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 !!!