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NSW HSC Mathematics Advanced

HSC · NESAMathematics Advanced623 cards

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Flashcards for the NSW HSC Mathematics Advanced 11–12 Syllabus (2024), first examined 2027, split into the syllabus's own areas of study and then by Year 11 and Year 12 focus area. Cards note whether a formula is given on the HSC reference sheet or has to be recalled.

Adding it gives you your own copy, with every subdeck below. Each card then comes back just before you would forget it, and every one you get right or wrong counts towards your mastery of its topic. You can delete or suspend the parts you are not studying once it is yours.

What is inside (68 subdecks)

  • 1. Functions149 cards
    • 1. Working with functions (Year 11)117 cards
      • Absolute value functions6 cards
      • Algebraic techniques37 cards
      • Circles and semicircles6 cards
      • Constructing and using functions5 cards
      • Direct and inverse variation4 cards
      • Introduction to functions and relations12 cards
      • Linear functions11 cards
      • Piecewise-defined functions7 cards
      • Properties of functions, relations and graphs11 cards
      • Quadratic and cubic functions14 cards
      • Reciprocal functions4 cards
    • 2. Graph transformations (Year 11)18 cards
    • 3. Further graph transformations and modelling (Year 12)14 cards
      • Modelling with functions7 cards
      • Transformations of trigonometric functions7 cards
  • 2. Trigonometric functions81 cards
    • 3. Trigonometry and measure of angles (Year 11)39 cards
      • Radians13 cards
      • Trigonometry with acute angles6 cards
      • Trigonometry with angles of any magnitude20 cards
    • 4. Trigonometric identities and equations (Year 11)42 cards
  • 3. Exponential and logarithmic functions39 cards
    • Exponential functions11 cards
    • Logarithmic functions28 cards
  • 4. Sequences and series35 cards
    • Arithmetic sequences and series12 cards
    • Geometric sequences and series17 cards
    • Sequences and series6 cards
  • 5. Calculus188 cards
    • 1. Introduction to differentiation (Year 11)56 cards
      • Calculations with the derivative24 cards
      • Estimating change9 cards
      • Graphical applications of the derivative6 cards
      • The derivative10 cards
      • The derivative as a rate of change7 cards
    • 2. Differential calculus (Year 12)25 cards
      • Differentiation with exponential functions8 cards
      • Differentiation with logarithmic functions5 cards
      • Differentiation with trigonometric functions8 cards
      • Using derivatives4 cards
    • 3. Integral calculus (Year 12)71 cards
      • Areas and the definite integral16 cards
      • Indefinite integrals9 cards
      • Integration with exponential functions8 cards
      • Integration with logarithmic functions6 cards
      • Integration with trigonometric functions8 cards
      • Primitive functions13 cards
      • The definite integral7 cards
      • The Fundamental Theorem of Calculus4 cards
    • 4. Applications of calculus (Year 12)36 cards
      • Optimisation7 cards
      • Rates of change16 cards
      • Turning points, inflections and graphing13 cards
  • 6. Statistical analysis109 cards
    • 1. Probability and data (Year 11)50 cards
      • Conditional probability11 cards
      • Data12 cards
      • Probability16 cards
      • Sets and set notation11 cards
    • 2. Random variables (Year 12)59 cards
      • Continuous random variables27 cards
      • Discrete random variables13 cards
      • The normal distribution19 cards
  • 7. Financial mathematics (Year 12)22 cards
    • Annuities11 cards
    • Reducing balance loans11 cards

Some of its cards

  • Describe the shape of f(x)=kxf(x)=\dfrac{k}{x}, for a constant k≠0k\neq0.
    A hyperbola with asymptotes on the xx-axis and yy-axis
  • What is an annuity?
    An investment plan built from equal regular deposits with interest added at the end of each period, or a lump sum from which equal regular withdrawals are made
  • What does f′(c)f'(c) represent, as a rate?
    The instantaneous rate of change of f(x)f(x) at x=cx=c
  • Differentiate y=xexy=xe^x using the product rule.
    y′=ex+xexy'=e^x+xe^x
  • How do you calculate a definite integral once you know a primitive F(x)F(x) of f(x)f(x)?
    ∫abf(x) dx=F(b)−F(a)\displaystyle\int_a^b f(x)\,dx=F(b)-F(a)
  • Define conditional probability P(A∣B)P(A|B).
    The probability that event AA occurs, given that event BB has already occurred
  • When is a function f(x)f(x) differentiable at x=ax=a?
    When lim⁡h→0f(a+h)−f(a)h\displaystyle\lim_{h\to0}\dfrac{f(a+h)-f(a)}{h} exists, that is, when there is a non-vertical tangent at (a,f(a))(a,f(a))
  • What is ddx(f(x))\dfrac{d}{dx}(f(x))?
    The derivative of f(x)f(x) with respect to xx; also written f′(x)f'(x)
  • What transformation of a graph does replacing xx by −x-x in its equation give?
    A reflection in the yy-axis
  • Denote the probability that a discrete random variable XX takes the value xx.
    P(X=x)P(X=x), or P(x)P(x) if XX is understood

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