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Level 1 - Math II (Physics)
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Probability
Vectors
Kinematics
ODEs
Fourier
Multivariable
Multivariable Functions
Graphs
Partial Derivatives
Higher Partial Derivatives
Clairaut Theorem
Differentials
Exact Differentials
Inexact Differentials
Directional Derivatives
Gradient
Multivariable Chain Rule
Single-Parameter Chain Rule
Multi-Parameter Chain Rule
Taylor Expansions
Critical Points
Two-Dimensional Critical Points
n-Dimensional Critical Points
PDEs
Vector Calculus
Integrals
Complex Analysis
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Questions
Question 1
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What is the main purpose of Graphs?
Question 2
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What does \(x,y\) mean in Graphs?
Question 3
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Identify another important piece of notation used in Graphs.
Question 4
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Before doing a graphs calculation, what setup information should be written down?
Question 5
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State a central formula or test for Graphs.
Question 6
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How is the formula or method in Graphs interpreted rather than just memorised?
Question 7
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For V(x,y)=x^2+y^2, describe the surface and the level curve V=4.
Question 8
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For T(x,y)=10+x+2y, find the level curve where T=16.
Question 9
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What method choice is usually needed in a standard graphs question?
Question 10
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Use the notation of Graphs to explain what is being calculated or tested.
Question 11
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What does it mean when contour lines for pressure are close together?
Question 12
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What physical or modelling interpretation can Graphs have?
Question 13
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Correct this mistake in Graphs: thinking a contour is the graph height.
Question 14
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Why is it important to check assumptions when using Graphs?
Question 15
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Correct this second mistake in Graphs: comparing slopes without axis scales.
Question 16
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What units, dimensions, or variable-dependence check is useful in Graphs?
Question 17
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Correct this third mistake in Graphs: ignoring units on the output.
Question 18
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Design an exam solution plan for a multi-step graphs problem.
Question 19
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How could an incorrect setup affect a graphs result?
Question 20
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Give an exam-ready summary rule for Graphs.