List

Differentiation and Integration

Mind your \Ps and \Qs
problem

Mind your Ps and Qs

Age
16 to 18
Challenge level
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Sort these mathematical propositions into a series of 8 correct statements.
Implicitly
problem

Implicitly

Age
16 to 18
Challenge level
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Can you find the maximum value of the curve defined by this expression?
Integration matcher
problem

Integration matcher

Age
16 to 18
Challenge level
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Can you match the charts of these functions to the charts of their integrals?
Brimful
problem

Brimful

Age
16 to 18
Challenge level
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Can you find the volumes of the mathematical vessels?
Brimful 2
problem

Brimful 2

Age
16 to 18
Challenge level
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Which of these infinitely deep vessels will eventually full up?
The right volume
problem

The right volume

Age
16 to 18
Challenge level
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Can you rotate a curve to make a volume of 1?
Calculus Countdown
problem

Calculus Countdown

Age
16 to 18
Challenge level
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Can you hit the target functions using a set of input functions and a little calculus and algebra?
Trig Trig Trig
problem

Trig Trig Trig

Age
16 to 18
Challenge level
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Can you make sense of this combination of trig functions?
Gradient match
problem

Gradient match

Age
16 to 18
Challenge level
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What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?
Turning to calculus
problem

Turning to calculus

Age
16 to 18
Challenge level
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Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.
Calculus analogies
problem

Calculus analogies

Age
16 to 18
Challenge level
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Consider these analogies for helping to understand key concepts in calculus.
The sign of the times
problem

The sign of the times

Age
16 to 18
Challenge level
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Can you make sense of this relationship between function and derivative?
Patterns of inflection
problem

Patterns of inflection

Age
16 to 18
Challenge level
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Find the relationship between the locations of points of inflection, maxima and minima of functions.
Curve Hunter
problem

Curve Hunter

Age
14 to 18
Challenge level
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This problem challenges you to sketch curves with different properties.