40 Questions
What are the important skills in relation to technology?
The ability to choose when, and when not, to use some form of technology, and the ability to work flexibly with technology.
What are the number formats learned in this unit?
Positive and negative numbers, decimals, fractions, percentages, rates, ratios, square and cubic numbers written with powers and square roots.
What do students learn to do with mathematical and statistical information?
Interpret, ascertain the reasonableness of their solutions to problems.
What is assumed knowledge for students in Year 12?
An understanding of the Year 11 content.
What do students do in topics 3.1, 3.2, and 3.3?
Apply the mathematical thinking process to real-world problems relating to the topic content.
What is the first step in the mathematical thinking process?
Interpret the task and gather the key information.
What is the next step after gathering information in the mathematical thinking process?
Identify the mathematics which could help to complete the task.
What is the purpose of verifying a solution in the mathematical thinking process?
To ensure the reasonableness of the solution.
How should findings be communicated in the mathematical thinking process?
In a systematic and concise manner.
What is the ultimate goal of the mathematical thinking process?
To obtain a solution to the problem.
What is the purpose of sampling in data collection?
To provide an estimate of population values when a census is not used.
What is the difference between a simple random sample and a self-selected sample?
A simple random sample is a sample where every individual in the population has an equal chance of being selected, whereas a self-selected sample is a sample where individuals choose to participate.
What is the target population in a survey?
The group of individuals that the survey is intended to describe or make inferences about.
What is the formula to calculate the surface area of a sphere?
$4\pi r^2$
What is a major consideration in questionnaire design?
Freedom from bias, with consideration of factors such as language, question ambiguity, and respondent privacy.
What is a source of error in surveys?
Sampling error and measurement error.
What is the relationship between volume and capacity?
1 cm3 = 1 mL, 1 m3 = 1 kL
What is a key aspect of bivariate data analysis?
Describing the association between two numerical variables in terms of direction, form, and strength.
What is the purpose of using scale drawings?
To estimate and compare quantities, materials and costs
What is the purpose of applying Pythagoras' theorem?
To solve problems in practical two-dimensional views
What is the purpose of a trend line in data analysis?
To identify patterns and relationships between variables and make predictions.
What is a critical consideration when extrapolating from a trend line?
Recognizing the dangers of extrapolation beyond the range of the data.
What is the name of the ratio used to determine unknown angles and sides in right-angled triangles?
Tangent ratio
What is the key distinction between correlation and causality?
Correlation describes an association between variables, whereas causality implies a cause-and-effect relationship.
What is the purpose of graphing linear functions?
To represent practical situations
What is an example of analysing bivariate data in a medical context?
Analysing the relationship between body ratios, such as hip height versus stride length.
What is the significance of the vertical intercept in practical situations?
Represents the initial value
What is the purpose of using time series data?
To identify trends and patterns
What is the name of the process used to solve statistical investigations?
Statistical investigation process
What is the name of the formula used to calculate the area of a trapezium?
(1/2) x (a + b) x h
What is the primary focus of Unit 3 in the Mathematics Essentials General Course Year 12?
To provide students with mathematical skills and understanding to solve problems related to measurement, scales, plans, models, graphs, and data collection.
How long will the Externally set task (EST) for 2024 be?
50 minutes
What is the weighting of the EST in the assessment table?
15%
What is the process that students use to apply the mathematical thinking in this unit?
The statistical investigation process
What are the four topics in this unit?
Measurement; Scales, plans and models; Graphs in practical situations; and Data collection
What are possible contexts for this unit?
Construction and design, and Medicine
What technologies will be used in teaching this unit?
An extensive range of technological applications and techniques
When will the EST be administered in schools?
Term 2, 2024
Who marks the EST?
Teachers in each school
Who sets the EST?
The Authority
Study Notes
Mathematics Essential General Course Year 12: Externally Set Task 2024
- The Externally Set Task (EST) is a 50-minute assessment task that will be administered in schools during Term 2, 2024, under standard test conditions.
- The EST is marked by teachers in each school using a marking key provided by the Authority, with a weighting of 15% for the pair of units.
Unit 3: Measurement, Scales, Plans and Models, Graphs, and Data Collection
- This unit provides students with mathematical skills and understanding to solve problems related to measurement, scales, plans, and models, drawing and interpreting graphs, and data collection.
- By the end of this unit, students will:
- Understand concepts and techniques used in measurement, scales, plans, and models, graphs, and data collection.
- Apply reasoning skills and solve practical problems in these areas.
- Communicate arguments and strategies when solving mathematical and statistical problems.
- Interpret mathematical and statistical information and ascertain the reasonableness of their solutions.
