1998 AB Multiple Choice – Mr R’s scratch work!
1. Okay, inflection point problem, let’s get to it! Oh look, the 3’s will cancel, great!
2. Integral (Watch out for NEGATIVE area, right? Yeah, rite!) Geometric areas!
Okay, 1 + 2 + 1 + (-1/2) + (-1) = 4 – 1.5 = 2.5
3. I converted the integrand to a power function, did you?
Mr R likes to keep that negative sign outside!
4. What’s this all about! Oh, wait f cont. on [a,b] and diff. on (a,b) sounds familiar...
Yup, this is a Mean Value Theorem! So there exists c such that a < c < b where … (A) is this, and our Extreme Value Thm says check critical x-values and endpoints and singular points. (C) and (D) are okay. Integral exists (E) is okay.
would be Rolle’s Theorem (if f(a) = f(b), then there must be a smooth turning point.)
5. d(cos x) = -sin x , right?! So…
6. ‘Weak Sauce’ implicit differentiation problem!
I’ve got to go back and find ‘y’ when x = 2. Let’s see, 4 +2y = 10 means y = 3, ok…
7. I hope you divided by ‘x’ first??? So…
8. I like to write down the givens on the scratch paper so I can see them. (You get to write on the AP Exam so you could circle or underline the givens!)
g(x) > 0 okay… no biggie there… f(0) = 1 why? I guess we’ll see soon enough!
integrate ‘0’ to get f(x) = C (weird…) f(0) = 1 so C must be 1, f(x)=1 constant!
1998 AB Multiple Choice – Mr R’s scratch work! Page 2
9. Another ‘flow rate’ problem! To find total barrels, find the area under the curve…
100(6) + 150(6) using the Merton Rule? + etc… = 600 + 900 + 900 + 600 = 3000
10. df/dx = darn! Yet, another quotient rule! Okay, here goes…
11. If f is linear (a line), then right?
D? WRONG! Yup, Mr R missed this one! Do you see the error?
12. Hmm… let’s try plugging in a ‘2’ (even though on tougher problems this won’t work).
13. f not differentiable on the open interval (-2, 4)? Sounds too easy to be true?
They had to tell us about the vertical tangent (no slope) at x = 2 and x=0 is obvious…
Hope I didn’t miss something here?
14. Easy physics problem. dx/dt = v(t) = 2t – 6 = 0 when t = 3 seconds.
15. They love this problem too! There’s not a whole lot they can do with it though!
16. Easy! This will give us more time for other problems!
17. Watch this one! It’s easy! Just focus on x = 1 and the graph: y’’ < y < y’ at x = 1 since .
18. Don’t even need point-slope form for a line since they gave us the y-intercept (b=1)
Just go for the slope (m) and use y = mx + b (slope-intercept form for a line).
19. See the number line for y’’ ??? Forget (x-2)2, it’s always positive, so I-pts only at…
1998 AB Multiple Choice – Mr R’s scratch work! Page 3
20.
21. Please tell me you recognize this ‘variable separable’ differential equation?
It’s an exponential growth/decay problem! The solution is y = Cekt
22. Too easy? Do a first derivative number line!
(2x2 +1) is always positive, so y is increasing only for x.> 0.
23. Careful, is the graph f or is it f’? Okay, it’s f(x) not it’s derivative.
Think, “Positive slope, then zero at the top, then negative slope.” It’s between A and E?
since concave up/down/up for f(x) means f’(x) has a slope of positive/neg/positive.
24. dv/dt = 3t2 – 6t +12 = a(t). I like to write the domain restriction down so I remember to check endpoints, [0,3]. Now we’re looking for a maximum ‘a’, so we need to take the derivative again a’(t) = 6t – 6 = 0. a’ ___- ______+_____ Hmm, this is a min!
t = 1
Check the endpoints. a(0) = 12 m/s2 and a(3) = 27 – 18 + 12 = 21 m/s2 so…
25. Actually, I did the Triangle Area = 2(2)/2 = 2 u2 and then did the area under the parabola and added them up.
1998 AB Multiple Choice – Mr R’s scratch work! Page 4
26. f(0)=1 and f(2)=2 ??? Let’s draw a graph…
Here’s one but f(x) won’t equal ½.
We need to bring the curve down at x = 1, so we need f(1) = k to be less than ½.
27.
28. Weak Sauce: Wait a sec! What about the trig!???
Review (don’t laugh!):
so…
Score: Mr R 27/28 in about 20 minutes. Theo? He couldn’t finish by the Fire Drill, then again… He wasn’t racing Mr R. Then again, we haven’t scored his test yet!