Mathematics

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Level 9

Level 9 Description

In Level 9, students develop familiarity with a broader range of non-linear and linear functions and relations, and related algebra and graphs.

Students apply index laws with integer indices to a...

Level 9 Content Descriptions

Number and Algebra

Real numbers
1. Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (VCMNA301)
2. Apply index laws to numerical expressions with integer indices (VCMNA302)
3. Express numbers in scientific notation (VCMNA303)
Money and financial mathematics
1. Solve problems involving simple interest (VCMNA304)
Patterns and algebra
1. Extend and apply the index laws to variables, using positive integer indices and the zero index (VCMNA305)
2. Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (VCMNA306)
3. Apply set structures to solve real-world problems (VCMNA307)
Linear and non-linear relationships
1. Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software (VCMNA308)
2. Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (VCMNA309)
3. Sketch linear graphs using the coordinates of two points and solve linear equations (VCMNA310)
4. Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (VCMNA311)

Measurement and Geometry

Using units of measurement
1. Calculate the areas of composite shapes (VCMMG312)
2. Calculate the surface area and volume of cylinders and solve related problems (VCMMG313)
3. Solve problems involving the surface area and volume of right prisms (VCMMG314)
4. Investigate very small and very large time scales and intervals (VCMMG315)
Geometric reasoning
1. Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (VCMMG316)
2. Solve problems using ratio and scale factors in similar figures (VCMMG317)
Pythagoras and trigonometry
1. Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (VCMMG318)
2. Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (VCMMG319)
3. Apply trigonometry to solve right-angled triangle problems (VCMMG320)

Statistics and Probability

Chance
1. List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (VCMSP321)
2. Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (VCMSP322)
3. Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians (VCMSP323)
Data representation and interpretation
1. Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (VCMSP324)
2. Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (VCMSP325)
3. Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (VCMSP326)

Level 9 Achievement Standard

Number and Algebra

Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students use the distributive law to expand algebraic expressions, including binomial expressions, and simplify a range of algebraic expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment using a range of strategies including the use of digital technology. Students sketch and draw linear and non-linear relations, solve simple related equations and explain the relationship between the graphical and symbolic forms, with and without...

Level 10

Level 10 Description

In Level 10, students extend their use of mathematical models to a wide range of familiar and unfamiliar contexts, involving the use of all types of real numbers. They recognise the role of logical...

Level 10 Content Descriptions

Number and Algebra

Real numbers
1. Solve simple problems involving inverse proportion (VCMNA327)
Money and financial mathematics
1. Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (VCMNA328)
Patterns and algebra
1. Factorise algebraic expressions by taking out a common algebraic factor (VCMNA329)
2. Simplify algebraic products and quotients using index laws (VCMNA330)
3. Apply the four operations to simple algebraic fractions with numerical denominators (VCMNA331)
4. Expand binomial products and factorise monic quadratic expressions using a variety of strategies (VCMNA332)
5. Substitute values into formulas to determine an unknown and re-arrange formulas to solve for a particular term (VCMNA333)
6. Implement algorithms using data structures in a general-purpose programming language (VCMNA334)
Linear and non-linear relationships
1. Solve problems involving linear equations, including those derived from formulas (VCMNA335)
2. Solve linear inequalities and graph their solutions on a number line (VCMNA336)
3. Solve simultaneous linear equations, using algebraic and graphical techniques including using digital technology (VCMNA337)
4. Solve problems involving gradients of parallel and perpendicular lines (VCMNA338)
5. Explore the connection between algebraic and graphical representations of relations such as simple quadratic, reciprocal, circle and exponential, using digital technology as appropriate (VCMNA339)
6. Solve linear equations involving simple algebraic fractions (VCMNA340)
7. Solve simple quadratic equations using a range of strategies (VCMNA341)
8. Solve equations using systematic guess-check-and-refine with digital technology (VCMNA342)

Measurement and Geometry

Using units of measurement
1. Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (VCMMG343)
Geometric reasoning
1. Formulate proofs involving congruent triangles and angle properties (VCMMG344)
2. Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (VCMMG345)
Pythagoras and trigonometry
1. Solve right-angled triangle problems including those involving direction and angles of elevation and depression (VCMMG346)

Statistics and Probability

Chance
1. Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence (VCMSP347)
2. Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language (VCMSP348)
Data representation and interpretation
1. Determine quartiles and interquartile range and investigate the effect of individual data values, including outliers on the interquartile range (VCMSP349)
2. Construct and interpret box plots and use them to compare data sets (VCMSP350)
3. Compare shapes of box plots to corresponding histograms and dot plots and discuss the distribution of data (VCMSP351)
4. Use scatter plots to investigate and comment on relationships between two numerical variables (VCMSP352)
5. Investigate and describe bivariate numerical data, including where the independent variable is time (VCMSP353)
6. Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data (VCMSP354)

Level 10 Achievement Standard

Number and Algebra

Students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, with and without the use of digital technology. Students substitute into formulas, find unknown values, manipulate linear algebraic expressions, expand binomial expressions and factorise monic and simple non-monic quadratic expressions, with and without the use of digital technology. They represent linear, quadratic and exponential functions numerically, graphically and algebraically, and use them to model situations and solve practical problems.

Measurement and Geometry

Students solve and explain surface area and volume problems relating to composite...