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#1 Pre-Calculus – Hustle
2007 FAMAT State Convention
#3 Pre-Calculus – Hustle
2007 FAMAT State Convention
Find the exact value of the expression:
cos 240  cos 0
Convert the rectangular coordinates to polar
coordinates of the form  r ,  where 0    2 :
3

3, 3 . Find  .
School:
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School:
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Answer:
Answer:
#2 Pre-Calculus – Hustle
2007 FAMAT State Convention
#4 Pre-Calculus – Hustle
2007 FAMAT State Convention
In ABC where side c is the largest side;
a = 4 cm, and b = 8 cm. Find the mean of all
possible perimeters of ∆ABC if c must be an
integer and ∆ABC is scalene.
Determine the classification of the following
conic: 3x2  4 xy  y 2  2 x  4
School:
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School:
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Answer:
Answer:
#5 Pre-Calculus – Hustle
2007 FAMAT State Convention
#7 Pre-Calculus - Hustle
2007 FAMAT State Convention
3x 4  x5  6 x 2  12
x 
3x 2  4  4 x5
Find the radian measure of the central angle of
Circle A with radiusA  6 cm and the intercepted
arc length sA  1.5 cm. Leave in terms of pi.
School:
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School:
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Answer:
Answer:
#6 Pre-Calculus – Hustle
2007 FAMAT State Convention
#8 Pre-Calculus – Hustle
2007 FAMAT State Convention
If x=A, x=B, and y=C are asymptotes of:
3x 2  6 x  24
y
2 x2  4
Find A+B-C.
(3  3 3i ) 4 = rcis with 0    2 .
lim
Find r.
School:
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School:
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Answer:
Answer:
#9 Pre-Calculus – Hustle
2007 FAMAT State Convention
#11 Pre-Calculus – Hustle
2007 FAMAT State Convention
Find the coefficient of the x 2 y 4 term of the
expansion of the following expression:
(2 x  y)6 .
Find the eccentricity of the conic section
described by the following polar equation:
45
r
3  12 cos 
School:
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School:
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Answer:
Answer:
#10 Pre-Calculus – Hustle
2007 FAMAT State Convention
#12 Pre-Calculus – Hustle
2007 FAMAT State Convention
6 2
Find A if A  
.
 8 2 
lim
1
A 
1
21
x 0
x3  2 x  6 x 4
x
=?
School:
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School:
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Answer:
Answer:
#13 Pre-Calculus – Hustle
2007 FAMAT State Convention
#15 Pre-Calculus – Hustle
2007 FAMAT State Convention
Given that x  10 , reduce to the simplified form
( x  a)( x  b)( x  c)
. Find a+b+c+d.
(x  d )
Find a unit vector in the same direction as
v  9, 40  . If u  u1 , u2  , find u2 .
( x  4)!( x  3)! x !
( x  2)!( x  6)!( x  1)!
School:
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School:
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Answer:
Answer:
#14 Pre-Calculus - Hustle
2007 FAMAT State Convention
 2, 4, 0    0,5, 1 
If the cross product =  a, b, c  ,
find a+2b-c.
#16 Pre-Calculus – Hustle
2007 FAMAT State Convention
Find the vertex of the following conic section:
5x  6 y 2  24 y  100
School:
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School:
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Answer:
Answer:
#17 Pre-Calculus – Hustle
2007 FAMAT State Convention
#19 Pre-Calculus – Hustle
2007 FAMAT State Convention
Given the following conic section, and that
M=LENGTH OF THE MAJOR AXIS and
M
m=length of minor axis, find
.
m
36 x 2  144 x  y 2  2 y  1
Simplify this trigonometric expression
sin 4 x cot 2 x(sin(2 x)) 2
to one of the
cos 4 x
form A cos 4 x  B cos 2 x  C . Given that

0  x  . Find A+B+C.
2
School:
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Answer:
School:
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Answer:
#18 Pre-Calculus - Hustle
2007 FAMAT State Convention
#20 Pre-Calculus – Hustle
2007 FAMAT State Convention
Find the harmonic mean of 5, 6, and 30.
Find the greatest possible value of x
3
where 2  x 
.
2
cot(4 x)  3
School:
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Answer:
School:
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Answer:
#21 Pre-Calculus – Hustle
2007 FAMAT State Convention
#23 Pre-Calculus – Hustle
2007 FAMAT State Convention
Convert the polar equation r  6sin  to the
rectangular form: Ax 2  By 2  Cy  0 .
Find A-B-C.
Find the area of triangle BCD. Figure not
drawn to scale.
A
70
E 50
C
5
4
B
8
6
School:
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Answer:
D
School:
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Answer:
#22 Pre-Calculus – Hustle
2007 FAMAT State Convention
Find the number of zeroes at the end of 2007!.
#24 Pre-Calculus– Hustle
2007 FAMAT State Convention
Find the remainder:
x  4 x4  x5  2007
School:
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School:
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Answer:
Answer:
#25 Pre-Calculus – Hustle
2007 FAMAT State Convention
Find the area of triangle ABC with vertices
A(1,2) B(3,-4) C(-1,5).
School:
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Answer: