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Final Countdown!
CEESA Math Counts
Q #1
x 
 
x
x
Evaluate x
at x = 2
Answer
Q #2
Each interior angle of a
regular polygon
measures 144. The
polygon has _____
sides.
Answer
Q #3
11213 = _______ as a
base 10 number
Answer
Q #4
3 and 2 are the first two
terms of a geometric
th
sequence. The 4 term
must be ______
Answer
Q #5
The hypotenuse of a
30-60-90 triangle measures
10. How long is the longest
leg?
Answer
Q #6
Consider the rhombus
0
with a 60 angle and
each side measuring 60.
What is its area?
Answer
Q #7
Consider the cube with
diagonal 1. Each side has a
a .
length of
b
Evaluate the sum a + b.
Answer
Q #8
How many of the first
100 positive integers
are divisible by 1,2,3
and 4?
Answer
Q #9
If three times the larger of
two numbers is four times
the smaller and they differ
by 8, what is the larger of
the two numbers?
Answer
Q #10
If x  5  3, thenx  5  ?
3
Answer
Q #11
The legs of a right
triangle measure 13 and
84. The length of its
hypotenuse is ______.
Answer
Q #12
The diagonal of a
square measures 20.
What’s the area of the
square?
Answer
Q #13
Find the largest whole
number such that 7
times the number is
less than 200.
Answer
Q #14
If the ratio of 2x-y to x+y is
2 , what’s the ratio of
3
x to y?
Answer
Q #15
AB, BC, CD, and DA of convex quadrilateral
ABCD have lengths of 6,8,24 and 26
respectively, with m ABC = 90. The area
of the quadrilateral is ________
C 8
24
B
D
6
26
A
Answer
Q #16
P(x) =
+
–
The degree of P is
____________
Answer
2
(x
5
3
1) (x
4
3x)
Q #17
Find the sum of the digits of the
largest even three digit
number which is not changed
when its units and hundreds
digits are interchanged.
Answer
Q #18
3 5 9 17 33 65
      7  ______
2 4 8 16 32 64
Answer
Q #19
Rectangle ABCD has area 72 with
E and G the midpoints of sides
AD and CD respectively. What is
the area of rectangle DEFG?
D
E
A
C
G
Answer
F
B
Q #20
4 4
If 1  

0
,
2
x x
2
then
x
must be ___
Answer
Q #21
If four times the reciprocal of
the circumference of a circle
equals its diameter, what
must its area be?
Answer
Q #22
Opposite sides of a regular
hexagon are 12 cm apart.
How long, in cm, is each
side? Express in a b form
Answer
Q #23
0
In the figure
shown,
m
E
=
40



and BA  BC  CD. Find m ACD
B
A
E
C
D
Answer
Q #24
In triangle ABC, AB = AC
and m A=80. CE = CD
and BF=BD. mEDF = ___
A
E
Answer
F
C
D
B
Q #25
If one minus the
reciprocal of (1-x) equals
the reciprocal of 1-x,
then x must be ______
Answer
Q #26
The sum of the distances from
one vertex of a square with
sides of length 2 to the
midpoints of each of the sides
of the square is
____________
Answer
Q #27
For how many real numbers x
2
is  ( x  1)
a real number?
Answer
Q #28
If the side of one square is the
diagonal of a second square,
what is the ratio of the area of
the first square to the area of
the 2nd one?
Answer
Q #29
The sum of the first 80
positive odd integers
subtracted from the sum of
the first 80 positive even
integers is ________
Answer
Q #30
What is the remainder when
51
x + 51 is divided by x+1?
Answer
Q #31
Quadrilateral ABCD is inscribed in
a circle with side AB extended
beyond B to pt. E. If m BAD = 92
and m ADC = 68, find m EBC .
Answer
Q #32
What is the smallest prime
number that divides the sum
3 11 + 5 13?
Answer
Q #33
If one gallon of paint is needed to
paint a statue 6 m high, then the
number of gallons it will take to
paint 540 statues similar to the
original but only 1m high is
___________
Answer
Q #34
The sum of all the integers
between 50 and 350 which
end in a 1 is _________
Answer
Q #35
A chord which is the
perpendicular bisector of a
radius with length 4 in a
circle, has length
_________
Answer
Q #36
.5 – .05 can be written as a simple
a
fraction in
form.
Evaluate a + b b
Answer
Q #37
Given the ratio of 3x-4 to y+15
is constant and y=3 when x=2,
find x when y=12.
Answer
Q #38
The length of the common chord of
two intersecting circles is 16 cm.
If their radii are 10 cm and 17 cm,
than the distance between their
centers will be _______ cm.
Answer
Q #39
The sides of triangle BAC are in the ratio
2:3:4. BD is the angle bisector drawn to
the shortest side AC , dividing it into
segments AD and CD. If the length of AC
is 10 then the length of the longer
segment of AC, in simple a form, is
b
_______
Answer
Q #40
The real value of x such that
64x-1 divided by 4x - 1 equals
2x
256 is _________
Answer
Q #41
ab
Let a  b 
ab
.
a
Evaluate, in simple form,
b
4  4  4
Answer
Q #42
A circle passes through the
vertices of a triangle with
sides having lengths of 9,
40, and 41. Find the radius
of this circle.
Answer
Q #43
The arithmetic mean of the
52 successive positive
integers beginning with 2 is
_____.
Answer
Q #44
How many points are
equidistant from a circle
and two parallel tangents
to the circle?
Answer
Q #45
A square and a circle have
equal perimeters. The ratio
of the area of the circle to
the area of the square is
______.
Answer
Q #46
The smallest value of
2
x + 8x for real values of x
is _______.
Answer
Q #47
x

x
If f(x) =
, then f(i) = ___
x 1
4
where i =
2
1
Answer
Q #48
If the point (x,-4) lies on
the line containing points
(0,8) and (-4,0), then
x= ______
Answer
Q #49
The number of digits in
12
8
the number N=2 · 5 is
_______
Answer
Q #50
When 0.363636 . . . is
a
written in simplest
b
form, a+b = _____
Answer
Q #51
y  2 xy
Given z  x  3x 
y2
2
2
Find the value of z when
x = 1 and y = 7.
Answer
Q #52
The equation x - 5  2 x  1
has two solutions for x.
Their product is ______.
Answer
Q #53
3
x

2
9
x

2
The equation

2x  5 x  4
has two solutions. The
smallest of the solutions is
____.
Answer
Q #54
If f(x) = – 3x + 5 and
2
f(n+4) = an +bn+c, find
the sum a+b+c.
2
x
Answer
Q #55
1
3
Two lines with slopes of and
4
4
have y-intercept of 2 and 4,
respectively. The lines intersect
at (a,b). Evaluate a÷b.
Answer
Q #56
Robert is currently three times
Mark’s age. In 17 years,
Robert will only be twice
Mark’s age. How old was
Robert when Mark was born?
Answer
Q #57
Solve for x:
-22x + 24 = (10)2 + 3(5x)
Answer
Q #58
Find the sum of all the
integral solutions for x
where 3  x ≤ 4.
Answer
Q #59
Solve for x:
2 x  2 x  4 + 2x = 3-5 + x
2
Answer
Q #60
If x=3, then 2  x  2 x  15 x  60
3
2
2x
must be _______.
Answer
Q #61
When
x 5  3
is solved,
what is the sum of the roots?
Answer
Q #62
The equation
– 10x -8 =0
has a discriminant of
________.
2
3x
Answer
Q #63
When the roots of
2
2x -2x-1 = 0 are found, their
product is ________.
Answer
Q #64
The solution to the system
2x+5y=4
-7x-20y=-4 is (a,b).
Evaluate
ab
ab
Answer
Q #65
2 x 6
y  2 y 3
4
If 2
and
2
x= -1, find all possible
values for y.
Answer
Q #66
John starts at a point A on a level
piece of land. He travels 20 miles
due north, 24 miles due east, and
30 miles due south. How many
miles is John from point A?
Answer
Q #67
If both diagonals are drawn in
a square, how many right
isosceles triangles are
contained in the figure?
Answer
Q #68
If the measures of the interior
angles of a triangle are in the
ratio 3:5:10, find the ratio of
the largest exterior angle to
the smallest exterior angle.
Answer
Q #69
Given isosceles triangle ABC
and square BCDE with
common side BC. The area of
the triangle is 70 and the area
of the square is 196. Find the
length of AD.
Answer
Q #70
If A represents the arithmetic
mean of 8 and 24 and B
represents the positive
geometric mean of 4 and 9,
then the simplified ratio of A:B
is ______.
Answer
Q #71
Find the circumference
of a circle with area 196

