General Mathematics Unit 2 Subject Matter

Unit 2: Applications of Linear Equations and Trigonometry, Matrices and Univariate Data Analysis

GM Unit 2 Topic 1: Applications of Linear Equations and Their Graphs

Sub-topic: Simultaneous Linear Equations and Their Applications (6 hours)

• Solve a pair of simultaneous linear equations, algebraically Use substitution and elimination, and graphically.

• Solve practical problems involving simultaneous linear equations.

Sub-topic: Piece-wise Linear Graphs and Step Graphs (5 hours)

• Draw piece-wise linear graphs and step graphs.

• Interpret piece-wise linear graphs and step graphs used to model practical situations.

GM Unit 2 Topic 2: Applications of Trigonometry

Sub-topic: Applications of Trigonometry (12 hours)

• Understand and Use the trigonometric ratios to Solve the size of an unknown angle, , or the length of an unknown side in a right-angled triangle.

• Calculate the area of a non-right-angled triangle, △, and solve related practical problems.

• , given two sides, and , and an included angle,

• Heron’s rule: where , given three sides, , and

• Solve two-dimensional problems involving a non-right-angled triangle, △, with sides, , and , and corresponding angles, , and .

• sine rule: (ambiguous case excluded)

• cosine rule:

• Solve two-dimensional practical problems involving the trigonometry of right-angled and non-right-angled triangles, including problems involving angles of elevation and depression and the use of true bearings.

GM Unit 2 Topic 3: Matrices

Sub-topic: Matrices and Matrix Arithmetic (10 hours)

• Use matrices for storing and displaying information that can be presented in rows and columns, e.g. tables, databases, links in social or road networks.

• Recognise different types of matrices, including row matrix, column matrix, square matrix, zero matrix and identity matrix, and Determine the size of the matrix.

• Perform matrix addition, subtraction and multiplication by a scalar.

• Perform matrix multiplication manually up to matrices but not limited to square matrices.

• Determine 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, e.g. 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.

GM Unit 2 Topic 4: Univariate Data Analysis 1

Sub-topic: Making Sense of Data Relating to a Single Statistical Variable (12 hours)

• Understand the meaning of univariate data.

• Identify a statistical variable as categorical or numerical.

• Classify a categorical variable as ordinal or nominal and use tables and pie, bar and column charts to organise and display the data, e.g. ordinal: income level (high, medium, low); nominal: place of birth (Australia, overseas).

• Classify a numerical variable as discrete or continuous, e.g. discrete: the number of people in a room; continuous: the temperature in degrees Celsius.

• Choose, Draw and justify an appropriate graphical display to Describe the distribution of a numerical dataset, including dot plot, stem-and-leaf plot, column chart and histogram.

• Describe a graphical display in terms of the number of modes, shape (symmetric versus positively or negatively skewed), measures of centre and spread, and outliers, and interpret this information in the context of the data.

• Understand and calculate the mean, median, mode, range and interquartile range (IQR) of a dataset, with and without technology.

• mean:

• median: data value

• Understand and calculate the (sample) standard deviation, , of a dataset, using technology only.

• Use statistics as measures of centre and spread of a data distribution, being aware of their limitations.

GM Unit 2 Topic 5: Univariate Data Analysis 2

Sub-topic: Comparing Data for a Single Numerical Variable across Two or More Groups (10 hours)

• Construct and use parallel box plots, including identifying possible outliers, to compare datasets in terms of median, spread (range and IQR) and outliers to interpret and communicate the differences observed in the context of the data.

• outliers (identifying): where is lower quartile and is upper quartile

• Compare datasets in terms of mean, median, range, IQR and standard deviation, interpret the differences observed in the context of the data, and report the findings in a systematic and concise manner.