Math Methods flashcards

43 TCE Math Methods cards across 2 modules (5 definitions, 26 key facts, 1 fill-the-gap, 11 formulas). Each session gives you 20 cards, due cards first. Swipe right for easy, left for hard, down for again. Keyboard: Space to flip, 1 to 4 to rate.

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Definition
Discrete random variables and the binomial distribution - TCE Mathematics Methods (Tasmania)
Define Conditions for a binomial distribution
There are a fixed number $n$ of trials; each trial has only two outcomes (success or failure); the probability of success $p$ is constant across trials; and the trials are independent.
Definition
Interval estimates and confidence intervals - TCE Mathematics Methods (Tasmania)
Define What "95% confidence" means
If you repeated the whole sampling process many times and built an interval each time, about 95% of those intervals would contain the true proportion $p$ .
Definition
Exponential and logarithmic functions (TCE Mathematics Methods, Tasmania)
Define The natural base e
$e \approx 2.71828$ is the base for which the curve $y = e^x$ has gradient exactly equal to its own height at every point.
Definition
Random sampling and the distribution of sample proportions (TCE Mathematics Methods, Tasmania)
Define The normal approximation
For a large random sample, the sampling distribution of $\hat{p}$ is approximately normal, centred at $p$ with standard deviation $\sqrt{p(1-p)/n}$ .
Definition
The second derivative, concavity and points of inflection (TCE Mathematics Methods, Tasmania)
Define Concave up and concave down
A curve is concave up on an interval if it bends upward like a cup, so the gradient is increasing and $f''(x)>0$ .
Key fact
Antiderivatives of exponential and trigonometric functions (TCE Mathematics Methods, Tasmania)
Tell me about Checking by differentiating back
The reliable way to confirm any antiderivative is to differentiate your answer and check you recover the original integrand. For instance, differentiating $-\tfrac{1}{3}\cos(3x)$ gives $-\tfrac{1}{3}\cdot(-3\sin(3x)) = \sin(3x)$ , which confirms the antiderivative of $\sin(3x)$ .
Fill the gap
Further differentiation and applications (TCE Mathematics Methods, Tasmania)
To classify them, use the ___: if $f''(x) > 0$ the point is a local minimum, if $f''(x) < 0$ it is a local maximum.
To classify them, use the second derivative: if $f''(x) > 0$ the point is a local minimum, if $f''(x) < 0$ it is a local maximum.
Key fact
Areas between two curves (TCE Mathematics Methods, Tasmania)
Tell me about Finding the limits
The limits are almost never given directly; you find them by setting the curves equal. Solve $f(x) = g(x)$ to find where the curves meet.
Key fact
Differentiation of trigonometric functions (TCE Mathematics Methods, Tasmania)
Tell me about Combining with the chain rule
The inner derivative is exactly the factor students most often drop.
Key fact
Continuous random variables and the normal distribution - TCE Mathematics Methods (Tasmania)
Tell me about Standardising to z-scores
Every normal distribution can be converted to the standard normal $Z \sim N(0,1)$ by standardising. This measures how many standard deviations $x$ is from the mean.