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Functions

HSC HSC Mathematics Advanced · 2024 content registry · first HSC 2027

Official NSW Curriculum syllabus and implementation timeline ↗Download questions and solutions PDF
F1.1F1.2F1.3
Assessment evidence

What these examples cover

These examples show assessable skills, not an official HSC topic weighting or prediction. The 2024 NSW syllabuses have their first HSC examination in 2027; students sitting the 2026 HSC continue under the applicable 2017 syllabus.

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Teacher verification note: check the mathematics, notation, permitted technology and syllabus fit for your cohort before classroom or assessment use.

3 deterministic examples

Functions questions with worked solutions

Each question is generated from an existing curriq QDSL archetype at a fixed seed. Marks and catalog content mappings travel with the generated question.

Worked example 1

2 marksadv-f1-1
Linear equation Solve 10−x=(2x)/(2)10-x=(2x)/(2).
Part a · 2 marks

Find xx.

Worked solution

Answer: 5

  1. Clear Denominator: 20
  2. Solve Linear Equation: 5

Catalog reference: adv_cssa24_linear_equation · seed 41001

Worked example 2

2 marksadv-f1-1
Rationalising a surd denominator Rationalise (6)/(3−sqrt(2))(6)/(3-sqrt(2)).
Part a · 2 marks

Give the exact simplified result.

Worked solution

Answer: (18 + (6 sqrt(2))) / 7

  1. Multiply By Conjugate: n(3+sqrt2)/7
  2. Simplify: (18 + (6 sqrt(2))) / 7

Catalog reference: adv_nsb20_rationalise_denominator · seed 41001

Worked example 3

2 marksadv-f1-2
Backpack break-even point A business has income 240x240x and cost 90x+1350090x+13500. Find the number of backpacks required to break even.
Part a · 2 marks

Find the break-even quantity.

Worked solution

Answer: 90

  1. Equate Income And Cost: 240x=90x+13500240x=90x+13500.
  2. Solve Linear Equation: x=90x=90.

Catalog reference: adv_pem23_q11c_break_even · seed 41001

Content mapping and common errors

Functions content identifiers

F1.1

Working with Functions

Understand the concept of a function; use function notation; determine domain and range; work with graphs of functions.

Common student mistakes
  • ·Incorrect domain/range for composite or restricted functions
  • ·Confusing f(x) with f(a) when substituting
  • ·Misidentifying whether a relation is a function (vertical line test errors)
F1.2

Linear, Quadratic and Cubic Functions

Represent, interpret and model linear, quadratic and cubic functions and their graphs.

Common student mistakes
  • ·Sign errors when completing the square
  • ·Misidentifying the vertex from vertex form
  • ·Forgetting to check turning point type (max vs min)
F1.3

Further Functions and Relations

Work with polynomial, absolute value, exponential, logarithmic and hyperbolic functions.

Common student mistakes
  • ·Incorrect absolute value graph — missing the reflection for negative x
  • ·Confusing transformations: horizontal shifts vs vertical shifts

Source and methodology

Examples are deterministic curriq catalog generations from existing QDSL archetypes at the published fixed seed. The generator copies only student-facing prompts, mark allocations, topic mappings, display tables or options, checked answers and marking-path results into this resource.

Review the official NSW Curriculum source ↗

Other Advanced topics

Trigonometric Functions
3 content identifiers
Calculus
6 content identifiers
Exponential and Logarithmic Functions
2 content identifiers
Statistical Analysis
3 content identifiers
Financial Mathematics
1 content identifier

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