There is no achievement standard for Level 10A.

Achievement standard – Level 10A

Content descriptions – Level 10A

define rational and irrational numbers and perform operations with surds and fractional indices

perform operations on numbers involving fractional exponents and surds

use the definition of a logarithm to establish and apply the laws of logarithms and investigate logarithmic scales in measurement

Number

investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems

devise and use algorithms and simulations to solve mathematical problems

simplify combinations of linear expressions with rational coefficients and the solution of related equations

explore the inverse relationship between exponential functions and logarithmic functions and the solution of related equations

describe, interpret, and sketch parabolas, hyperbolas, circles and exponential functions and their transformations

apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation

factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts

use function notation to describe the relationship between dependent and independent variables in modelling contexts

solve linear and non-linear simultaneous equations using graphing or systematic guess-check-and-refine with digital tools

experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

Algebra

solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids

explore the effect of increasingly small changes in the value of variables on the average rate of change and in relation to limiting values

Measurement

prove and apply relationships between angles and various lines associated with circles (radii, diameters, chords, tangents)

establish the sine, cosine and area rules for any triangle and solve related problems

use the unit circle to define the simple trigonometric functions of $y=\sin(x)$ , $y=\cos(x)$ and $y=\tan(x)$ as functions of a real variable, and graph them with and without the use of digital tools

apply Pythagoras’ theorem and trigonometry to solving three-dimensional problems in right-angled triangles

design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions 

Space

calculate and interpret the mean and standard deviation of data and use these to compare data sets; investigate the effect of individual data values, including outliers, on the standard deviation

identify measures of spread, and understand their interpretation and usefulness with respect to different data distributions

use digital tools to investigate bivariate numerical data sets; where appropriate use a straight line to describe the relationship allowing for variation, make predictions based on this straight line and discuss limitations

Statistics

explore counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities

investigate reports of studies in digital media and elsewhere for information on their planning and implementation

Probability

Mathematics

Level 10A provides optional, additional content to extend students in their mathematical studies in number, algebra, function, geometry, probability and statistics.
Level 10A does not include an achievement standard and does not require reporting.
Students may extend their studies in the Number and Algebra strands to investigate the structure and properties of number systems, with further algebraic and graphical analysis of higher-order polynomials, and relations such as circles, hyperbolas and other inequalities. They could extend the study of trigonometry to include an introduction to simple equations and graphs of circular functions, and extend the study of exponents and exponential functions to logarithm laws, including an introduction to logarithmic functions. Students could extend their study of graphing to explore the limiting value of rates of change.
Students could extend their studies in Measurement and Space to proving a broader range of geometric propositions solving trigonometric problems in non-right-angled triangles, or solving three-dimensional problems involving surface area and volume of cones, spheres and composite shapes.
Students could extend their studies in Statistics and Probability to explore the concepts of conditionality, dependence and independence in depth, or consider how various measures of location and spread can be used to describe the distribution of a data set, and investigate how robust these are with respect to variation in the data, in particular with respect to measurement error. They could explore factorials and how these may facilitate efficient counting in multiplicative and probabilistic contexts.

Level description – Level 10A

As the Victorian state election will be held on [Saturday, and date] the Victorian Government has assumed a caretaker role from [insert day and date]. During the caretaker period, content will only be added to this website or digital channel in accordance with caretaker conventions.

You are viewing the Victorian Curriculum F–10 Version 2.0.