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Published byLillian Parsons Modified over 9 years ago
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The 50 questions in 50 minute Challenge Are you in the IBZ? (that would be IB Zone)
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#1- #5 are non-calc 1) Can you find the inverse of y = 4e x-3 ? 2) What is the vertex-ready form for f(x) = 2x 2 – 5x + 12 ? 3) What are the x-intercepts for the function y = 3cos(2x) + 1.5 for [ - π, 2 π] ? 4) The functions y = 2x and y = x 2 form a region that has an area of _________. 5) Find the probability that exactly 5 questions out of 8 questions will be answered correctly, assuming a student guesses on each question, each of which has 4 choices.
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#6 - #10 non-calc #6) On a calculus test with 6 questions each having 5 choices a student randomly selects a result for each. Find the probability that exactly 3 of them will be correct. #7) The vector 3i + 5j – 6k is perpendicular to the vector 4i – aj + 2k. Find the value of a. #8) Find the second derivative for y = e lnx 2 #9) Derive the rate of change for y = 1/x using the definition of the derivative. #10) X is normally distributed with a Mean of 46 and a standard deviation of 6. Find P(34 > x i or x i > 61).
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#11 - #15 Calc ?
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#16 - #18 Calc ? 16) What is the inverse of ? 17) If sinθ = -3/5 with θ in Q 4. Find cos (2 θ). 18) Given a central angle of 2.1 radians w/ r = 8cm, then find the area of the segment. 2.1
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#19 19) Find Area 32° 32° 100 m
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#20 - 23 20) Solve the equation for the values of θ, correct to the nearest 10 th of a degree for [0, 2θ]: 24sin(2 θ) + 10cos θ = 0 21) P(z > a) =.994 ; find a 22) A sequence of terms 4, 6.5, 9, ….. has a sum of 74. How many terms are there? 23) 8 + 6 + 4.5 + 27/8 + ……will approach what value ?
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#24 - 26 24) Find the area between the x –axis and the y = cos 3x curve for [ 0, 2π/3] 25) Find d 2 y/dx 2 @ x = e for y = (2x + 2) 5 26) (3,3) Find (8, -2) (6,0) (8, 0)
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#27 - 30 27) Find the frequency, period, and amplitude for the function defined by f(x) = -3sin(4x) + 6 28) For the function named in #27 transform f(x) such that it is translated by the vector. What is the name of the new function? 29) If f(x) has a first derivative at x = 3 of -2 and a second derivative of 0 at x = 3, sketch two possible curves near x = 3 that would support the derivative data. 30) A line passing through (3, 5) and (-6, 2) can be named in vector form r = p + td. Do so.
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#31 - 35 31) Find the dot product of 2i – 4j + 6k and 3i – 2j + k and find the angle between the vectors. 32) g(x) = 3x – e x and h(x) = 4/x; Find (g º h)(4) 33) Form the inverse of g(x) = 3ln(x + 3) 34) Find the third quartile value for a class set of calculus grades where 9 students got a 93, 6 got a 90, 5 received a 96, and 2 students received a grade of 84. 35) What is the local minimum value for xe x ?
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#36 - Find the values for the following table: SinCosTan 0º0º 30 45º 60º 90º 180º
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#37 - 40 37) Find the other 5 trigonometric values for the angle θ, given that sec θ = -4/3 and θ is in quadrant III. 38) P (Q U L) =.9 with P(Q) =.7 and P(L) =.6; Determine if Q and L are independent events. 39) Determine whether the two vectors 4i – 3j + 6k and 8i – 6j + 12k are parallel. 40) How many triangles can be formed from sides of AB = 10 cm, BC = 8 cm, and m A = 30º ?
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#41 - 45 41) Sketch -2f(x – 3) knowing that f(x) = (x + 2) 2 + 4 42) (3x + e 2x + sin(3x)) dx 43) (3x -1 + e - 2x + cos(3x)) dx 44) Represent in the form a + 45) Find the exact sum of the first 12 terms of the sequence defined as 2, -3, 9/2, -27/4, ……, u 12
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#46 – 49, Almost the End !!! 46) cos x = m + 3 and sin x = m – 3; Find csc(2x) 47) Find dy/dx at x = 2.4 for y = sin x / (x – 1) 48) Sketch the velocity function from s(t) = t 3 + 4 49) A probability density function has outcomes as listed with probabilities in the table below: X1359 P(X).2.3m3m FIND E(X)
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#50 Find the 50 th (how appropriate) derivative of cos(50x) HAVE A GREAT AFTERNOON !!!
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