Download Theta Applications FAMAT State Convention 2015 For all questions

Theta Applications
FAMAT State Convention 2015
For all questions, “E. NOTA” means “none of
the above answers is correct”.
1. A boy on a bicycle went up a hill at 5 mph
(miles per hour) and down the same distance at
15 mph. Find the average speed for the entire
trip.
3
A. 10 mph
B. 9 mph
C. 8 mph
4
1
D. 7 mph
E. NOTA
2
2. A 60 foot pole is cut into two parts in the ratio
of 11 to 4. How much longer in feet is the longer
part than the shorter part?
A. 16
B. 20
D. 44
E. NOTA
C. 28
3. Find the number of ways Hal can fix a
hamburger (dropping the beef patty or bun is not
an option) if only the following toppings can be
chosen: cheese, pickle, tomato, ketchup,
mustard.
A. 15
D. 120
B. 32
E. NOTA
C. 72
7. Suppose that a sheet of paper with dimensions
8 in. by 8 in. had the four corners folded toward
the center with the vertices/corners meeting in
the center in such a way as to form another
square. By what percentage is the area of the
smaller square less than that of the larger
square?
A. 25%
D. 100%
5. The second angle of a triangle has a degree
measure three times the first angle, and the third
is 12 less than twice the first angle. Find the
measure in degrees of the largest angle.
A. 115.2
B. 102
C. 96
D. 52
E. NOTA
6. The product of three consecutive positive
integers is eight times their sum. Find the value
of the middle number.
A. 1
B. 3
C. 5
D. 6
E. NOTA
C. 75 %
8. One rectangle is drawn inside another with no
common points. The width of the inner rectangle
is one inch less than the outer rectangle’s width.
The outer rectangle’s length is twice its width
and 2 inches more than the length of the inner
rectangle. If the width of the inner rectangle is 4
inches, find the area, in square inches, of the
region between the two rectangles.
A. 18
D. 50
B. 20
E. NOTA
C. 32
9. Find the area of the figure determined by
2 x  y  3  0, x  2 y  1  0, y  3  0.
A. 5
D. 8
4. Find the result when the sum of the 100
smallest positive odd integers is subtracted from
the sum of the 100 smallest positive even
integers, and that result added to the sum of the
100 smallest positive integers.
A. 5050
B. 5150
C. 15050
D. 25150
E. NOTA
B. 50%
E. NOTA
1
2
E. NOTA
B. 5
C. 7
10. Let f , m and a represent three distinct
natural numbers. Find the least possible value of
the sum of the squares of their immediate
successors.
A. 14
B. 29
D. 144
E. NOTA
C. 36
11. If the sum of 5 consecutive positive integers
is w, in terms of w, which of the following
represents the sum of the next 5 consecutive
positive integers?
A. w  5
B. 5w  5
D. 5w  25
E. NOTA
C. w  25
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Theta Applications
FAMAT State Convention 2015
12. A pile of bricks has 85 bricks in the bottom
row, 79 in the second row, 73 in the third row,
and so on until there is only 1 brick in the top
row. Find the total number of rows.
A. 12
D. 19
B. 13
E. NOTA
C. 15
13. Regular hexagon ABCDEF is inscribed in
circle O. The length of an arc cut off by a side of
the hexagon is 3 . Find the area of smaller
sector AOC.
A. 6
D. 54
B. 9
E. NOTA
C. 27
14. The diagonals of a rectangle are 8 units long
and intersect at a 60  angle. Find the area of the
rectangle.
A. 8
D. 64
B.16
E. NOTA
C. 32
15. The brightness B of a light varies directly as
the power P of the lamp and inversely as the
square of the distance d from the lamp. If a
brightness of 0.25 lumens is obtained from a
light of 30 candle power at 8 feet, how close, in
feet, must a 40 candle power light be placed to
obtain a brightness of 0.5 lumens?
A.
2 30
3
B.
8 3
3
D.
8 10
3
E. NOTA
C.
8 6
3
16. A financial planner wants to invest $8000,
some in stocks earning 15% annually and the
rest in bonds earning 6% annually. The
investment return is $930. Find the amount he
invested at 6%.
A. $3000
D. $6000
B. $4500
E. NOTA
C. $5000
17. A student adds enough water to 20 ounces of
a 90% solution of acid to make the result a 60%
acid solution. When he finds that he needs an
80% acid solution, he then adds enough acid to
get the desired result. How much acid was
added?
A. 20 oz.
D. 32 oz.
B. 24 oz.
D. NOTA
C. 30 oz.
18. Find the volume of the solid generated when
an isosceles trapezoid with bases 6 and 8 and
height 1 is rotated about the shorter base.
A. 28
B. 8
C.
26

