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Vectors

HSC HSC Mathematics Extension 1 · 2024 content registry · first HSC 2027

Official NSW Curriculum syllabus and implementation timeline ↗Download questions and solutions PDF
ME-V1
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.

Teacher check

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

3 deterministic examples

Vectors 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

1 markext1-v1-1
Dot product Let bold(u)=(2,−1)bold(u)=(2,-1) and bold(v)=(3,2)bold(v)=(3,2).
Part a · 1 mark

Calculate bold(u)dotbold(v)bold(u) dot bold(v).

Worked solution

Answer: 4

  1. Dot Product: 4

Catalog reference: ext1_sgs25_vector_dot_product · seed 41001

Worked example 2

2 marksext1-v1-1
Magnitude of a vector sum Let bold(u)=(15,36)bold(u)=(15,36) and bold(v)=(9,9)bold(v)=(9,9).
Part a · 2 marks

Calculate abs(bold(u)+bold(v))abs(bold(u)+bold(v)).

Worked solution

Answer: sqrt(2601)

  1. Vector Addition: [24,45]
  2. Vector Magnitude: sqrt(2601)

Catalog reference: ext1_cssa25_vector_sum_magnitude · seed 41001

Worked example 3

2 marksext1-v1-4
Canister fall time A canister is released horizontally from 240 metres above the water. Its vertical position is y=240−5t2y=240-5t^2. How long does it take to hit the water?
Part a · 2 marks

Find the positive time in seconds.

Worked solution

Answer: sqrt(48)

  1. Set Height Zero: 0=240−5t20=240-5t^2.
  2. Positive Square Root: t=sqrt(24s)t=sqrt(24{{s}}).

Catalog reference: ext1_nsb_2025_q13c_i_projectile_fall_time · seed 41001

Content mapping and common errors

Vectors content identifiers

ME-V1

Introduction to Vectors

Represent vectors in two dimensions; perform vector arithmetic; resolve vectors into components; apply to geometric proofs and motion.

Common student mistakes
  • ·Confusing column vectors with position vectors
  • ·Incorrect vector subtraction direction
  • ·Forgetting to express magnitude using Pythagoras

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 ↗

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From the blog

Formula sheet
Official NESA HSC Maths Reference Sheets
Reasoning
What Makes an HSC Band 6 Maths Question?
Practice
HSC Maths Past Papers by Topic

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