3-median method (page 123)

Fitting a straight line – least-squares regression (page 127)

WE 3, 4a-d

Ex 3C Fitting a straight line – least-squares regression (page 132)Interpretation, interpolation and

extrapolation (page 136)

WE 5a-c, 6, 7Ex 3D Interpretation, interpolation and extrapolation (page 139)

March 28 to April 11

Holidays and Easter Holiday Homework

TERM 2 Transformation of some forms of non-linear Residual analysis (page 141) Application Task

Page 6: Mcc Further Maths Course Outline

9

11/4

data to linearity by transforming one of the axes scales using a square, log or reciprocal transformation WE 8, 9

Ex 3E Residual analysis (page 146)Transforming to linearity (page 149)WE 10, 11, 12a-b

Ex 3F Transforming to linearity (page 155)

10

18/4

Application Task (Core Statistics – exc. Univariate)

(Given out 12/4, submitted by 26/4, 6 class sessions plus out of class time as timetabled with teacher – in during or after school study sessions )

Summary (page 157)

Chapter review (page 159)

‘Test yourself’ multiple choice questions (page 162)

Topic tests (4)

Application Task

11

25/4ANZAC HOLIDAY

Application Task (Core Statistics – exc. Univariate)

(Given out 12/4, submitted by 26/4, 6 class sessions plus out of class time as timetabled with teacher – in during or after school study sessions)

12

2/5

MODULE 2: GEOMETRY AND TRIGONOMETRYGeometry use and applications of similarity and

Pythagoras’ theorem in two and three dimensions

construction and use of scale diagrams to represent practical situations

effect on surface area and volume of changing linear dimensions (ie. if linear

Page 7: Mcc Further Maths Course Outline

factor is k, then area factor is k2 and volume factor is k3)

13

9/5

Trigonometry

solving right- angled triangles using trigonometric ratios

solving triangles using the sine (incl. Ambiguous case) and cosine rules (program on using rules)

evaluation of areas of non-right-angled triangles using the formula ½.bc.sin A.

14

16/5

Applications specification of location (distance and

direction) in two dimensions using compass bearings (including true bearings)

interpretation and use of a contour map to calculate distances and the average slope between two points

15

23/5

use of information provided in field sketches of traverse surveys (particularly those using offset distances at right angles to the base line) to find distances and bearings

calculation of unknown angles and distances given triangulation measurements

Page 8: Mcc Further Maths Course Outline

16

30/5

Practice Analysis Task for Geometry and Trigonometry

17

6/6

START SEMESTER 2

– VCAA Exams

– GAT 9/6

18

13/6

SAC 3

Analysis Task for Geometry and Trigonometry (1hr duration, summary sheet, in class

19

20/6

Displaying, summarising and describing time series data

median smoothing (as a graphical technique) and smoothing using a moving average, consideration of the number of terms required and centring where required

fitting a trend line to data by eye, by three median fit, and by the least squares method

TERM 3

1

11/7

qualitative analysis of time series; recognition of trend, seasonal, cyclic and random patterns

seasonal adjustments; seasonal effects and indices, deseasonalisation of the data using

Page 9: Mcc Further Maths Course Outline

yearly averages

2

18/7

3

MODULE 3: GRAPHS AND RELATIONS

Construction and interpretation of graphs

construction and interpretation of straight line graphs, line segment graphs and step graphs to represent real situations (which could include, for example, conversion graphs, income tax schedules, and postal charges);

graphical and algebraic solution of linear simultaneous equations in two unknowns; applications which could include, for example, break even analysis, which cost and revenue functions are linear;

interpretation of given non-linear graphs that represent real situations including significance of intercepts, slope, maximum/minimum points and average rate of change; for example, distance-time graphs, tidal heights, pulse rates at different level of exercise

4 construction of non-linear graphs from tables of data; interpolation and extrapolation to predict values; estimation of maximum/minimum values and location; reading coordinates of points of intersection for application such as break even analysis; interpretation of slope

graphical representation of relations of the

Page 10: Mcc Further Maths Course Outline

form y = kxn for n = 1,2,3, -1, -2; obtaining a linear graph by plotting y and against xn; applications to determining the constant of proportionality and to testing the appropriateness of a particular model of a given set of data, for example, braking distances, volumes, light intensity.

5

6

7

8

Linear programming transferring from a description of an

optimisation problem to its mathematical formulation, including the introduction of variables, constraints and an objective function;

graphing systems of linear inequations

using graphical methods to solve simple linear programming problems with two decision variables, such as blending and manufacturing problems.

Revision of ModuleAnalysis Task for Graphs and Relations Maths (1hr duration, summary sheet)

9 Preparation for exams

Tidy uip summary notes

Revision of Core

TERM 4 Revision,

Practice exams

Practice exam: VCAA SAC: Immunology

Page 11: Mcc Further Maths Course Outline