3
22
D.
E. NOTA

3
19. The arch of a bridge is in the form of half an
ellipse, with the major axis horizontal. The span
of the bridge (the length of the major axis) is
12m. and the height of the arch above the water
at the center is 4m. How high in meters above
the water is the arch at a point on the water 2m.
from one of the ends of the arch?
4 5
4 15
4 5
A.
B.
C.
9
9
3
4 15
D.
E. NOTA
3
20. Mr. Smith is laying carpet in his living room.
The length of his living room is 4 feet greater
than its width. His 4 foot wide fireplace
protrudes 2 feet into his living room, and he
does not carpet the floor there. The total area
that he carpets is 213 square feet. Find the length
of the living room.
40
A. 13 ft
B.
ft.
C. 15 ft.
3
D. 17 ft.
E. NOTA
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Theta Applications
FAMAT State Convention 2015
21. Find 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.
C. 2  2 5
A. 2 5
B. 4
D. 4  4 5
E. NOTA
D. 15
E. NOTA
26. A quarter has a height of 1.3mm,
a nickel 1.5 mm, and a penny 1.0 mm. If a stack
is built alternating quarter, nickel, and penny in
that order, with the quarter on the bottom, what
coin will be on top when the stack first reaches a
height of at least 55mm?
A. quarter
B. nickel
C. penny
22. In a geometric sequence, the common ratio
D. dime
is given as the value of log7 3 49 . If the first
27. The numerator of a fraction is one more than
triple the denominator. Adding 4 to each makes
the numerator double the denominator. Find the
numerator of the original fraction.
3
term is the value of x in log4 x   , find the
2
fourth term.
A.
1
9
D.
3
243
B.
1
27
C.
2
81
B. 11
E. NOTA
B. 12 inches
E. NOTA
C. 18 inches
25. Mary has 19 coins consisting of half-dollars,
quarters and dimes. The number of quarters is
twice the number of half-dollars. If she has
$4.70 altogether, find the sum of the number of
dimes and quarters.
A. 8
B. 7
D. 14
E. NOTA
C. 10
B. 12
28. Find the quotient of the sum of the odd
prime factors of 7854 and the number of its even
prime factors.
A. 4
B. 17
D. 187
E. NOTA
C. 38
C. 13
24. A bathtub in the shape of a right rectangular
prism has dimensions: length 6 ft, width 3 ft,
depth 3 ft. Suppose the bathtub is filled with a
certain amount of water, and a person begins to
submerge himself in the tub. At the point in time
where 62208 cubic inches of the person is
submerged, the tub begins to overflow onto the
floor. What was the depth of the water before
the person got into the tub?
A. 1 inch
D. 30 inches
A. 3
E. NOTA
23. The sum of five numbers in an arithmetic
progression is 45, and the product of the first
and fifth is 5/8 of the product of the second and
fourth. Give the largest of the five numbers.
A. 10
D. 15
E. NOTA
29. For a two digit integer, the units digit is 1
more than 3 times the tens digit. The number
represented when the digits are interchanged is 8
times the sum of the digits. Find the sum of the
digits.
A. 5
B. 9
D. 11
E. NOTA
C. 10
30. A metal ball with radius 6 inches is melted
down and recast as a cone with the same radius.
Find the height of the cone in mm.
A. 6
B. 12
D. 24
E. NOTA
C. 18
C. 14
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Theta Applications
FAMAT State Convention 2015
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