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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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3 questions found

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2025HSC
Q3

What is the domain of the function y=6−x2y=\sqrt{6-x^2}y=6−x2? A. B. C. D.

​

(0,6)(0,\sqrt{6})(0,6​)

[0,6][0,\sqrt{6}][0,6​]

(−6,6)(-\sqrt{6},\sqrt{6})(−6​,6​)

[−6,6][-\sqrt{6},\sqrt{6}][−6​,6​]
1 mark
Multiple choice
2025HSC
Q11 (a)

The graph of a quadratic function represented by the equation h=t2−8t+12h=t^2-8t+12h=t2−8t+12 is shown.

Find the values of ttt and hhh at the turning point of the graph.

[Visual: A graph of the parabola h=t2−8t+12h=t^2-8t+12h=t2−8t+12, with hhh on the vertical axis and ttt on the horizontal axis. The graph crosses the -axis at and , and the -axis at .]

2 marks
Short answer
2025HSC
Q11 (b)

The graph of a quadratic function represented by the equation h=t2−8t+12h=t^2-8t+12h=t2−8t+12 is shown.

The graph shows h=12h=12h=12 when t=0t=0t=0.

What is the other value of ttt for which h=12h=12h=12?

[Visual: A graph of the parabola h=t2−8t+12h=t^2-8t+12h=t2−8t+12, with hhh on the vertical axis and ttt on the horizontal axis. The graph crosses the -axis at and , and the -axis at .]

1 mark
Short answer
tt
t
t=2t=2t=2
t=6t=6t=6
hhh
h=12h=12h=12
tt
t
t=2t=2t=2
t=6t=6t=6
hhh
h=12h=12h=12