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AP CALCULUS AB PRACTICE EXAM
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1)Multiply by clever form of 1 3 and 1/3
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2) Factor First then use direct substitution
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3)Sub in 2 set equal to each other: (2) 2 – 3(2) + 9 = 2k + 1 7 = 2k + 1 6 = 2k 3 = k
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4) Chain Rule: Peel the onion
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5) F’ sign chart look for where it changes from – to +
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6)Chain rule Then sub in 1
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7)Multiply and divide by 2 & 1/2 – u-substitution
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8) LRAM = 2 (4 + k + 8) = 2 (12 + k) RRAM = 2(12 + 8 + k) = 2(20 + k) (24 + 2k + 40 + 2k)/2 = 52 64 + 4k = 104
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Work backwards 9)
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10) Horizontal asymptote y = 3 a = 3 since debrees are the same Vertical asymptote x = 2 How will x 2 + b give you an answer of 2
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11)Quotient Rule Sub in x = 1 right away- don’t simplify first
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12) Work backwards antiderive
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13) Foil First- then anitderive
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14) on 2012 exam Just use the formal definition of derivative
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15) Think about what graph the slope field would make
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16) f’(x) is defined for all real numbers so f(x) must be continuous, thus eliminating d Also f’(x) is always going to positive so f must be always increasing- only choice E
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17)Set equations equal to each other x – 2x 2 = -5x 2x 2 – 6x = 0 2x(x – 3) x = 0, x = 3 Top curve- bottom curve
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18) f’(1) = 2(1) + 1 = 3 y – 4 = 3(x – 1) Y = 3x +1 Y= 3(1.2) + 1 Y = 3.6 + 1 = 4.6
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19) f’(x) = 3x 2 -12 F’’(x) = 6x -12 6x – 12 = 0 X = 2 Set up chart
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20)g’(x) = 2x – 3
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21) x – 2 = 20 x = 22
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22) set up chart
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SECTION 1 PART B
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76)A particle moves along the x-axis so that any time t > 0 its velocity is given by v(t) = t 2 ln(t + 2). What is the acceleration of the particle at time t = 6? Could do by hand or use calculator: A(t) = v’(t) Calculator: Enter v(t) on calculator Use dy/dx key and evaluate at x = 6 By Hand: A(t) = 2t ln (t + 2) + t 2 ( 1 ) t + 2 Evaluate a(6)
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77) If and then
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78) Derivative is the RATE of change in the temperature
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79) The rate of change in the water is given by the equation Y = 9sin(√(x + 1) Enter into calculator and evaluate the integral from 0 min to 6 min. Get 45.031019 Subtract from 81.637
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80)Since graph is increasing from left to right, Left Sum is an underestimates. Trapezoidal underestimates when graph is concave down. (overestimate when graph is concave up) Show graph
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81) The first derivative of the function f is given by How many points of inflection does the graph of f have on the interval 0 < x < 2pi ? Graph on calculator setting window from 0 to 2pi and find how many times it crosses the x-axis (Where it is equal to 0) Note: Could also look at the graph of the first derivative and see how many mins and maxs there are
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82) Think of a horizontal line or a cubic curve Only c is true has greater than or equal to D) is what Theorem? E) is what theorem
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83) x2.52.83.03.1 f(x)31.2539.204548.05 Find the rate of change between 2.8 and 3 (45 – 39.2)/(3 – 2.8) = 29 Find the rate of change between 3 and 3.1 (48.05-45)/(3.1-3.0) = 30.5 The only value it could be is 30 between those two.
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84) Where the first derivative is negative (below the x-axis) is where the graph can be decreasing Answer E Where is the graph increasing?
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85) Skip Didn’t do cross perpendicular sections 86 & 87 Use table
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88)The rate at which water is sprayed on a field of vegetables is given by where t is in minutes and R(t) is in gallons per minute. During the time interval 0 < t < 4, what is the average rate of water flow, in gallons per minute? Average Value: Set up and solve using your calculator
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89) h(x) = (2f(x) + 3)(1 + g(x)) Hint: FOIL, Derive, and then substitute h(x) =2f(x) + 2f(x)g(x) + 3 + 3g(x) H’(x) = 2f’(x) + 2f’(x)g(x) +2f(x)g’(x) + 0 + 3g’(x) H’(1) = 2(-2) + 2(-2)(-3) + 2(3)(4) + 3(4)
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90) f & g are ____Inverse_______ functions Set up a table- slopes are reciprocals (not opposite reciprocals)
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91) A particle moves along the x-axis so that its velocity at any time t > 0 is given by. At t = 0, the particle is at position x = 1. What is the total distance traveled by the particle from t = 0 to t = 4? Take the absolute value and integrate from 0 to 4
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92) Calculator method Enter y = sin(x 3 ) in y = screen and use zero key Make sure do left and right bound between 0 and 2 OR Use solver key
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