Download 15 Seconds Stop

Directions
• You will have 4 minutes to answer each question.
• The scoring will be 16 points for a correct response in
the 1st minute, 12 points for a correct response in the 2nd
minute, 8 points for a correct response in the 3rd minute,
4 points for a correct response in the 4th minute. A
sliding scale will be used.
• Once your hand has been raised with the answer sheet,
it must stay up. If you put your hand down, your
answer will be disqualified for that question.
• Your answer must be submitted on the official answer
sheet that has been correctly filled out. Otherwise your
answer will be disqualified.
• Your answer must be in the specific form that the
question asks for.
Directions……
• If not otherwise noted, the answers should be in one of the
following generally accepted forms:
– Denominators rationalized
– Simplest radical form
– Fractions, improper fractions, or mixed numbers in
simplest form
– Equations should have integral coefficients in standard
form
• No units are necessary
• Calculators are not allowed in any division except Statistics.
• Headphones, beepers, cell phones, or electronic devices are
not permitted.
• Sunglasses and hats are not to be worn during the
competition.
Minute
15
Seconds
1…….
2
3
4
Stop
1. Figure BCEF is a rectangle.
Triangles ABF and DEC are
F
congruent.
AG DG. AG BC.
Segment lengths are:
AG = 21, BC = 5, BF = 12
E
D
Find the area ABCDEF.
A
B
C
G
Minute
15
Seconds
1…….
2
3
4
Stop
2. A convex n-gon has at least 100 diagonals.
What is the minimum number of sides of the
n-gon, and exactly how many diagonals does
it have?
Minute
15
Seconds
1…….
2
3
4
Stop
3. A convex n-gon has a total sum of its interior
angles at least 20160. What is the minimum
number of sides of the n-gon, and exactly
what is the sum of its interior angles?
Minute
15
Seconds
1…….
2
3
4
Stop
4. What is the
area of the
pentagon?
Minute
15
Seconds
1…….
2
3
4
Stop
5. Two plane figures are “equal” if they have the
same area.
If a square of side x and a regular hexagon
of side y are equal, what is the ratio of their
sides, x/y ?
Stop
Minute
15
Seconds
1…….
2
3
4
6. The triangle shown has a perimeter
of 128. The value of x is integral.
What are the lengths of the three
sides?
𝒙3 − 5𝒙 + 18
𝒙3 − 13𝒙 + 58
3𝒙2 − 14𝒙 + 67
Minute
15
Seconds
1…….
2
3
4
Stop
7. A set of encyclopedia volumes is on a shelf
in proper sequential order. Each volume is a
bound hardback with covers 1/8 inch thick.
The pages of each volume are 1 inch thick.
A worm eats its way from the title page of
volume two to the last page of volume eight.
How far did the worm travel?
(Your answer may be in mixed form, if you
𝟏
wish, e.g. 𝟐 𝟒 .)
8. Five squares of side 5
are arranged in a
plus sign as shown.
What is the area of
the plus sign formed
by rectangles
𝑯
BCFG and
AHED?
Minute
15
Seconds
1…….
2
3
4
Stop
𝑨
𝑩
𝑪
𝑫
G
𝑭
𝑬
Minute
15
Seconds
1…….
2
3
4
Stop
9. Give the displayed trapezoid with its angles
given in terms of x and y, what are the degree
measures of the largest and smallest angles?
𝑴
𝟐𝟎𝟎 − 𝟖𝒙
𝑳
𝟐𝟓𝒚 − 𝟔
𝑱
𝟏𝟎𝒙 + 𝟒𝟐
𝟐𝟖𝒚 + 𝟐
𝑲
Minute
15
Seconds
1…….
2
3
4
Stop
10. Two plane figure, repeated endlessly,
cover the entire plane. One of the
figures is a regular octagon. What is
the other?
Minute
15
Seconds
1…….
2
3
4
Stop
11. One sphere has a volume 40 times
larger than another sphere. What
is the ratio of their areas, larger to
smaller?
Minute
15
Seconds
1…….
2
3
4
Stop
12. A pyramid has a square
base and equilateral
triangle faces. Its edges
are length 8. Point X is a
quarter of the way down
edge DV. What is the
length BX?
𝑽
𝑿●
𝑩
𝑫
𝑨
Minute
15
Seconds
1…….
2
3
4
Stop
13. v
Minute
15
Seconds
1…….
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Stop
14. v
Minute
15
Seconds
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Stop
15. v
Answers
1. 156
8. 150
2. 16 sides, 104 diagonals
9. largest is 1360, smallest is 440
3. 14 sides, 21600
10. a square
4. 33.5
11. 4 25
𝟒
12. 2 21
5.
𝟏𝟎𝟖
𝟐
6. 30, 46, 52
7. 6.5 inches
3
13. -14. --
15. --.