

Understanding Necessary and Sufficient Conditions
Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Liam Anderson
FREE Resource
Standards-aligned
Read more
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean when we say 'P is necessary for Q'?
If P, then Q
If Q, then P
P and Q are independent
P is not related to Q
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does 'P is sufficient for Q' imply?
P and Q are independent
If Q, then P
If P, then Q
P is not related to Q
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of necessary and sufficient conditions, what does 'P if and only if Q' mean?
P and Q are unrelated
P is both necessary and sufficient for Q
P is sufficient for Q
P is necessary for Q
Tags
CCSS.8.F.A.3
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of calculus, what is true if a function is differentiable at a point?
It must be undefined at that point
It must be non-differentiable at that point
It must be continuous at that point
It must be discontinuous at that point
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is an example of a function that is continuous but not differentiable at a point?
f(x) = e^x
f(x) = x^2
f(x) = |x|
f(x) = sin(x)
Tags
CCSS.8.F.A.3
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the function f(x) = |x| not differentiable at x = 0?
It has a discontinuity at x = 0
It has a sharp corner at x = 0
It is not defined at x = 0
It is a linear function
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is necessary for a function to be differentiable at a point?
The function must be linear at that point
The function must be undefined at that point
The function must be non-continuous at that point
The function must be continuous at that point
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