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The 50 questions in 50 minute Challenge Are you in the IBZ? (that would be IB Zone) #1- #5 are non-calc • 1) Can you find the inverse of y = 4ex-3 ? • 2) What is the vertex-ready form for f(x) = 2x2 – 5x + 12 ? • 3) What are the x-intercepts for the function y = 3cos(2x) + 1.5 for [ - π, 2π] ? • 4) The functions y = 2x and y = x2 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. #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 = elnx2 • #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 > xi or xi > 61). #11 - #15 Calc ? x 11) 4 8t dt ; find x 0 7 1 12) dx 2x 3 13) f ( x ) 3 ln(3 x 5); Find f ' (2) 14) Solve : 5 x 2 8 x 2 1 2 3p 15) ; find p 4 6 p 4 #16 - #18 Calc ? 3 g ? 4 2 • 17) If sinθ = -3/5 with θ in Q4. Find cos (2 θ). • 18) Given a central angle of 2.1 radians w/ r = 8cm, 2.1 then find the area of the segment. • 16) What is the inverse of #19 • 19) Find Area 32° 32° 100 m #20 - 23 • 20) Solve the equation for the values of θ, correct to the nearest 10th 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 ? #24 - 26 • 24) Find the area between the x –axis and the y = cos 3x curve for [ 0, 2π/3] • 25) Find d2y/dx2 @ x = e for y = (2x + 2)5 • 26) (3,3) (6,0) (8, 0) 8 Find f ( x)dx 0 (8, -2) #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 2 . What is the name of the new function? 5 • 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. #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 – ex 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 xex ? #36 • Find the values for the following table: Sin 0º 30 45º 60º 90º 180º Cos Tan #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 ? #41 - 45 • 41) Sketch -2f(x – 3) knowing that f(x) = (x + 2)2 + 4 • 42) • 43) (3x + e2x + sin(3x)) dx (3x-1 + e-2x + cos(3x)) dx • 44) Represent 4x 3 2x 1 in the form a + q 2x 1 • 45) Find the exact sum of the first 12 terms of the sequence defined as 2, -3, 9/2, -27/4, ……, u12 #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) = t3 + 4 • 49) A probability density function has outcomes as listed with probabilities in the table below: X 1 3 P(X) .2 .3 5 9 m 3m FIND E(X) #50 • Find the 50th (how appropriate) derivative of cos(50x) • HAVE A GREAT AFTERNOON !!!