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Smith's Hill High School

Smith's Hill High School

Promoting excellence in a spirit of trust and cooperation

Telephone02 4229 4266

Emailsmithshill-h.school@det.nsw.edu.au

Mathematics

By studying mathematics, students learn to work mathematically – developing fluency, understanding, problem-solving, reasoning and communication skills.

The syllabus consists of the following strands:

  • number and algebra
  • measurement and geometry
  • statistics and probability.

In Year 11 and 12, the study of mathematics is optional.

Mathematics is used to identify, describe and apply patterns and relationships. It provides a precise means of communication and is a powerful tool for solving problems both within and beyond mathematics. Mathematical ideas are constantly developing, and mathematics is integral to scientific and technological advances in many fields of endeavour. Digital technologies provide access to new tools for continuing mathematical exploration and invention. In addition to its practical applications, the study of mathematics is a valuable pursuit in its own right, providing opportunities for originality, challenge and leisure.

Mathematics in Years 7–10 focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, communication, logical reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing strategies to make informed decisions and solve problems relevant to their further education and everyday lives.

Stage 4 - Years 7 and 8

Year 7

Mathematics in Years 7–10 focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, communication, logical reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing strategies to make informed decisions and solve problems relevant to their further education and everyday lives.

Topics studied include: Number Theory; Fractions; Introductory Algebra; Introductory Geometry; Units, Area, Volume and Time; Decimals; The Number Line and the Number Plane; Equations; Probability; Percentages and Ratios; Angles and Constructions; and Statistics, Graphs and Tables.

Year 8

Topics studied include: Equations; Harder Percentages; Pythagoras’ Theorem; Geometry; Ratio and Rates; Formulae and Factorisation; Probability; Statistics; Congruent Triangles and Special Quadrilaterals; Circles, Area, Volume and Time; Graphing Straight Lines; Surds; and Algebraic Expressions.

NESA syllabus link: https://www.educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10

Stage 5 - Years 9 and 10

Year 9

Mathematics in Years 7–10 focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, communication, logical reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing strategies to make informed decisions and solve problems relevant to their further education and everyday lives.

Topics studied include: Earning Money; Factorisation; Equations and Inequations; Congruency; Formulae; Enlargements and Similarity; Index Laws; Coordinate Geometry; Probability; Trigonometry; Further Factorisation; Quadratic Equations; and Area, Volume and Time.

Year 10

Topics studied include: Algebra Review; Spending Money; Surds Review; Surface Area and Volume; Simultaneous Equations; Lines and Linear Equations; Quadratic Equations; Statistics; The Parabola; Indices and Logarithms; Circles and Hyperboles; Further Trigonometry; Probability; Circle Geometry; and Direct Proportion.

Stage 6 - Years 11 and 12

Mathematics Standard 2

The Mathematics Standard courses are focused on enabling students to use mathematics effectively, efficiently and critically to make informed decisions in their daily lives. They provide students with the opportunities to develop an understanding of, and competence in, further aspects of mathematics through a large variety of real-world applications for a range of concurrent HSC subjects.

Mathematics Standard 2 is designed for those students who want to extend their mathematical skills beyond Stage 5 but are not seeking the in-depth knowledge of higher mathematics that the study of calculus would provide. This course offers students the opportunity to prepare for a wide range of educational and employment aspirations, including continuing their studies at a tertiary level.

Units: 2 units

Pre-requisite: The outcomes and content in the Stage 6 Mathematics Standard syllabus are written with the assumption that students studying this course will have engaged with all sub-standards of Stage 5.1 and with the following sub-standards of Stage 5.2 - Financial mathematics, Linear relationships, Non-linear relationships, Right-angled triangles (Trigonometry), Single variable data analysis and Probability.

Exclusions: Students may not study any other Stage 6 Mathematics course in conjunction with Mathematics Standard.

Preliminary course

Financial Mathematics-Money Matters Statistical Analysis-Relative Frequency and Probability, Data Analysis Measurement-Applications of measurement, Working with Time, Algebra-Formulae and Equations, Linear Relationships.

HSC course

Financial Mathematics-Investments and Loans; Annuities, Statistical Analysis-Bivariate Data Analysis; The Normal Distribution Measurement-Non Right-Angled Triangles; Rates and Ratios Networks-Network Concepts; Critical Path Analysis, Algebra-Types of Relationships.

NESA syllabus link: https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/stage-6-mathematics/mathematics-standard-2017

Mathematics Advanced

The study of Mathematics Advanced in Stage 6 enables students to enhance their knowledge and understanding of what it means to work mathematically, develop their understanding of the relationship between ‘real-world’ problems and mathematical models and extend their skills of concise and systematic communication.

Units: 2 units

Pre-requisite: The course is constructed on the assumption that students have achieved the outcomes in the core of the Stage 5.3 Mathematics course and demonstrated general competence in all the skills included in that course.

Exclusions: Cannot be studied concurrently with Standards Mathematics.

Preliminary course

Working with Functions, Trigonometry and Measure of Angles, Trigonometric Functions and Identities, Introduction to Differentiation, Logarithms and Exponentials, Probability and Discrete Probability Distributions.

HSC course

Graphing Techniques, Trigonometric Functions and Graphs, Differential Calculus, Applications of Differentiation, Integral Calculus, Modelling Financial Situations, Descriptive Statistics and Bivariate Data Analysis, Random Variables.

NESA syllabus link: http://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/stage-6-mathematics/mathematics-syllabus

Mathematics Extension 1

The study of Mathematics Extension 1 in Stage 6 enables students to extend their knowledge and understanding of what it means to work mathematically, develop their skills to reason logically, generalise and make connections, and enhance their understanding of how to communicate in a concise and systematic manner.

Units: 1 Units for each of Preliminary and HSC Board Developed Course. Studied in conjunction with Mathematics Advanced.

Pre-requisite: The course is constructed on the assumption that students have achieved a mastery of the skills of the Stage 5.3 Mathematics course and who are interested in the study of further skills and ideas in Mathematics.

Exclusions: Cannot be studied concurrently with Standards Mathematics.

Preliminary course

Topics covered: Further Work with Functions, Polynomials, Inverse Trigonometric Functions, Further Trigonometric Functions, Rates of Change, Working with Combinatorics.

HSC course

Topics covered: Proof by Mathematical Induction, Introduction to Vectors, Trigonometric Equations, Further Calculus Skills, Applications of Calculus, The Binomial Distribution.

NESA syllabus link: https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/stage-6-mathematics/mathematics-extension-1-2017

Mathematics Extension 2 - HSC only

The study of Mathematics Extension 2 in Stage 6 enables students to extend their knowledge and understanding of working mathematically, enhance their skills to tackle difficult, unstructured problems, generalise, make connections and become fluent at communicating in a concise and systematic manner.

Units: 1 unit for HSC Board Developed Course. Studied in conjunction with Mathematics Advanced and Mathematics Extension 1.

Pre-requisite: This course is designed for students with a special interest in Mathematics who have shown that they possess special aptitude for the subject.

HSC course

Topics covered: The Nature of Proof, Further Proof by Mathematical Induction, Further Work with Vectors, Introduction to Complex Numbers, Using Complex Numbers, Further Integration, Applications of Calculus to Mechanics.

NESA syllabus link: https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/stage-6-mathematics/mathematics-extension-2-2017