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Mathematics Advanced

Stage 6 · HSC questions by topic

About this subject

Mathematics Advanced

Atlas organises human-reviewed questions against the NSW Stage 6 Mathematics Advancedsyllabus. Every published question retains its exam source and page.

Syllabus: NESA Stage 6 (2017)
Explore the NESA Stage 6 (2017) syllabus topics

Functions

  • Working with Functions
  • Graphing Techniques

Trigonometric Functions

  • Trigonometry and Measure of Angles
  • Trigonometric Functions and Identities
  • Trigonometric Functions and Graphs

Calculus

  • Introduction to Differentiation
  • Differential Calculus
  • Applications of Differentiation
  • Integral Calculus

Exponential and Logarithmic Functions

  • Logarithms and Exponentials

Statistical Analysis

  • Probability and Discrete Probability Distributions
  • Descriptive Statistics and Bivariate Data Analysis
  • Random Variables

Financial Mathematics

  • Modelling Financial Situations
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2025HSC
Q15 (b)

A sound wave can be modelled using a function P(t)=ksin⁡(at)P(t)=k\sin(at)P(t)=ksin(at), where PPP is air pressure in Pascals, is time in milliseconds (ms) and and are constants.

ttt
kkk
aaa

The graph of P1(t)P_1(t)P1​(t) from part (a) is shown.

On the diagram, sketch the graph of

P2(t)=4sin⁡(π10t)P_2(t)=4\sin\left(\frac{\pi}{10}t\right)P2​(t)=4sin(10π​t)

for 0≤t≤100\leq t\leq100≤t≤10.

2 marks
Short answer