Topic 3.1: Measurement
- Linear measure:
- Calculate perimeters of polygons, circles, and composites of familiar shapes.
- Calculate areas of parallelograms, trapeziums, circles, and semi-circles.
- Determine the area of composite figures by decomposition into familiar shapes.
- Determine the surface area of familiar solids, including cubes, rectangular and triangular prisms, spheres, and cylinders.
- Area measure:
- Calculate the area of composite figures by decomposition into familiar shapes.
- Determine the surface area of familiar solids.
- Examples in context:
- Calculating surface area of various buildings to compare costs of external painting.
- Interpreting dosages for children and adults from dosage panels on medicines, given age or weight.
- Volume and capacity:
- Recognise relations between volume and capacity.
- Calculate the volume and capacity of cylinders, pyramids, and spheres.
- Examples in context:
- Interpreting dosages for children and adults from dosage panels on medicines.
- Calculating and interpreting dosages for children from adults' medication using various formulas.
- Comparing the capacity of rainwater tanks.
Topic 3.2: Scales, Plans and Models
- Geometry:
- Recognise the properties of common two-dimensional geometric shapes and three-dimensional solids.
- Interpret different forms of two-dimensional representations of three-dimensional objects.
- Use terminology of geometric shapes.
- Interpret scale drawings:
- Interpret commonly used symbols and abbreviations in scale drawings.
- Determine actual measurements of angle, perimeters, and areas from scale drawings.
- Estimate and compare quantities, materials, and costs using actual measurements from scale drawings.
- Create scale drawings:
- Understand and apply drawing conventions of scale drawings.
- Construct scale drawings by hand and by using appropriate software/technology.
- Three-dimensional objects:
- Interpret plans and elevation views of models.
- Sketch elevation views of different models.
- Interpret diagrams of three-dimensional objects.
- Right-angled triangles:
- Apply Pythagoras' theorem to solve problems in practical two-dimensional views.
- Apply the tangent, sine, and cosine ratios to determine unknown angles and sides in right-angled triangles.
- Work with the concepts of angle of elevation and angle of depression.
- Solve problems involving trigonometric ratios in practical two-dimensional views.
- Examples in context:
- Drawing scale diagrams of everyday two-dimensional shapes.
- Interpreting common symbols and abbreviations used on house plans.
- Using the scale on a plan to calculate actual external or internal dimensions.
- Using technology to translate two-dimensional house plans into three-dimensional building designs.
- Creating landscape designs using technology.
Topic 3.3: Graphs in Practical Situations
- Cartesian plane:
- Demonstrate familiarity with Cartesian co-ordinates in two dimensions.
- Generate tables of values for linear functions drawn from practical contexts.
- Graph linear functions drawn from practical contexts with pencil and paper and with graphing software.
- Using graphs:
- Interpret and use graphs in practical situations.
- Draw graphs from given data to represent practical situations.
- Describe trend as increasing or decreasing for time series data.
- Identify the rate of change of the dependent variable.
- Determine and describe the significance of the vertical intercept in practical situations.
- Use the rate of change and the initial value to determine the linear relationship in practical situations.
- Interpret the point of intersection and other important features of given graphs of two linear functions.
- Examples in context:
- Interpreting graphs showing growth ranges for children.
- Interpreting hourly hospital charts showing temperature and pulse.
- Interpreting graphs showing life expectancy with different variables.
Topic 3.4: Data Collection
- Census:
- Investigate the procedure for conducting a census.
- Investigate the advantages and disadvantages of conducting a census.
- Surveys:
- Understand the purpose of sampling to provide an estimate of population values when a census is not used.
- Investigate the different kinds of samples.
- Recognise the advantages and disadvantages of these kinds of samples.
- Simple survey procedure:
- Identify the target population to be surveyed.
- Investigate questionnaire design principles.
- Sources of bias:
- Describe the faults in the collection of data process.
- Describe sources of error in surveys.
- Describe possible misrepresentation of the results of a survey due to the unreliability of generalising the survey findings to the entire population.
- Bivariate scatterplots:
- Describe the patterns and features of bivariate data.
- Describe the association between two numerical variables in terms of direction, form, and strength.
- Trend lines:
- Identify the dependent and independent variable.
- Fit a trend line by eye.
- Interpret relationships in terms of the variables.
- Use the trend line to make predictions, both by interpolation and extrapolation.
- Recognise the dangers of extrapolation.
- Distinguish between causality and association through examples.
- Examples in context:
- Analysing data obtained from medical sources, including bivariate data.
- Analysing and interpreting tables and graphs that compare body ratios.
This quiz covers the selected Unit 3 syllabus content for the Externally set task 2024 in Mathematics Essentials General Course Year 12. It features all the relevant content for the course.
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