Math Methods flashcards

What this deck covers

• Unit 1: Functions, relations and graphs (64 cards, 12 dot points)

  • Algebra, indices and equations: VCE Math Methods Unit 1 Year 11 (6)
  • Cubic and quartic polynomials (VCE Maths Methods Unit 1) (3)
  • Factor and remainder theorems (VCE Maths Methods Unit 1) (3)
  • Functions, relations and graphs: VCE Math Methods Unit 1 Year 11 (5)
  • Inverse and composite functions (VCE Maths Methods Unit 1) (5)
  • Linear functions and graphs (VCE Maths Methods Unit 1) (4)
  • Probability and counting: VCE Math Methods Unit 1 Year 11 (7)
  • Probability rules and combinations (VCE Maths Methods Unit 1) (7)
  • Quadratic functions and parabolas (VCE Maths Methods Unit 1) (6)
  • Rates of change and the derivative: VCE Math Methods Unit 1 Year 11 (7)
  • Surds and rational exponents (VCE Maths Methods Unit 1) (7)
  • Transformations of functions (VCE Maths Methods Unit 1) (4)
• Unit 2 (53 cards, 12 dot points)

  • Antidifferentiation introduction: VCE Math Methods Unit 2 Year 11 (5)
  • Applications of differentiation (VCE Maths Methods Unit 2) (2)
  • Bernoulli trials, sample data and simulation: VCE Math Methods Unit 2 Year 11 (7)
  • Circular functions extended (VCE Maths Methods Unit 2) (3)
  • Derivatives of exponential and logarithmic functions (VCE Maths Methods Unit 2) (4)
  • Derivatives of trigonometric functions (VCE Maths Methods Unit 2) (4)
  • Discrete random variables, expected value and variance (VCE Maths Methods Unit 2) (5)
  • Exponential functions and graphs (VCE Maths Methods Unit 2) (3)
  • Inverse and composite functions: VCE Math Methods Unit 2 Year 11 (6)
  • Logarithmic functions and equations (VCE Maths Methods Unit 2) (4)
  • The binomial distribution (VCE Maths Methods Unit 2) (4)
  • Trigonometric functions: VCE Math Methods Unit 2 Year 11 (6)
• Unit 3 (63 cards, 13 dot points)

  • Bernoulli trials and the binomial distribution: VCE Math Methods Unit 3 (6)
  • Circular (trig) functions and graphs: VCE Math Methods Unit 3 (5)
  • Differentiation from first principles (Unit 2 assumed knowledge): VCE Math Methods (6)
  • Differentiation rules and standard derivatives: VCE Math Methods Unit 3 (4)
  • Discrete random variables: VCE Math Methods Unit 3 (5)
  • Exponential and logarithmic functions: VCE Math Methods Unit 3 (2)
  • Factor and remainder theorems: VCE Math Methods Unit 3 (3)
  • Optimisation and rates of change: VCE Math Methods Unit 3 (5)
  • Polynomial, power and modulus functions: VCE Math Methods Unit 3 (6)
  • Probability, conditional probability and independence: VCE Math Methods Unit 3 (6)
  • Solving polynomial, exponential, logarithmic and circular equations: VCE Math Methods Unit 3 (4)
  • Tangents, stationary points and curve sketching: VCE Math Methods Unit 3 (6)
  • Transformations, composite and inverse functions: VCE Math Methods Unit 3 (5)
• Unit 4 (59 cards, 11 dot points)

  • Anti-differentiation by recognition (reverse chain rule): VCE Math Methods Unit 4 (5)
  • Antidifferentiation and indefinite integrals: VCE Math Methods Unit 4 (5)
  • Area under and between curves: VCE Math Methods Unit 4 (6)
  • Average value and applications of integration: VCE Math Methods Unit 4 (4)
  • Confidence intervals for a population proportion: VCE Math Methods Unit 4 (6)
  • Continuous random variables: VCE Math Methods Unit 4 (5)
  • Definite integration and the fundamental theorem: VCE Math Methods Unit 4 (5)
  • Hybrid functions and inverse functions: VCE Math Methods Unit 4 (7)
  • Related rates of change (Specialist Mathematics content): notes for VCE Math Methods (2)
  • Sample proportions and sampling distributions: VCE Math Methods Unit 4 (7)
  • The normal distribution: VCE Math Methods Unit 4 (7)

Sample cards from this deck

1. Definition

   Algebra, indices and equations: VCE Math Methods Unit 1 Year 11

   Define Linear

   Single step or simple multi-step manipulation.

2. Definition

   Inverse and composite functions: VCE Math Methods Unit 2 Year 11

   Define Solve for $y$

   4. Write $f^{-1}(x) = $ (the solved expression).

3. Definition

   Bernoulli trials and the binomial distribution: VCE Math Methods Unit 3

   Define Bernoulli trial

   Bernoulli trial is a single experiment with exactly two outcomes (commonly called "success" and "failure"), where the probability of success is some fixed $p$ (and probability of failure is $1 - p$).

4. Definition

   Area under and between curves: VCE Math Methods Unit 4

   Define If you want the geometric area (always non-negative)

   1. Find where $f$ changes sign on $[a, b]$. Solve $f(x) = 0$ to get the roots; check which lie inside $(a, b)$.

5. Definition

   Rates of change and the derivative: VCE Math Methods Unit 1 Year 11

   Define Normal

   Perpendicular to the tangent at the same point.

6. Definition

   Bernoulli trials, sample data and simulation: VCE Math Methods Unit 2 Year 11

   Define Bernoulli sequence

   Bernoulli sequence is $n$ independent Bernoulli trials with the same success probability $p$.

7. Definition

   Circular (trig) functions and graphs: VCE Math Methods Unit 3

   Define Amplitude

   $= |a|$. Vertical dilation by factor $|a|$; reflection in the x-axis if $a < 0$.

8. Definition

   Confidence intervals for a population proportion: VCE Math Methods Unit 4

   Define Margin of error (MoE)

   $z^* \times \text{SE}$, the half-width of the interval.

9. Definition

   Functions, relations and graphs: VCE Math Methods Unit 1 Year 11

   Define Linear

   $y = mx + c$. Gradient $m$, $y$-intercept $c$. Sketched as a straight line.

10. Definition

    Trigonometric functions: VCE Math Methods Unit 2 Year 11

    Define Equations with composite argument

    Equations with composite argument (like $\sin(2x) = 1/2$): solve for the composite first, then divide by the coefficient and adjust the range accordingly.