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VCE Mathematical Methods

VCE · VCAAMathematics465 cards

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Flashcards for VCE Mathematical Methods Units 3 and 4 (VCAA), split into the study design's four areas of study and then by topic within each area: graphs and functions, algebra, calculus, then probability and statistics. A card says whether a formula is on the exam 1 formula 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 (45 subdecks)

  • Algebra, number and structure70 cards
    • 2.1 Inverse functions10 cards
    • 2.2 Composition of functions6 cards
    • 2.3 Solving polynomial equations12 cards
    • 2.4 Exponential and logarithmic equations12 cards
    • 2.5 Circular function equations10 cards
    • 2.6 Simultaneous and literal equations12 cards
    • 2.7 Newton's method and graphical solutions8 cards
  • Calculus136 cards
    • 3.1 Limits and continuity7 cards
    • 3.2 The derivative and differentiability9 cards
    • 3.3 Derivatives of standard functions23 cards
    • 3.4 The chain rule7 cards
    • 3.5 The product rule6 cards
    • 3.6 The quotient rule6 cards
    • 3.7 The graph of a derivative and an antiderivative8 cards
    • 3.8 Stationary points and increasing and decreasing functions13 cards
    • 3.9 Optimisation8 cards
    • 3.10 Anti-differentiation19 cards
    • 3.11 The definite integral and the fundamental theorem of calculus10 cards
    • 3.12 The trapezium rule8 cards
    • 3.13 Applications of integration12 cards
  • Data analysis, probability and statistics90 cards
    • 4.1 Random variables7 cards
    • 4.2 Discrete random variables and probability mass functions9 cards
    • 4.3 Mean, variance and standard deviation of a discrete random variable8 cards
    • 4.4 The binomial distribution16 cards
    • 4.5 Continuous random variables and probability density functions10 cards
    • 4.6 Mean, variance and standard deviation of a continuous random variable8 cards
    • 4.7 The normal distribution13 cards
    • 4.8 Sample proportions9 cards
    • 4.9 Confidence intervals for a population proportion10 cards
  • Functions, relations and graphs169 cards
    • 1.1 Functions and function notation11 cards
    • 1.2 Domain, codomain and range10 cards
    • 1.3 Polynomial functions and their graphs15 cards
    • 1.4 Power functions17 cards
    • 1.5 Transformations of graphs15 cards
    • 1.6 Radians and the unit circle15 cards
    • 1.7 Exact values of circular functions21 cards
    • 1.8 Graphs of circular functions14 cards
    • 1.9 Exponential functions and their graphs15 cards
    • 1.10 Logarithmic functions and their graphs14 cards
    • 1.11 Combining functions: sums, products and composites12 cards
    • 1.12 Modelling with functions10 cards

Some of its cards

  • What is a probability mass function?
    A function that gives the probability that a discrete random variable takes each of its possible values.
  • What is sin⁡(π6)\sin\left(\dfrac{\pi}{6}\right)?
    12\dfrac{1}{2}
  • What is the quotient rule, for y=uvy = \dfrac{u}{v} where uu and vv are functions of xx?
    dydx=vdudx−udvdxv2\dfrac{dy}{dx} = \dfrac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}
  • What is one radian?
    The angle subtended at the centre of a circle by an arc equal in length to the radius.
  • At a point where the graph of y=f(x)y = f(x) has a local maximum, what value does the graph of y=f′(x)y = f'(x) take?
    Zero: the graph of f′f' crosses the xx-axis there.
  • How do you find the area between the curve y=f(x)y = f(x) and the xx-axis on [a,b][a,b], when f(x)≥0f(x) \geq 0 throughout?
    ∫abf(x) dx\int_a^b f(x)\,dx
  • What condition must a function satisfy for its inverse to be a function?
    It must be one-to-one.
  • What is a literal equation?
    An equation involving more than one pronumeral, solved for one variable in terms of the others.
  • What are the mean and standard deviation of the standard normal distribution N(0,1)N(0,1)?
    Mean 00, standard deviation 11
  • What is a random variable?
    A function that assigns a real number to each outcome in a sample space.

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