mcc further maths course outline
DESCRIPTION
Brenda's Further Math 2010TRANSCRIPT
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.
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
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)
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)
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
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
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
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
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
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