1. AP Calculus Exam Format
May 14, 8 AM

2. Today in review If you do all activities, showing work on paper
Classwork
Homework
Calculus with the Graphing Calculator
1-13
Justifications
None
8 out of 8 FRQs

3. Read about the test you’re taking Straight from the source
Scan the QR code on your phone  OR
Type all this into your Browser

4. Graphing Calculator you should be able to…
Plot the graph of a function within a given window.
Solve an equation by finding zeros or points of intersection on a graph.
Calculate a numerical derivative & definite integral.

5. Graphing Calculator you will not be able to…
Use a calculator to justify an answer.
Write calculator syntax instead of mathematical expressions.
Use TI-89s to calculate algebraic derivatives and integrals.

6. One very common issue…
TRYING TO WORK OUT A PROBLEM BY HAND WHEN A CALCULATOR IS AVAILABLE.
You will run out of time.
You will probably make a mistake.

7. Go to Join.Quizizz.com Time to see if you really read 

8. Go to Kahoot.it Time to see how calculator Savvy you are

9. Justification Dos and don’ts
Be PRECISE & CONCISE
If you write extra and contradict your correct answer or say something incorrect and you’ll forfeit the points you earned.
Don’t say “it”, “the graph” or “the function” unless you have clearly stated what “it” is already. Name f(x), f’(x), etc.
State the conditions for a theorem are true before using a theorem.

10. Main things you need to be able to justify
Riemann Sums as over/under estimate of area because…
Tangent line approximation is an over/under estimate because…
Function is increasing/decreasing because…
Relative Max/Min of a function because…
Absolute Max/Min of a function because…
Point of inflection because…
Continuous at x=a because…
Speed is increasing/decreasing because…
There exists c on (a,b) such that f(a)<f(c)<f(b) because…
There exists c on (a,b) such that f’(c) = (f(b) – f(a))/(b-a) because…

11. Card 1 : Definition of Continuity
To show f(x) is continuous at x=a
1. f(a) is defined.
show that f(a)=L
2. lim 𝑥→𝑎 𝑓 𝑥 exists
show left hand limit and right hand limit both equal L, THEREFORE lim 𝑥→𝑎 𝑓 𝑥 = L
3. lim 𝑥→𝑎 𝑓 𝑥 =𝑓(𝑎)
THEREFORE, f(x) is continuous at x=a  don’t leave that off!

12. What’s wrong with me?
The left Riemann Sum is an under approximation because the rectangles are all underneath the graph.

13. What’s wrong with me?
The trapezoidal approximation is an underestimate because f(x) is decreasing.

14. What’s wrong with me?
The speed of the particle is increasing on (3, 4) because a(t)>0

15. What’s wrong with me?
The tangent line approximation at x=2 is greater than f(2) because I got y=5 for the tangent line approximation and f(2) = 4.

16. What’s wrong with me?
There is at least one value c in (1, 2) such that 𝑓 ′ 𝑐 = 𝑓 𝑏 −𝑓(𝑎) 𝑏−𝑎 .

17. What’s wrong with me?
There exists at least one value c in (1,3) such that f(c)=2.

18. What’s wrong with me?
It has a relative minimum because the graph changes from negative to positive.

19. What’s wrong with me?
There is a point of inflection when x=2 because f’’(2)=0

20. What’s wrong with me?
f(x) is continuous because f(2)=3, and lim 𝑥→2 𝑓 𝑥 =3

21. Interpreting solutions in context
Reference the bounds of integration with proper units
Include units of measurement
Definite integral = accumulation of stuff or total