The course is completed over year 11 and year 12 in four units. The first two are covered in year 11 and the third and fourth in year 12. The topics covered in year 11 are categorized under Consumer Arithmetic, Algebra and Matrices, Shape and Measurement, Univariate Data Analysis and the Statistical Investigation Process, Applications of Trigonometry, and Linear Equations and their Graphs. The technology necessary to support the computational aspects of the topics is taught.
Applications of Rate and Percentage Change, Earning and Managing Money
* Calculate weekly or monthly wage from an annual salary, wages from an hourly rate, including situations involving overtime and other allowances, and earnings based on commission or piecework.
* Calculate payments based on government allowances and pensions.
* Prepare a personal budget for a given income taking into account fixed and discretionary spending.
* Compare prices and values using the unit cost method.
* Apply percentage increase or decrease in contexts, including determining the impact of inflation on costs and wages over time, calculating percentage mark-ups and discounts, calculating GST, calculating profit or loss in absolute and percentage terms, and calculating simple and compound interest.
* Use currency exchange rates to determine the cost in Australian dollars of purchasing a given amount of a foreign currency, or the value of a given amount of foreign currency, when converted to Australian dollars.
* Calculate the dividend paid on a portfolio of shares given the percentage dividend or dividend paid for each share, and compare share values by calculating a price-to-earnings ratio.
Use of Spreadsheets and Classpad
* Use a spreadsheet/ Classpad to display examples of the above computations when multiple or repeated computations are required; for example, preparing a wage sheet displaying the weekly earnings of workers in a fast food store where hours of employment and hourly rates of pay may differ, preparing a budget, or investigating the potential cost of owning and operating a car over a year.
· Algebra and Matrices
* Linear and Non-linear Expressions
Substitute numerical values into algebraic expressions, and evaluate (with the aid of technology where complicated numerical manipulation is required).
* Determine the value of the subject of a formula, given the values of the other pronumerals in the formula (transposition not required).
Use a spreadsheet or an equivalent technology to construct a table of values from a formula, including tables for formulas with two variable quantities; for example, a table displaying the body mass index (BMI) of people of different weights and heights.
Matrices and Matrix Arithmetic
* Use matrices for storing and displaying information that can be presented in rows and columns; for example, databases, and links in social or road networks.
* Recognise different types of matrices (row, column, square, zero, identity) and determine their size.
* Perform matrix addition, subtraction, multiplication by a scalar, and matrix multiplication, including determining the power of a matrix using technology with matrix arithmetic capabilities when appropriate.
* Use matrices, including matrix products and powers of matrices, to model and solve problems; for example, costing or pricing problems, squaring a matrix to determine the number of ways pairs of people in a communication network can communicate with each other via a third person.
· Shape and Measurement
* Use Pythagoras’ theorem to solve practical problems in two dimensions and for simple applications in three dimensions.
* Solve practical problems requiring the calculation of perimeters and areas of circles, sectors of circles, triangles, rectangles, parallelograms and composites.
* Calculate the volumes of standard three-dimensional objects, such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations, for example, the volume of water contained in a swimming pool.
* Calculate the surface areas of standard three-dimensional objects, such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations; for example, the surface area of a cylindrical food container.
Similar Figures and Scale Factors
* Review the conditions for similarity of two-dimensional figures, including similar triangles.
* Use the scale factor for two similar figures to solve linear scaling problems.
* Obtain measurements from scale drawings, such as maps or building plans, to solve problems.
* Obtain a scale factor and use it to solve scaling problems involving the calculation of the areas of similar figures and surface areas and volumes of similar solids.
· Univariate Data Analysis and Statistical Investigation
The Statistical Investigation Process
* Review the statistical investigation process; identify a problem and pose a statistical question, collect or obtain data, analyze the data, interpret and communicate the results.
Making Sense of Data Relating to a Single Statistical Variable
* Classify a categorical variable as ordinal, such as income level (high, medium, low), or nominal, such as place of birth (Australia, overseas) and use tables and bar charts to organize and display data.
* Classify a numerical variable as discrete, such as the number of rooms in a house, or continuous, such as the temperature in degrees Celsius.
* With the aid of an appropriate graphical display (chosen from dot plot, stem plot, bar chart, or histogram), describe the distribution of a numerical data set in terms of modality (uni or multimodal), shape (symmetric versus positively or negatively skewed), location and spread and outliers, and interpret this information in the context of the data.
* Determine the mean and standard deviation of a data set using technology and use these statistics as measures of location and spread of data distribution, being aware of their limitations.
* Use the number of deviations from the mean (standard scores) to describe deviations from the mean in normally distributed data sets.
* Calculate quantiles for normally distributed data with known mean and standard deviation in practical situations.
* Use the 68%, 95%, 99.7% rule for data one, two, and three standard deviations from the mean in practical situations.
* Calculate probabilities for normal distributions with known mean m and standard deviation s in practical situations
Comparing Data for a Numerical Variable across 2 or more groups
Construct and use parallel box plots to compare groups in terms of location (median), spread (IQR and range), and outliers, and interpret and communicate the differences observed in the context of the data.
Compare groups on a single numerical variable using medians, means, IQRs, ranges, or standard deviations, and as appropriate; interpret the differences observed in the context of the data and report the findings in a systematic and concise manner.
Implement the statistical investigation process to answer questions that involve comparing the data for a numerical variable across two or more groups.
· Applications of Trigonometry
* Use trigonometric ratios to determine the length of an unknown side or the size of an unknown angle in a right-angled triangle.
* Determine the area of a triangle, given two sides and an included angle by using the rule Area = ½ absinC, or given three sides by using Heron’s rule, and solve related practical problems.
* Solve problems involving non-right-angled triangles using the sine rule (acute triangles only when determining the size of an angle) and the cosine rule.
* Solve practical problems involving right-angled and non-right-angled triangles, including problems involving angles of elevation and depression and the use of bearings in navigation.
· Linear Equations and their Graphs
Straight Line Graphs and their Applications
Simultaneous Linear Equations and applications
Piece-wise Linear Graphs and Step Graphs
Key features of the syllabus:
Students graduating out of year 11, learn to solve problems involving financial modeling, geometric and trigonometric analysis, graphical and network analysis and statistical investigation using univariate and bivariate data. Learners are able to choose and use technology appropriately and effectively.
Edugraff tutors have the core understanding and expertise to teach the topics covered under Mathematical Application. They provide in depth concept clarity so that students become adept at applying these concepts in practical problems. Hands-on practice provided by the Edugraff teachers works towards achieving excellence.
How can Edugraff help me prepare for University?
Edugraff teachers are familiar with the assessment systems and the kind of tutoring required to achieve grades that will meet the eligibility criteria for university admissions. This proves to be extremely helpful for students looking at tertiary education.