Flashcards and recall.

Try this with Mathematical Methods

1. Write one prompt per card. Use definitions, explanations or examples from your current topic.
2. Answer aloud before turning the card. Split a card if it asks for several unrelated facts.
3. Set aside missed cards and revisit them in a later session.

View Mathematical Methods resources on ATARMAXXING ↗

Recall topics

• State the law: log_a(mn)
• State the law: log_a(m/n)
• State the law: log_a(mⁿ)
• State the law: a^(log_a(x))
• State the law: log_a(a^x)
• Exact value: sin(0°), sin(30°), sin(45°), sin(60°), sin(90°)
• Exact value: cos(0°), cos(30°), cos(45°), cos(60°), cos(90°)
• Exact value: tan(0°), tan(30°), tan(45°), tan(60°)
• Derivative: d/dx[e^(f(x))]
• Derivative: d/dx[ln(f(x))]
• Derivative: d/dx[sin(f(x))]
• Derivative: d/dx[cos(f(x))]
• Derivative: d/dx[tan(f(x))]
• State the chain rule
• State the product rule: d/dx[u(x)·v(x)]
• State the quotient rule: d/dx[u(x)/v(x)]
• Condition for stationary points
• Nature of stationary point: if f''(x) < 0
• Nature of stationary point: if f''(x) > 0
• Second derivative test: concavity when f''(x) > 0
• Second derivative test: concavity when f''(x) < 0
• Binomial probability formula: P(X = k)
• E(X) for a binomial distribution X ~ B(n, p)
• Var(X) for a binomial distribution X ~ B(n, p)
• E(X) for a general discrete distribution
• Var(X) for a general discrete distribution
• Definition of a Bernoulli trial
• Antiderivative: ∫xⁿ dx
• Antiderivative: ∫e^(ax+b) dx
• Kinematic relationships: v = ?, a = ?
• What does a probability density function (PDF) require?
• How do you calculate E(X) for a continuous random variable?
• What is the formula for Var(X) using E(X²)?
• Write the z-score standardisation formula.
• State three key properties of the normal distribution.
• What is the 68–95–99.7 rule?
• What does σ represent in a normal distribution N(μ, σ²)?
• Describe the trapezoidal rule for numerical integration.
• Write the sine rule for a triangle.
• Write the cosine rule for a triangle (two forms).