Answer
Q #72
(12345)(12345) – (12350)(12340) =
_____
Answer
Q #73
An equilateral triangle has an
area of 432 3. Determine the
radius of the circle which
circumscribes it.
Answer
Q #74
Expressed in radian measure and
in terms of  , an exterior angle
of a regular 16-sided polygon has
what measure?
Answer
Q #75
Given:  is not a quadrantal angle


Evaluate:
7sin (2csc)(sec2  – tan2 )
Answer
Q #76
What percent of 650 is 143?
Answer
Q #77
1
2
1
2
(.5) (1.5) (27)
1
2
.5
is what whole number?
Answer
Q #78
Evaluate
 
 9  .08

 2  51



Answer
3
Q #79
If 2
x
.6
5
 64 then x = ____
Answer
Q #80
A trapezoid has area 58. If its
altitude is 4 and one base is
21, what is the length of its
median?
Answer
Q #81
Given c= {A,I,S,B,!}. Excluding
Φ, how many subsets does c
have?
Answer
Q #82


0
When (7tan )(sin 90 )(cos ) is written in a b
4
4
form,
a b
= ________.
Answer
Q #83
Consider the 7-digit palindrome
_ _ 23_ _5 where the only given
digits are those shown. How
many possible palindromes exist
here?
Answer
Q #84
The sum of the first
eight Fibonacci
numbers is ______.
Answer
Q #85
Excluding itself, what
is the sum of all the
factors of 96?
Answer
Q #86
Consider the graph of
2
y = -2x + 20x – 46. The
largest value y can be is
_____.
Answer
Q #87
If a1 = 1, a2 = 2, and
an = an-1-an-2 for n>2,
then a6 must be
_______. Answer
Q #88
Given the arithmetic
sequence 5,9,. . . , which
term of the sequence is
113?
Answer
Q #89
Evaluate
7
3  8(2  [5  10]  2)  1
22
Answer
Q #90
Consider the rhombus
ABCD where AB=25 and
AC=48. The area of this
rhombus is __________.
Answer
Q #91



Consider the graph of y  4 sin  x  
6
3
In radians, the function has a period
of _________.
Answer
Q #92
Given the equation 6x2+2x+38= -4-25x has
two roots. When written in simplest a form
the sum of these roots is ______. b
Answer
Q #93
When changed to the Fahrenheit
scale,  6 2 0C = ________ 0F
3
Answer
Q #94
The decimal numeral 49 is
equivalent to which binary
numeral?
Answer
Q #95
0
26
When
is written in radian
a
form, simplified to  , then
b
ab = _______.
Answer
Q #96
When
1
sin  
2
0
3 cos 0
1
is written in
degree form, the result is _______.
Answer
Q #97
110 5 = _____2
Answer
Q #98
4 and 16 are the 1st and 3rd terms
(respectively) of two sequences, one
arithmetic and one geometric with
r<0. Find the sum of the 4th terms in
these two sequences.
Answer
Q #99
There are _____ prime
numbers smaller than
30.
Answer
Q #100
( 9 )! !  (
16 )!  _____
Answer
Q #101
Let A be the origin and B have
(3,3) as coordinates in the
coordinate plane. You start at A
and end at B by moving up and to
the right only. How many such
paths are possible?
Answer
Q #102
The line 5x+2y-18 = 0 has an
x-intercept of a and a yintercept of b. In simplest
rational form, a+b = _____.
Answer
Q #103
The sum of the squares
of the first three
composite numbers is
________.
Answer
Q #104
The square of the sum
of the first four prime
numbers is ____.
Answer
Q #105
If the diameter of a sphere is
15 ,

