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Differentiation: lesson checks flashcards

This deck has 7 check-yourself questions and 6 spot-the-error cards. The misconception each lesson corrects, and its check-yourself question with the worked answer. Rate each answer, and the card comes back sooner or later depending on how you rated it.

Years 12–13 · all 584 maths cards

How the five kinds differ

Standard results ask you to recall a formula or a value. Definitions ask you to state a mathematical term precisely. Recall prompts ask for a rule, condition or method. Check yourself cards are a short question with its answer. Spot the error cards ask you to correct a statement that is wrong.

Every card in this deck

Choose any card to try it in the player above. Each card links to the lesson that teaches it.

• The gradient of a curve at a point is the gradient of the line to a nearby point.Spot the error
• From first principles, find the gradient of y = 3x² at the point (2, 12).Check
• To differentiate a product, differentiate each factor.Spot the error
• Differentiate y = x⁴ − 2/√x + 7, and evaluate the gradient at x = 1.Check
• f''(x) = 0 means x is a point of inflection.Spot the error
• The curve y = x³ − 12x has two stationary points. Find and classify them, and state the interval on which the curve is decreasing.Check
• Differentiate y = 3 ln x − cos 4x, and find the gradient at x = π/4.Check
• The derivative of a quotient is the quotient of the derivatives.Spot the error
• Differentiate y = x² ln x, and find the gradient where x = e.Check
• You cannot differentiate a curve that will not give you y = f(x).Spot the error
• The curve C is given by y² + 2xy = 8. Find dy/dx in terms of x and y, and the gradient of C at (1, 2).Check
• If two quantities are linked, their rates of change are equal.Spot the error
• The area of a circular oil slick grows at a steady 12 m² per hour. Find the rate at which the radius grows when r = 6 m.Check

The lessons these cards come from

• Differentiating powers of x
• Differentiating trig, exponentials and logs
• Implicit and parametric differentiation
• Rates of change and building differential equations
• Tangents, turning points and curve behaviour
• The derivative from first principles
• The product, quotient and chain rules

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