Official 2010 Calculus AB/BC FRQs Discussion

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81

<p>1a)1 for integrand 1 for answer
1b)1 for equation 1 for answer
1c) 2 for h(t)
1d) 1 for equation 1 for answer</p>

<p>2a) 1 for computations 1 for answer
2b) 1 for sum 1 for answer 1 for meaning
2c) 1 for equation 1 for answer
2d) 1 for answer 1 for reason</p>

<p>3a) 1 for computations 1 for answer
3b) 1 for answer 1 for answer
3c)1 for time 1 for amount 1 for reason
3d) 1 for limits 1 for equation</p>

<p>4a) 1 for integrand 1 for antiderivative 1 for answer
4b) 1 for limits 2 for equation
4c)1 for limits 2 for equation</p>

<p>5a) 1 for g(3) 1 for g(-2)
5b) 2 for the points 2 for the reasoning
5c) 2 for the points one for the reasoning</p>

<p>6a) 1 for the equation
6b) 1 for the answer 1 for the reason
6c) 1 for separation of variables 2 for antiderivatives 1 constant of integration 1 use of initial condition 1 for domain</p>

<p>These in no way are correct just my own guesses and how I’m calculating my frqs score</p>

82

<p>^ Is that for AB or are you just missing 6d? Also every problem is worth 9 points and for some your point values add to 8?</p>

83

<p>I think I got maybe a 70-72ish raw score if the scorers are nice to me. Would that be a 5?</p>

84

<p>That, I believe is guaranteed 5. Usually the estimate is 70+ is a 5 for AB. The BC curve is usually around 65 give or a take a few.</p>

85

<p>Oh yeah my bad that’s my guesses for AB</p>

86

<p>Whoever said they didn’t understand how to determine if the approximation is an over or under approximation, you use d^2y/dx^2 to determine that the function is concave up so the tangent line is below the curve => under approximation</p>

87

<p>If I got about 32/50ish points on FRQ’s and if I skipped around 9 questions on MC, the rest of which I answered fairly confidently (so say I missed around 5 extra), would that place me at a 4? Weak 4? Or am I crazy? Sigh…</p>

88

<p>@WorriedJunior10</p>

<p>It’s a borderline 4/5.</p>

89

<p>Hey guys, for BC this is how i did, can you guys see wat my potential score is:
MC: Non-cal is ■■■■■■■■ + cal is easy: ~35/45, ~7 wrong
FR: 1. all
2. a,b,1/2 of d (what is the answer for C) pls?)
3. a,c,d
4.all
5.all
6.all</p>

90

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91

<p>@WorriedJunior10 - I would say that’s probably anywhere from a 4 to a very low 5.</p>

92

<p>Posted by TheMathProf:</p>

<p>"Here are my tentative solutions for BC. Ran through it in about 35 minutes today, so these might be off.</p>

<p>1.(a) 142.274 or 142.275
(b) -59.583
(c) h(t) = 0 for 0 <= t < 6 ; h(t) = 125(t-6) for 6 <= t < 7 ; h(t) = 125 + 108(t-7) for 7 <= t < 9
(d) 26.335</p>

<p>2.(a) E’(6) = [E(7) - E(5)]/(7-5) = 4 hundred entries per hour
(b) 10.6875; Between noon and 8 p.m., an average of 1068.75 entries per hour were received for the contest.
(c) 6950 entries not yet processed (approximately)
(d) t = 9.184, since P’(t) changes from positive to negative at this point</p>

<p>3.(a) 2sqrt(2) m/sec.
(b) 11.588
(c) t = 2.208, particle moving to the right since dx/dt|t = 2.208 > 0
(d) (i) At times t = 1 and t = 3
(ii) dy/dx| t= 1 = .432; dy/dx|t = 3 = 1
(iii) y(1) = y(3) = 4</p>

<ol>
<li><p>(a) 18
(b) pi * integral (0, 9) of [(7 - 2sqrt(x))^2 - 1^2] dx
(c) integral (0, 6) of (3y^4/16) dy</p></li>
<li><p>(a) y = -5/4
(b) 1/3
(c) y = 1 - e^(1-x)</p></li>
<li><p>(a) cos x = 1 - x^2/2! + x^4/4! + … + (-1)^n<em>x^(2n)/(2n)!
[cos x - 1]/x^2 = -1/2! + x^2/4! - x^4/6! + … + (-1)^n</em>x^(2n-2)/(2n)!</p></li>
</ol>

<p>(b) relative min since f’(x) = 0 and f"(x) = 2/4! > 0, by the Second Derivative Test</p>

<p>(c) g(x) = 1 - x/2! + x^3/(4!<em>3) - x^5/(6!</em>5)</p>

<h2>(d) g(1) = 37/72. By the Alternating Series Remainder, the maximum error is less than the first omitted term, which is 1^5/(6!*5), which is less than 1/6! "</h2>

<p>I think these solutions are extremely accurate overall… however, for 2d, it should be t = 12… the endpt is the absolute maximum. Also, 2c and 2b seem to be a bit weird as well.</p>

93

<p>2c is 700, I think.</p>

<p>2b is the right number. I personally said that there were 10.6875 was the number of hundred of entries per hour. Hopefully the readers understand.</p>

94

<p>^ They should understand. I said 7 hundreds of entries instead of 700 lol.</p>

95

<p>Are the curves different for form b and form a? Or combined into one curve?</p>

96

<p>I think the curves are different. I think I would have done way worse on form b so I think that form b would be curved more.</p>

97

<p>Can somebody post his answers to form b of AB? I’ll write what I remember here when I come back from school.</p>

98

<p>I left out the 1 in 6(c) and instead had an extra term x^7/(8!<em>7), meaning I used x^5/(6!</em>5) in my estimation of g(1). No wonder it was some rediculous fraction…</p>

99

<p>For ab form a, if i get 3b, 3c, and 4a wrong, what is the maximum deduction of points? -9?</p>

100

<p>@Jamezz93: Actually, I’m sure it’s wrong, I misread what E(t) represented in #2 entirely.</p>