then its surface area must be _______.
Answer
Q #106
An angle of 77  radians is
90
supplementary to an angle of
________ degrees.
Answer
Q #107
1000002-102 = _____ 10
Answer
Q #108
Two sides of a triangle have
lengths of 7 and 11 and the 3rd
side also has an integral
length. What is the largest
perimeter this triangle can
have?
Answer
Q #109
2
2
x -4x+y +6y-12=0
is the
equation for a circle whose
circumference is exactly
___________.
Answer
Q #110
A bag has 35 green marbles, 3 red
marbles, and the others are all black.
Reaching in blindfolded, the
1
probability of picking a red one is
.
24
How many black
marbles must be in the bag?
Answer
Q #111
Tom sold all his corn in one day to
three customers. The first bought half
the corn plus half an ear of corn. The
second bought half the remaining
plus half an ear. The third customer
did the same. How many ears of corn
did Tom sell?
Answer
Q #112
6
(
3
n

5
)


n 0
Answer
________.
Q #113
2
log4 64
– 2(4!) = _____
Answer
Q #114
Given y= 2sinx+9, find the
smallest possible value for
y.
Answer
Q #115
Given f(x)=3x-5 and
3
g(x)=5-x , evaluate
f(g(1))-g(f(1))
Answer
Q #116
10223 = ______13
Answer
Q #117
One fifth of the sum of the
first 24 counting numbers is
________.
Answer
Q #118
If a sphere has diameter 3 192
, then it
must

have a volume of ________.
Answer
Q #119
5 2
y  x  20 x  48
2
is a
parabola with vertex at (h,k).
Find the value of k÷h.
Answer
Q #120
3.125.32 
.0625
__________
Answer
Q #121
An equilateral triangle of 300
area circumscribes a circle.
The diameter of the circle is
_________.
Answer
3
Q #122
A diagonal of a cube has
length 8 3. Find the
surface area of this cube.
Answer
Q #123
Given the arithmetic
progression -5,-4.6, -4.2, ...,
find the 86th term.
Answer
Q #124
Evaluate
2
[5!-(4-4)! – 4!]
Answer
Q #125
Evaluate
12  12  12  ...
Answer
Q #126

3
If 68  2 x   .5 
40  4 x   10 x ,
4
then x = _________
Answer
Q #127
It’s known that M is the midpoint of AB with
A (x,-8) and B (20,4) and MB = 2 10 .
There are two values of x that satisfy
these requirements and their sum is ____.
Answer
Q #128
If
13
1
1


2
x 1 4x  4 4x  4
then x = _____.
Answer
,
Q #129
If v = 3+i and w= 1-i where i= 1
then, in simplest a+bi form,
v = _________.
w
Answer
Q #130
A dodecagon (12-sided
polygon) has _______ distinct
diagonals.
Answer
Q #131
When rolling a pair of fair 6sided dice, the probability
their sum will be 3 or 8 is
_______.
Answer
Q #132
It’s known that x >10 and
3
2
x -23x +92 = 4x. Solve
for x.
Answer
Q #133
2 3i 
3
4
6
= _____ where
i  1
Answer
Q #134
If the diagonals of a
rhombus are 32 and 60, find
its perimeter.
Answer
Q #135
If a convex polygon
has 135 diagonals,
then it must have
_____ sides. Answer
Q #136
2
ax +84x+36
The quadratic
will be a perfect square
for what value of a?
Answer
Q #137
A right circular cone has a
9
height of and a base

circumference of 6 .
Find its volume.
Answer
Q #138
The hypotenuse of a right
5!
triangle has a length of  0! ,
3
8
n

