Math Methods flashcards

What this deck covers

• Topic 1: Further Differentiation and Applications (24 cards, 5 dot points)

  • Curve sketching with derivatives (SACE Stage 2 Mathematical Methods) (5)
  • Optimisation problems (SACE Stage 2 Mathematical Methods) (5)
  • The chain rule (SACE Stage 2 Mathematical Methods) (5)
  • The product and quotient rules (SACE Stage 2 Mathematical Methods) (5)
  • The second derivative and concavity (SACE Stage 2 Mathematical Methods) (4)
• Topic 2: Discrete Random Variables (17 cards, 3 dot points)

  • Discrete random variables and distributions (SACE Stage 2 Mathematical Methods) (5)
  • Expected value and variance (SACE Stage 2 Mathematical Methods) (5)
  • The Bernoulli and binomial distributions (SACE Stage 2 Mathematical Methods) (7)
• Topic 3: Integral Calculus (19 cards, 4 dot points)

  • Antidifferentiation (SACE Stage 2 Mathematical Methods) (5)
  • Area under a curve (SACE Stage 2 Mathematical Methods) (5)
  • Areas between curves (SACE Stage 2 Mathematical Methods) (4)
  • The definite integral and Fundamental Theorem (SACE Stage 2 Mathematical Methods) (5)
• Topic 4: Logarithmic Functions (18 cards, 4 dot points)

  • Derivatives of exponential and log functions (SACE Stage 2 Mathematical Methods) (5)
  • Graphs of logarithmic functions (SACE Stage 2 Mathematical Methods) (4)
  • Solving exponential equations (SACE Stage 2 Mathematical Methods) (3)
  • The laws of logarithms (SACE Stage 2 Mathematical Methods) (6)
• Topic 5: Continuous Random Variables and the Normal Distribution (14 cards, 3 dot points)

  • Continuous random variables and PDFs (SACE Stage 2 Mathematical Methods) (5)
  • The normal distribution (SACE Stage 2 Mathematical Methods) (5)
  • Z-scores and normal probabilities (SACE Stage 2 Mathematical Methods) (4)
• Topic 6: Sampling and Confidence Intervals (16 cards, 3 dot points)

  • Confidence intervals for a mean (SACE Stage 2 Mathematical Methods) (4)
  • Margin of error and sample size (SACE Stage 2 Mathematical Methods) (7)
  • Sample means and sampling distributions (SACE Stage 2 Mathematical Methods) (5)

Sample cards from this deck

1. Definition

   Curve sketching with derivatives (SACE Stage 2 Mathematical Methods)

   Define Intercepts

   Find the $y$-intercept by evaluating $f(0)$, and $x$-intercepts by solving $f(x)=0$ where practical.

2. Definition

   Discrete random variables and distributions (SACE Stage 2 Mathematical Methods)

   Define Discrete random variable

   A discrete random variable $X$ is a variable whose possible values form a countable set $\{x_1, x_2, \dots\}$, where each value $x_i$ occurs with a known probability $P(X=x_i)$.

3. Fill the gap

   Antidifferentiation (SACE Stage 2 Mathematical Methods)

   To ___ is to undo differentiation - to find a function $F(x)$ whose derivative is the given function $f(x)$.

   To antidifferentiate is to undo differentiation - to find a function $F(x)$ whose derivative is the given function $f(x)$.

4. Definition

   Graphs of logarithmic functions (SACE Stage 2 Mathematical Methods)

   Define Domain

   $x>0$ (you cannot take the log of zero or a negative number).

5. Fill the gap

   Continuous random variables and PDFs (SACE Stage 2 Mathematical Methods)

   A ___ can take any value in a range - a height, a time, a mass - not just a list of separate values.

   A continuous random variable can take any value in a range - a height, a time, a mass - not just a list of separate values.

6. Definition

   Margin of error and sample size (SACE Stage 2 Mathematical Methods)

   Define Confidence level

   Confidence level ($z^*$): higher confidence ⇒ larger $z^*$ ⇒ larger $E$.

7. Definition

   The second derivative and concavity (SACE Stage 2 Mathematical Methods)

   Define Concavity

   A curve is concave up on an interval if $f''(x)>0$ throughout (it curves like a cup, gradient increasing) and concave down if $f''(x)<0$ (it curves like a cap, gradient decreasing).

8. Definition

   The Bernoulli and binomial distributions (SACE Stage 2 Mathematical Methods)

   Define Bernoulli random variable

   A Bernoulli random variable takes the value $1$ (success) with probability $p$ and $0$ (failure) with probability $1-p$.

9. Fill the gap

   Area under a curve (SACE Stage 2 Mathematical Methods)

   The definite integral $\int_a^b f(x)\,dx$ measures ___: regions above the x-axis count positively and regions below count negatively.

   The definite integral $\int_a^b f(x)\,dx$ measures signed area: regions above the x-axis count positively and regions below count negatively.

10. Definition

    The laws of logarithms (SACE Stage 2 Mathematical Methods)

    Define Logarithm

    The logarithm and the exponential are inverse operations.