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VCE Specialist Mathematics

VCE · VCAAMathematics468 cards

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Flashcards for VCE Specialist Mathematics Units 3 and 4 (VCAA), split into the study design's areas of study and then by topic. Follows the Mathematics Study Design, accredited from 2023. Where a formula is given on the exam formula sheet, a card's note says so; otherwise it 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 (21 subdecks)

  • 1 Discrete mathematics50 cards
    • 1.1 Logic and proof50 cards
  • 2 Functions, relations and graphs43 cards
    • 2.1 Rational and quotient functions43 cards
  • 3 Algebra, number and structure55 cards
    • 3.1 Complex numbers55 cards
  • 4 Calculus123 cards
    • 4.1 Differential calculus and integral calculus64 cards
      • 4.1.1 Differentiation28 cards
      • 4.1.2 Integration and applications36 cards
    • 4.2 Differential equations27 cards
    • 4.3 Kinematics: rectilinear motion32 cards
  • 5 Space and measurement108 cards
    • 5.1 Vectors50 cards
    • 5.2 Vector and Cartesian equations31 cards
    • 5.3 Vector calculus27 cards
  • 6 Data analysis, probability and statistics89 cards
    • 6.1 Distribution of linear combinations of random variables20 cards
    • 6.2 Distribution of the sample mean14 cards
    • 6.3 Confidence intervals for the population mean25 cards
    • 6.4 Hypothesis testing for a population mean30 cards

Some of its cards

  • What is the null hypothesis, H0H_0, in a hypothesis test?
    A single specific value proposed for the population parameter, assumed true unless the evidence says otherwise.
  • What is a confidence interval for a population mean?
    A range of values, calculated from a sample, likely to contain the true population mean.
  • For a random variable X1X_1 with mean μ\mu, what is E(aX1+b)E(aX_1+b)?
    aμ+ba\mu+b
  • What is a conjecture in mathematics?
    A statement proposed as possibly true, which is then proved or disproved.
  • What is a differential equation?
    An equation relating a function to one or more of its derivatives.
  • What does the position vector r(t)\mathbf{r}(t) describe as tt varies?
    The path traced out by a moving point, as a function of time.
  • What is a vector equation of a curve in terms of a parameter tt?
    r(t)=x(t)i+y(t)j(+z(t)k)\mathbf{r}(t)=x(t)\mathbf{i}+y(t)\mathbf{j}(+z(t)\mathbf{k}), giving the position vector at each value of tt.
  • On a velocity-time graph, what does the area between the graph and the time axis represent?
    The change in displacement, signed, so area below the axis counts as negative.
  • What does the sign of f′(x)f'(x) over an interval tell you about ff?
    Where f′(x)>0f'(x)>0, ff is increasing; where f′(x)<0f'(x)<0, ff is decreasing.
  • What is a rational function?
    A function that can be written as the quotient of two polynomials, P(x)Q(x)\frac{P(x)}{Q(x)}.

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