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P1; 0m 1):)? r NAME CALCULUS “ DATE ’ CALCULUS PRACTICE WORKSHEET These are some of the problems that were in my AP Book as samples. I picked out the ones that I thought all of you should be able to
do at this point. (or at least have a good idea of where to start.) They are from the multiple choice section of the test but I did not give
you choices (conservation of paper and I thought you could do them on your own). I picked 15 of the 28 in the section. The time
limit for the 28 is 55 minutes with NO CALCULATOR! Key points to remember:
1. Unless otherwise speciﬁed, the domain of a ﬁmction f is assumed to be the set of all Real numbers 3: for which f (x) is a Real number.
2. The inverse of a trigonometric function f may be indicated using the inverse function notation f’1 or with the preﬁx “are” (e.g., sin‘I x = arcsin x ). l.Ify=(x3+l)2,thenﬁnd “tzi’éwd‘g‘”; 2 8-4de :QGZLffSI—ldil‘D‘I
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\lJ’ZKOmg‘ ~K 'U/LX K4“ 5:: “0 la rte-3‘37» K * Dd“ 11. Let f be the function given by f (x) = 21:21. Find where the 1x2. A curve has slope 2x +3 at each point (x, y) on the curve.
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K_ (:3? ’23:) {"2- 752} 2,3- +x ~33 13. Let f be the function deﬁned by f ( x) = 4x3 — 5x + 3 , Find 14. A particle :11 ves along the x~axis so that at time I 2 D it
the equation of the line tangent to ﬁliegra‘ph of f atjthe point 9031mm is given by 3‘0) = 2t} ‘2”; + 72‘ _ 53 - At What
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61ft#—~ 71—7— A. TLJET f ‘\ These are also some of the problems that were in my AP Book as sampies. l picked out the ones that l thought’all of you should be
able to do at this point (or at least have a good idea of where to Start.) They are also from the multiple choice section of the test (with
a Calculator) but I did not give you choices (conservation of paper and I thought you could do them on your own). i picked 6 of the
17 in the section. The time limit for the 17 is 50 minutes with a CALCULATOR! Key points to remember:
1. The exact numerical value may not appear in a multiple choice answer so be ready to approximate the best numerical value (by rounding or truncating.) 2. Unless otherwise speciﬁed, the domain of a function f is assumed to be the set of all Real numbers x for which f (x) is a Real number. 3. The inverse of a trigonometric function f may be indicated using the inverse function notation f‘] or with the preﬁx “are” (e. g., sin"1 x = arcsinx ). 1. A particle moves along the x—axis so that at any time t 2 0 , its 2. The radius of a circle is increasing at a constant rate of 0.2
velocity is given by V“) 2 3 +4_lcos (Q90 _ What is the meters/second . What is the rate of increase in the area of the
circle at the instant when the circumference of the circle is acceleration of the particle at time t = 4 ? (decimals) 20” metequ (exact in S of z ) 3. Let f be the ﬁmction with derivative given by 4. The velocity, in feet/second= of a particle moving aféng the
x-axis is given by the function v(t) 2 e' +te' . What is the f ‘(x) = sin(x2 +1) . How many relative extrema does f have
average velocin of the particle from time t = 0 to time t z 3 ‘2 ontheinterval 2<x <4? (decimals)
5. The function f has ﬁrst derivative given by 6_ Let g be the function given by g (x) : fsin (r2) dtfm,
fr(x) = _....1G_3 I What is the wwordimte ofthe inﬂection —l S x 5 3 . Find the interval on which g is decreasing?
. 1+x+x (decimals) ‘ any: "tat ( 'lz)( hr? pomt‘ofthe graph of f? (decimals) hi, I. B L” F V»: r ic-‘JJLIIEX i : y‘ I 3’2
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- Spring '12
- Ristah
- Calculus