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

• What distinguishes e among positive exponential bases in the limit (a^h−1)/h as h approaches zero?
• How do you differentiate y=7e^(−2x)?
• For N(t)=120e^(0.03t), what does N′(t)/N(t) represent?
• What is the tangent to y=e^x at x=0?
• How does a horizontal shift affect the derivative of y=e^(x−4)?
• Why is d/dx(e^(3x)) not simply e^(3x)?
• For A(t)=80e^(−0.2t), find the initial amount and initial rate of change.
• Does a positive exponential decay model reach zero at a finite time?
• If y′=ky and y is positive, how does the sign of k affect the model?
• What angle convention is required for d/dx(sin x)=cos x?
• Differentiate y=4sin(3x−1).
• Differentiate y=5cos(2t)+7 and interpret the constant term.
• What are the slope and tangent equation for y=sin x at x=π/2?
• For h(t)=6+2sin(πt/4), what is the period?
• Find the greatest positive rate of change of h(t)=6+2sin(πt/4).
• For position s(t)=3cos(2t), state velocity and acceleration.
• How do you find intervals of increase for a sinusoidal model on a stated domain?
• Why does a sinusoidal model have zero rate at its highest and lowest levels?
• Differentiate y=sin x+cos x and find its slope at x=0.
• State the product rule and explain why multiplying derivatives is incorrect.
• Differentiate y=xe^x.
• Differentiate y=x sin x.
• State the quotient rule for y=u/v.
• Differentiate y=(x+1)/(x−1), retaining the domain restriction.
• What is the chain rule for y=f(g(x))?
• Differentiate y=(2x−3)^5.
• Differentiate y=e^(−x)sin x.
• How can the derivative of tan x be obtained from a quotient?
• If y=f(4x−2), how is its derivative expressed in terms of f′?
• What does the second derivative measure geometrically?
• When does the second derivative test establish a local minimum?
• Why is f″(a)=0 not sufficient to establish an inflection point?
• Classify the stationary points of f(x)=x³−3x.
• Locate the inflection point of f(x)=x³−3x.
• How should endpoints be handled in a closed-interval optimisation problem?
• A rectangle has perimeter 20. How do you prove its maximum area is 25?
• Can an object have zero velocity and nonzero acceleration?
• What should a derivative-based curve sketch show beyond stationary points?
• What does the average rate of change of f over [a,b] measure, when a<b?
• Derive the derivative of x² from first principles.