with one leg having
n 1
for its length. How long is the
other leg?
Answer
Q #139
An isosceles trapezoid has two
base angles of 135, a leg of 3 2
and a base of 4. Find its area.
Answer
Q #140
2
9x +30x+18
A quadratic
will
be a perfect square if
________ is added to the
constant term.
Answer
Q #141
A rectangle’s length is three
more than its width, and the
product of its diagonals is
369. How wide is the
rectangle?
Answer
Q #142
1+2+3+ …+n = 406
therefore, n=______
Answer
Q #143
The slope of a line through the
origin that is perpendicular to
1
the line x  7 y  1
2
must be ________. Answer
Q #144
The product of the
diagonals of a square is
50. What is the
perimeter of the square?
Answer
Q #145
The surface areas of two
spheres are 36 and 4
respectively. What is the ratio
of their respective volumes?
Answer
Q #146
If log 50 + logx = 3
then x = ______
Answer
Q #147
36x=2345
x=_
Answer
Q #148
The complement of angle
A is 12 less than half of
its supplement. How
many degrees is angle
A?
Answer
Q #149
The number ten trillion
has how many zeros?
Answer
Q #150
To the nearest radian,
0
630 = _____
Answer
Q #151
If
x  z (the set of
integers), and 0 ≤ y≤ 81,
then there are ______
solutions for x.
Answer
2
y=x ,
Q #152
If
 9x

 3

9  27 x 2

,then
2
x
= ___
Answer
Q #153
If
x  12  x  6,
then x must be _______.
Answer
Q #154
are two chords of a
circle that intersect at B. If
AB=6, DB=3, and BE=4
than AC must be _______.
Answer
AC and DE
Q #155
A cube circumscribes a
sphere with surface area 9 .
What is the surface area of the
cube?
Answer
Answers!
A #1
256
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A #2
•10
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A #3
•43
•Next Question
A #4
8
9
• Next Question
8
9
A #5
5 3
• Next Question
A #6
1800 3
• Next Question
A #7
•6
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A #8
•8
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A #9
•32
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A #10
•729
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A #11
•85
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A #12
•200
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A #13
•28
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A #14
5
4
• Next Question
A #15
•144
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A #16
•22
•Next Question
A #17
•25
•Next Question
A #18
1
64
• Next Question
A #19
•18
•Next Question
A #20
•1
•Next Question
A #21
•1
•Next Question
A #22
4 3
• Next Question
A #23
0
•15
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A #24
0
•50
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Question
•
A #25
•-1
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•
A #26
22 5
• Next Question
A #27
•1
Next
Question
•
A #28
•2:1
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•
A #29
•80
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Question
•
A #30
•50
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A #31
•68
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A #32
•2
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A #33
•15
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A #34
•5880
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A #35
4 3
• Next Question
A #36
•149
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A #37
7
3
• Next Question
A #38
•21
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A #39
40
7
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A #40
1
3
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A #41
4
3
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A #42
•20.5
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A #43
•27.5
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A #44
•3
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A #45
4

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A #46
•-16
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A #47
•0
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A #48
•-6
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A #49
•10
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A #50
•15
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A #51
•11
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A #52
•-8
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A #53
3
5
• Next Question
A #54
•15
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A #55
4
5
or .8
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A #56
•34
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A #57
•-4
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A #58
•27
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A #59
•-2
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A #60
•3
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A #61
•10
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A #62
•196
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A #63
1
2
• Next Question
A #64
•-6
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A #65
•-1
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A #66
•26
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A #67
•8
•Next Question
A #68
15
8
• Next Question
A #69
•25
•Next Question
A #70
•8:3
•Next Question
A #71
•28
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A #72
•25
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A #73
•24
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A #74

8
• Next Question
A #75
•14
•Next Question
A #76
•22
•Next Question
A #77
•18
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A #78
•8
•Next Question
A #79
•33
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A #80
•14.5
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A #81
•31
•Next Question
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