Level 10A

Filter
Filter
View

Mathematics

Mathematics Level Description

Level 10A provides optional, additional content for students to be extended in their mathematical studies.

Students could extend work in number and algebra to investigate the structure and properties of number systems, with further analysis of order relations and inequalities. They could extend the study of trigonometry to include an introduction to circular functions and equations, or extend...

Mathematics Content Descriptions

Number and Algebra

Real numbers
1. Define rational and irrational numbers and perform operations with surds and fractional indices (VCMNA355)
2. Use the definition of a logarithm to establish and apply the laws of logarithms and investigate logarithmic scales in measurement (VCMNA356)
Patterns and algebra
1. Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (VCMNA357)
2. Devise and use algorithms and simulations to solve mathematical problems (VCMNA358)
Linear and non-linear relationships
1. Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (VCMNA359)
2. Solve simple exponential equations (VCMNA360)
3. Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (VCMNA361)
4. Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts (VCMNA362)
5. Use function notation to describe the relationship between dependent and independent variables in modelling contexts (VCMNA363)
6. Solve simultaneous equations using systematic guess-check-and-refine with digital technology (VCMNA364)

Measurement and Geometry

Using units of measurement
1. Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (VCMMG365)
Geometric reasoning
1. Prove and apply angle and chord properties of circles (VCMMG366)
Pythagoras and trigonometry
1. Establish the sine, cosine and area rules for any triangle and solve related problems (VCMMG367)
2. Use the unit circle to define trigonometric functions as functions of a real variable, and graph them with and without the use of digital technologies (VCMMG368)
3. Solve simple trigonometric equations (VCMMG369)
4. Apply Pythagoras’ theorem and trigonometry to solving three-dimensional problems in right-angled triangles (VCMMG370)

Statistics and Probability

Chance
1. Investigate reports of studies in digital media and elsewhere for information on their planning and implementation (VCMSP371)
Data representation and interpretation
1. 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 (VCMSP372)
2. Use digital technology 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 (VCMSP373)