General Mathematics Unit 1 Subject Matter

General Mathematics Unit 1: Money, Measurement, Algebra and Linear Equations

GM Unit 1 Topic 1: Consumer Arithmetic

Sub-topic: Applications of Rates, Percentages and Use of Spreadsheets (14 hours)

• Understand the meaning of rates and percentages.

• Calculate weekly, fortnightly or monthly wages from an annual salary, and wages from an hourly rate, including situations involving overtime and other allowances and earnings based on commission or piecework.

• Calculate income support 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 use the unit cost method.

• Apply percentage increase or decrease in various contexts, e.g. inflation of costs and wages, percentage mark-ups and discounts, percentage profit and loss, GST, simple interest.

• where is simple interest, is principal, is interest rate per year and is number of years

• Use currency exchange rates to convert between the Australian dollar and foreign currencies.

• Calculate the dividend paid on a portfolio of shares, given the dividend yield or dividend paid per share, and compare share values by calculating a price-to-earnings (P/E) ratio.

• Use a spreadsheet to display examples of the above computations when multiple or repeated computations are required, e.g. preparing a wage sheet displaying the weekly earnings of workers in an organisation, preparing a budget, investigating the potential cost of owning and operating a car over a year.

GM Unit 1 Topic 2: Shape and Measurement

Sub-topic: Pythagoras’ Theorem (3 hours)

• Understand and use Pythagoras’ theorem to solve practical problems in two dimensions and simple applications in three dimensions.

• where is length of the hypotenuse and and are lengths of the two perpendicular sides

Sub-topic: Mensuration (9 hours)

• Calculate perimeters, , of standard two-dimensional objects in practical situations, including circles, sectors, triangles, rectangles, trapeziums, parallelograms and composites.

• circle: where is circumference and is radius

• sector: , where is central angle and is radius

• Calculate areas, , of standard two-dimensional objects in practical situations, including circles, sectors of circles, triangles, rectangles, parallelograms, trapeziums and composites.

• circle: where is radius

• sector: where is central angle and is radius

• triangle: where is base length and  is perpendicular height

• parallelogram: where is base length and is perpendicular height

• trapezium: where and are parallel lengths and is perpendicular height

• Calculate surface areas, , of standard three-dimensional objects in practical situations, including rectangular prisms, cylinders, pyramids, cones, spheres and composites.

• cylinder: where is radius and is perpendicular height

• cone: where is radius and is slant height

• sphere: where is radius

• Calculate volumes, , and capacities of standard three-dimensional objects in practical situations, including rectangular prisms, cylinders, pyramids, cones, spheres and composites.

• prism: where is base area and is perpendicular height

• cylinder: where is radius and is perpendicular height

• pyramid: where is base area and  is perpendicular height

• cone: where is radius and is perpendicular height

• sphere: where is radius

• Solve practical problems involving shape and measurement.

GM Unit 1 Topic 3: Similarity and Scale

Sub-topic: Similar Figures and Scale Factors (8 hours)

• Understand the conditions for similarity of two-dimensional figures, including similar triangles.

• Use the scale factor for two similar figures to solve linear scaling problems.

• Determine measurements from scale drawings (e.g. maps and building plans) to solve problems.

• Determine a scale factor and use it to solve scaling problems, e.g. calculating lengths and areas of similar figures; and calculating surface areas, volumes and capacities of similar solids.

GM Unit 1 Topic 4: Algebra

Sub-topic: Linear and Non-linear Relationships (8 hours)

• Substitute numerical values into linear and simple non-linear algebraic expressions, and Evaluate.

• Solve the value of a pronumeral in linear and simple non-linear equations given the values of the other pronumerals, transposing equations where necessary.

• Use a spreadsheet or an equivalent technology to construct a table of values from a formula, including two-by-two tables for formulas with two variable quantities.

GM Unit 1 Topic 5: Linear Equations and Their Graphs

Sub-topic: Linear Equations (5 hours)

• Solve linear equations, including equations with variables on both sides and equations with rational solutions.

• Develop a linear equation from a description in words.

• Solve practical problems involving linear equations.

Sub-topic: Straight-line Graphs (8 hours)

• Understand and use the slope-intercept form of a linear function, where is slope (gradient) and is -intercept.

• Construct a straight-line graph using a linear function of the form, where is slope (gradient) and is -intercept.

• Determine the slope (gradient), -intercept and -intercept of a straight line from both its equation and its graph.

• Interpret, in context, the slope (gradient) and intercept of a linear function used to model and analyse a practical situation.

• Construct and analyse a straight-line graph to model a given linear relationship, e.g. modelling the cost of filling a fuel tank of a car against the number of litres of petrol required.