Standards to be learned / assessed during Unit 1
*If a standard does not have a 'Calculator OK' designation, it is assumed the standard must be demonstrated without the use of a grapher*
Corresponding Basic Skills which are required for the Standard
*Some Standards will not have previous skills necessary.
1.1 -- I understand the purpose and contextual meaning of a tangent line to a curve.
(specifically, I can explain the difference between an INSTANTANEOUS rate of change and an AVERAGE rate of change.)
1.2 -- I understand there exists (and can use) an equation which can be used to find the slope of a tangent line at any point on a continuous curve. (this standard will not be specifically assessed)
**This equation is called the derivative function**
1.3 -- I am comfortable with all of the different notations which can (and will) be used to represent the instantaneous rate of change equation. (this standard will not be specifically assessed)
1.4 -- I can use the f function and it's f' function to write the equations of tangent lines
Standards 1.5 thru 1.7 are basically the same idea with different demonstrations
1.5 -- I can use a function's graph (the f(x) graph) to sketch the graph of the function's derivative graph (the f'(x) graph)
1.6 -- I can use the f'(x) graph to determine features of the corresponding f(x) graph
1.7 -- I can use the f'(x) equation to determine features of the corresponding f(x) graph
1.8 -- I can match the graph of f with the graph of f' with the graph of f''
Standards 1.9 thru 1.11 are seemingly unconnected to our previous standards, but will be paramount to your understanding and ability to demonstrate standards 1.12 and 1.13
1.9 -- I can determine the limit of a function graphically (as it approaches a point with a finite x - coordinate)
1.10 -- I can determine the limit of a function analytically (analytically means the same, more or less, as algebraically)
1.11 -- I can determine the limit of a function graphically and analytically (as the x values increase without bound ... in other words, as the x approaches infinity)
Understanding of standard 1.9 & 1.10 is absolutely required for the next two important standards
1.12 -- I can determine the continuity of a function at a point. I can also graphically identify points where a function is not continuous (or, in other words, the function is discontinuous)
1.13 -- I can find the derivative equation for a function using the concept of a limit
(This is called the limit definition of a derivative and will be assessed most likely on the multiple choice portion of the AP exam)
i -- I can find the slope of a line between 2 points (will also require the recollection of what a tangent line is (from geometry).
ii -- I can write the equation of a line in point slope form (and, for purposes of the AP multiple choice test, can algebraically convert from point-slope form to slope-intercept form)
iii -- Determine graphical features of a function
iv -- I can factor a quadratic equation
v -- I can find the zeros of a quadratic function
see basic skill iv--factoring