HSC Mathematics
Comprehensive resources for NSW HSC Mathematics students, covering all courses from Standard to Extension 2.
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The HSC Mathematics curriculum offers multiple pathways to suit different student abilities and career aspirations.
HSC Mathematics Overview
HSC Mathematics Advanced
Mathematics Advanced is designed for students who have demonstrated a mastery of the skills of Stage 5 Mathematics and are interested in the study of further skills and ideas in mathematics. The course provides a basis for further studies in disciplines in which mathematics has a vital role at a tertiary level.
Functions
Working with various types of functions and their properties
Trigonometric Functions
Trigonometric functions and their applications
Calculus
Differential and integral calculus
Exponential and Logarithmic Functions
Properties and applications of exponential and logarithmic functions
Statistical Analysis
Probability and statistical analysis techniques
Financial Mathematics
Applications of mathematics in financial contexts
Calculus: Differentiation
Differentiation is a fundamental concept in calculus that measures the rate of change of a function with respect to a variable. In HSC Mathematics Advanced, you'll learn various differentiation techniques and their applications.
Key Concepts
- First Principles: Understanding the limit definition of the derivative.
- Differentiation Rules: Power rule, product rule, quotient rule, and chain rule.
- Applications: Finding rates of change, tangent lines, and optimization problems.
Common Misconceptions
- Misconception: The derivative of a product is the product of the derivatives.
Correction: The product rule states that (f·g)' = f'·g + f·g'. - Misconception: The derivative of a composite function is the composition of derivatives.
Correction: The chain rule states that (f(g(x)))' = f'(g(x))·g'(x).
Example Problem
Find the derivative of f(x) = x³sin(x)
Step 1: Identify that this is a product of two functions: g(x) = x³ and h(x) = sin(x)
Step 2: Apply the product rule: f'(x) = g'(x)·h(x) + g(x)·h'(x)
Step 3: Find the derivatives of each function:
g'(x) = 3x²
h'(x) = cos(x)
Step 4: Substitute into the product rule:
f'(x) = 3x²·sin(x) + x³·cos(x)
Therefore, f'(x) = 3x²sin(x) + x³cos(x)
Exam Tip
Example Problems
Differentiation of a Composite Function
Calculus - Chain Rule
Find the derivative of f(x) = sin(3x² + 2x)
Exponential Growth Model
Exponential Functions - Exponential Models
A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 15 hours?
HSC Exam Preparation
Study Tips for HSC Mathematics Advanced
- Practice regularly with past papers to familiarize yourself with exam format and timing
- Create summary notes for each topic, focusing on key formulas and concepts
- Form study groups to discuss challenging problems and share different approaches
- Use the NESA reference sheet to familiarize yourself with provided formulas
- Practice with your approved calculator to ensure you can use all necessary functions
Common Exam Mistakes to Avoid
- Not showing sufficient working out, even when you know the answer
- Misreading questions or not answering what was actually asked
- Forgetting to include units in your final answers when required
- Not checking calculator settings (degrees vs. radians) for trigonometry questions
- Poor time management, spending too long on difficult questions
Past Papers and Resources
Past Papers
Practice with previous HSC examination papers
Formula Sheets
Essential formulas for quick reference
Official Resources
Links to NESA official materials
HSC Mathematics Resources
Approved Calculators
Information about calculators permitted in HSC examinations
NESA maintains a list of approved calculators for HSC examinations. It's essential to ensure your calculator complies with these requirements.
Popular Approved Models:
- • Casio fx-82AU PLUS II
- • Sharp EL-531THB
- • Abacus SX-II MATRIX
- • HP 10s+
Reference Sheets
Standard reference materials provided in HSC exams
In HSC Mathematics examinations, students are provided with a reference sheet containing key formulas. Familiarizing yourself with this sheet is crucial for exam success.
Reference Sheet Includes:
- • Differentiation and integration formulas
- • Trigonometric identities
- • Statistical formulas
- • Geometric formulas
Textbooks & Study Guides
Recommended resources for HSC Mathematics
While our website provides comprehensive resources, many students benefit from additional textbooks and study guides.
Popular Resources:
- • Cambridge Mathematics (Year 11 & 12 series)
- • Excel Success One HSC Mathematics
- • Maths in Focus (Mathematics Extension 1 & 2)
- • Understanding HSC Mathematics (Standard)
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